The environment

2.1 Environmental data requirements

2.1 .I Overview

A knowledge of the winds, waves, currents, tides and other environmental factors is critical for the design of all forms of offshore structure and is particularly important for floating systems which often have more complicated dynamic responses than fixed structures. Such dynamic response to waves may occur at wave frequencies or may be driven by non-linear effects to occur at frequencies significantly higher or lower than the wave frequencies. The system will also respond to the steady forces and fluctuating forces applied by the wind. Consequently when designing a floating structure great effort must be invested in the definition of the time-varying environmental forces.

Reliability methods are becoming increasingly popular and these require a more extensive definition of environmental loading and response statistics.

The following considerations are likely to be paramount:

The floating system must be fit for the purpose of operatmg safely in potentially hostile marine environments. Wave induced, and any other, motions must be sufficiently low to allow continuous operation in the very worst weather condtions, or to permit operations to be conducted without excessive interruption, i.e. weather down-time must be kept to a minimum. All certification, inspection and maintenance requirements must be satisfied. Construction and operating costs must be within reasonable limits, given the purpose of the installation and the value of the resources which are to be exploited.

Obtaining the best data to describe the environment, and using it to best advantage in the design, is therefore of central importance. The weather processes that control the main features of the environment are largely random by nature, and unpredictable in any long-term deterministic sense. The statistical properties of these processes can be defined, but there are particular problems in predicting the probability of extreme events, or in selecting 'design conditions', especially when limited measured data exists for the location of interest.

Furthermore it is often not obvious for a floating system what constitutes the 'worst environmental condition' that it should be designed to meet. When dynamic responses are important it is necessary to focus on the conditions that give rise to the worst responses (they may not occur in the most severe storm), and consequently it is almost always necessaql to consider different environmental conditions in some form of sensitivity analysis.

Environmental data measurement is difficult and expensive in the harsh ocean environment, but there is always a need for long data records if reliable operating and design criteria are to be estimated. Unfortunately most offshore environmental measurements have been made for a relatively short period of time, and even in the 'mature' North Sea where there are about 20 years of good quality data from fixed structures, there is still debate over the extreme wind speed and wave height values that should be used. Section 2.8 discusses extreme environmental values in detail.

The most important environmental influences for floating structures are usually: waves, winds, currents, and water levels, although ice can also be very important in the high latitudes. Winds, waves and currents all give rise to steady components of force or moment, tending to displace or overturn the system. Waves, and to a lesser extent

2-2 Floattng structures a gutde for des~gn and analysts

winds. and currents also escrt dynamic or time-vqlng con~ponents of forcc, which can excite dynamic responses or even resonant responses in compliant floating systems. The properties of waves. winds and currents are discussed in detail in Sections 2.7. 2.5, and 2.6 respectively.

The main classes of floating systems, and their primary sensitivities to the environment, can be summarised as follows:

Semi-submersible vessels Characterised by a small water plane area and large submerged hull or pontoons, they have small wave frequency responses and quite long natural periods. They usually maintain station using catenary mooring lines or dynamic positioning. Wind and current will cause large steady offsets. Vessel motions tend to be dominated by wave frequency loading and to a lesser extent low frequency (second-order) wave and low frequency wind gust excitation. Due to the similar length and breadth dimensions, motion responses are not very sensitive to the drection of the weather. Very commonly used for exploratory drilling, they may also be built or converted for permanent oil production.

Tension Leg Platforms Although similar in some respects to semi-submersibles, they tend to have more buoyancy in the columns (i.e. greater water plane area), and are distinguished by taut vertical mooring tethers. They have short natural periods in roll, pitch and heave and long natural periods in surge, sway and yaw. The horizontal motions are llke a semi-submersible but because the TLP moves on an arc 'set-down' coupling to heave reduces air gap. Vertical responses can be driven by short period waves, and non-linear high frequency (second-order) wave forcing which allows a large e.g. 8 sec wave to excite perhaps a 4 sec heave or pitch natural period. Although these vertical motions are likely to have a small amplitude, their frequency and the possibility for resonant response make fatigue an important design issue. These systems are used for permanent oil production.

Ship-shaped units There is a large range of shlp- and/or barge- shaped m t s used in oil exploration and production. Ship-shaped bodies are characterised by their small beam and long length, and consequently forces and motion responses are strongly dependent on the direction of the weather. Wind, waves and current on the head result in the smallest forces, wllilst environmental components on the beam can lead to very large forces and resonant rolling motions. Permanent installations will therefore nearly always have positioning systems or mooring systems whleh permit the vessel to weathervane in order to maintain a favourable heading. Turret moorings or single point moorings permit this. Some exploration drill ships are dynamically positioned and have no mooring system. Shp- or barge-shaped vessels are used extensively for permanent oil production and storage. The freedom to weathervane can lead to some extremely complex low frequency fishtailing and surging motions.

During its life cycle, a floating structure can go through a number of phases which each may have different environmental mfluences. Dunng constructio~l transportation, installation and installed operation the system will experience Qfferent types of weather and is likely to have Qfferent levels of vulnerability to a severe environment. The special requirements of these different phases are discussed in more detail in the following sub-sections.

2.1.2 Construction in sheltered waters

Many fixed and floating offshore structures require to be partly constructed or completed (e.g. deck mating) in sheltered deep water. This raises two important issues: the sometimes unusual floating properties of the part- constructed structure, and the sometimes unusual properties of the weather in the sheltered construction location (Section 2.12). In these circumstances the environmental parameters of most importance are likely to be wind and current rather than waves.

The unusual floating properties of the s9stem might mean that it is sensitive to particular types of excitation (say at low frequency for a very deeply submerged concrete structure with low water plane area and high inertia). Lack

The envlronrnent 2-3

of freeboard or reserve buoyancy may also bc a problem, n ~ a k ~ n g ~t Important that waves are not too large and responses to wmds and waves are small

Criteria calculated using data from other than the specific site may be untypical of the site.

2 . 1 . 3 Transportation

Even components for fixed offshore installations need to be transported to the installation site and this involves floating on a barge, on a heavy lift vessel, or in some cases relying on the buoyancy of the unit itself.

Some structures such as self-elevating (jack-up) platforms are particularly vulnerable during tow from one site to another, causing special problems for the designer, and a detailed knowledge of the possible weather conditions along the route becomes very important for the proper planning of the towing operation.

Some marine transportation is over very long distances, and slow tows making 5 knots or less are very much at the mercy of any storms which occur. The wave motions that occur during long distance tows can also have a significant effect on the fatigue life of the transported item, even before it is installed.

It is very important to hstingwsh between local tows and long &stance tows. The former, if they are short enough, can often rely on good weather forecasting and the designer can presume that the worst weather conditions will not be met. However, in the latter case the design must be able to cope with extreme conditions.

Environmental requirements for such operations include design wind speeds, wave heights and periods, information about directionality and seasonality of winds, waves and currents, frequency tables of wave height against period (scatter dagrams) and wave height against direction for fatigue calculations and voyage planning.

2 . 1 . 4 Offshore installation

The installation of offshore fixed or floating structures usually requires extended periods of fine weather, particularly whilst critical tasks, heavy crane lifts for example, are being carried out.

The environmental data required in this application are therefore rather different from most other applications. The requirements centre around the likelihood that there will be fine weather for a sufficient duration to perform these critical tasks, and how long it may be necessary to wait for one of these fine periods.

These requirements are therefore often related to economic issues, and particularly the trade-off between spending more on engineering, or on installation equipment so that the operations can be performed in worse weather, versus the likely cost of non-productive weather 'down-time'. The data needed therefore concentrates on day-to- day weather conditions, and the persistence of calm periods. These issues are discussed further in Section 2.9.

It should also be remembered that some installation operations can be strongly sensitive to particular aspects of the environment. For example a heavy lift operation might be prevented from progressing by a very small amplitude swell, the frequency of which happens to coincide with a natural frequency of the crane barge or the load on the hook. Careful response analysis is therefore required before the critical aspects of the environment for the operation are clear.

Requirements for environmental data may include design winds, waves and currents by direction and month. Frequency distributions of wave height against period (scatter diagrams), wave height against month, weather down-time and persistence data will often be required for planning purposes.

2-4 Float~ng structures' a gutde for d e s ~ g n and analysts

2.1.5 Design criteria

Design criteria for offshore structures fall into two broad areas. Extreme load cases are selected as severe environmental conditions that the structure or vessel is designed to withstand. The assumption is that, if the designer can demonstrate that he has designed the system to withstand the effects of this condition, then, once various safety factors have been added, the probability of ths loadmg condition being exceeded is adequately low. Fatigue is also a design consideration, and in ths case environmental design data is needed to describe the loading cycles that will be experienced over the whole life of the structure.

For fixed structures it is normally relatively easy to demonstrate that the extreme load case will occur in the highest wave height or the highest wind speed. For floating systems, however, with their frequency dependent responses, this may not be the case. The worst structural loading condition for a floating system may occur in higher frequency waves than those of maximum height. Floating systems therefore often require that a broader range of environmental conditions be investigated.

Floating systems must not only be able to withstand extreme forces and responses; but they must also remain sufficiently stable so that the operations for whlch they were designed may be conducted safely and continuously.

In the case of single-point m o o ~ g systems the worst loadmg condition will normally occur when the wind, waves and current have a particular directional relationship. A key requirement from the environmental data may therefore be to define the occurrence of this type of condition (see Section 2.1 1).

2.1.6 Operating criteria

Floating systems tend to be much more weather-sensitive in their operation than fixed systems, with the result that weather can have a significant influence on total productivity. Common limitations might be wave motions too great to permit the production equipment to function correctly, vessel excursions too great for safe operation of a production or export riser, or weather too bad to operate a tanker off-loading system. The decision on whether to design a floating structure to operate in all possible weather conditions, or whether to accept a certain amount of weather down-time (periods when the weather is too bad for operations to continue safely) is essentially an economic one.

For systems where some weather down-time is to be accepted, it is obviously important to estimate these effects at the design concept stage so that the economic viability of the concept can be verified. It is equally important that at the detailed design stage the operating limit conditions (when the operators must shut down production) are properly documented. These require the provision of environmental climate information which describe the characteristics and probability of meeting particular conditions on a day-to-day basis.

The requirement for environmental data for operating conhtions has some similarity with that for fatigue analysis in design, but one dfference is the importance of persistence statistics in the consideration of weather down-time. Persistence (see Section 2.9.1) describes the duration of storms or periods of bad weather, and this is an important issue when just a short period of bad weather may potentially cause a much longer interruption in oil production due, for example, to the time taken to reconnect risers and re-establish a production flow.

2.1.7 Relevant metocean parameters

Table 2.1 is a summary of all the metocean parameters likely to be required for design and operational requirements.

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Parameter Information

Winds

Waves

Water levels

Currents

Temperatures

Ice and snow

Marine growth

Other meteoroIo- gical iplfarmation

Seabed in for- mation

Extreme wind speed * Extreme wind speed by direction Frequency of occurrence of wind speed and direction * Persistence of sustained wind speeds above certain thresholds * Vertical profile Gust speeds and spectra

Extreme sea state * Extreme sea state by direction Cumulative frequency distribution of individual wave heights Joint probability of significant wave height and period * Joint probability of significant wave height and period by direction Wave energy spectra and directional spreading Persistence of storms and calms

Chart datum water depth Extreme tidal rise and storm surge Extreme tidal, surge and wave crest elevation

Extreme current speed * Extreme current speed by direction Vertical profile with depth Fatigue design current speed

Masimum and minimum air temperatures * Maximum and minimum sea temperatures * Vertical profile of sea temperature with depth

Maximum thickness and density of snow Maximum thickness and density of ice Occurrence of sea ice and icebergs

Type and thickness of growth

Precipitation, fog, wind chill, occurrence and forecastability of storms

Slope (including direction) of seabed Soil conditions

Per cent

Table 2.1 - Metocean parameters

Notes: 'Extreme' indicates month, year, 10 year, 50 year, 100 year return period maximum values. * indicates data would normally be provided as seasonal (monthly) and whole year values.

2-6 Float~ng structures a gu~de for des~gn and analys~s

2.1.8 Marine transportation and other operations afloat

A number of guidelines and recommended practice documents exist which are available from marine warrant), surveyors. (These documents generally give more detailed marine operations information than is contained in design guidance documents .)

Transportation - Reference parameters are usually related to extreme values with a recurrence interval of 10 times the expected duration of the operation during the month or season when the operation takes place. If the marine transportation is scheduled to take a month or more then the extreme wind speed and wave height which are reached or exceeded once on average every 10 years during the month or season may be specified. Other criteria are specified in terms of 'risk of exceedance' such that some value of wind speed or wave height has some defmed probability of exceedance during the transportation. The magnitude of the transportation criteria can be reduced if the risk of meeting bad weather is reduced and this can be achieved by scheduling or routing the transportation so as to avoid the worst weather. Near to departure time weather forecasting is likely to be employed to reduce the risk of meeting bad weather and once under way weather forecasting can be used to assist with route navigation. If appropriate a survey may be carried out to identifjr 'safe havens' which could be used in the event that a marine transportation needs to seek shelter.

The design wind speed is usually taken as the extreme one minute mean wind speed and the design sea state is usually taken as the extreme significant wave height which together with a range of peak energy periods is specified for motion analysis. Bollard pull (a measure of towing capacity) requirements for the specification of a tug may be calculated from considerations such as maintaining zero forward speed against 20 m/s wind, 5 m significant wave height and 0.5 m/s current acting simultaneously.

Other marine operations - There are few, if any, marine operations (e.g. load out, float out, lifting, mating and installation) whlch are not weather sensitive. Inshore operations are likely to be conducted in well known sheltered areas such as enclosed bays, fjords and the Ilke, but nevertheless planning prior to the operation is often essential. It is particularly important to establish that weather windows (when wind speed: wave height, current speed and water level are all within pre-defined limits for a period long enough to complete the required operation) occur sufficiently frequently to avoid long and costly delays. If the required information is not available then steps should be taken to obtain it well in advance.

Offshore the weather window will also include consideration of wave period which even if associated with small amplitude waves can cause unacceptable motions. Once again it is important to establish that suitable conditions will occur sufficiently frequently to allow the operation to proceed without undue delay.

In all cases weather forecasts are likely to be required before and during the operation and it could be advantageous to make observations of the critical parameters to assist with the accuracy and timing of such forecasts.

2.2 Rules, guidance and recommended practice

2.2.1 Introduction

The offshore enpeering industry generally has a requirement for a variety of environmental data. The two most common may be classified as extreme data which, with safety factors, determines the conditions which the unit should survive, and operating data which define conditions which are regularly experienced. The documents referred to in this section describe design processes and the environmental parameters required for design. It is important to emphasise that the design processes described in recommended practice documents should be considered as a package and it is not advisable to choose one part of a package from one recommended practice document and combine that with some other method from another document. This is because a less conservative approach at one stage in the design process (e.g. choosing 50-year rather than 100-year return period extremes) may be offset by a more conservative approach at some other stage (e.g. a higher safety factor).

The env~ronrnent 2-7

Documents commonly used as a bass for dcsign arc.

American Bureau of Shipping - Rules for Building and Classing Mobile Offshore Drilling Units. 1994.

American Petroleum Institute - Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms - Working Stress Design. API RP 2A-WSD. Twentieth Edition July 1, 1993. See also Annex 1B.

American Petroleum Institute - Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms - Load and Resistance Factor Design. API RP 2A-LRFD. First edition 1993.

American Petroleum Institute - Recommended Practice for Design, Analysis and Maintenance of Moorings for Floating Production Systems. API RP 2FP 1. First edition February 1, 1993.

Bureau Veritas - Rules and Regulations for the Classification of Mobile Offshore Drilling Units. 1987.

Det Norske Veritas - Rules for the Classification of Fixed Offshore Installations. 1989

Det Norske Veritas - Rules for the Classification of Mobile Offshore Units. 1990

Det Norske Ventas - Environmental Condtions and Environmental Loads. Classification Notes No. 30.5. March 1991.

Health & Safety Executive - Offshore Installations : Guidance on Design, Construction and Certification. Fourth Edition - 1993. See also Annex IC.

Lloyd's Register - Rules and Regulations for the Classification of Mobile Offshore Units. 1989.

Some other documents exist but for the purpose of reviewing the methods of obtaining and manipulating environmental data the documents listed above present a comprehensive selection. IS0 is producing standards for fixed and floating structures that are currently (1 998) in draft form. Documents referring to fixed offshore platforms are included because information about environmental conditions is not repeated in all documents published by the same organisation. The documents are surnrnarised in Annex 2B. A selection of useful mathematical relationships is presented in Annex 2C.

2.3 The world climate

2.3.1 The main features

The climate of a locality is defined as the synthesis of the day-to-day values of meteorological elements that affect the locality (Meteorologd Office, 199 1). In thls book the definition must be broadened to include oceanographic elements as well. Synthesis is meant to imply representation using a variety of statistical devices such as mean, standard deviation, frequency etc. The meteorological and oceanographic elements with which we are concerned are listed in Table 2.1; the range of magnitude of each one can vary enormously from one part of the Earth to another and also &om one season to another. The purpose of this section is to give the engineer some insight into how and why natural conditions change from place to place and from month to month so that decisions can be made on an informed basis.

Meteorolog~i and oceanography are the scientific studies of the atmosphere and oceans respectively. The climate of a location is mady governed by latitude and geographical location with respect to oceans and continents etc. To understand variations in climate it is necessary to first understand some basic mechanisms of atmosphere and ocean.

2-8 Floating structures: a guide for design and analys~s

The atmosphere is a mixture of gases which envelop the Earth under the influence of gravity. The lowest layer which contains most of the weather and interacts with the oceans is called the troposphere and this layer has a depth (from sea level to the top of the troposphere i.e. the tropopause) which varies from approximately 10 km at the poles to 15 krn at the Equator. Atmospheric pressure is exerted by the weight of the atmosphere above and at sea level this amounts to approximately 10 tomes for each square metre. Atmospheric pressure is measured in millibars (1 millibar = 1 O2 Pa) and has an average value of 10 13.3 millibars over the surface of the Earth at sea level.

The atmosphere is composed mainly of nitrogen and oxygen but other very important gases which are present include water vapour, carbon dioxide, ozone and methane. Particularly near the surface of the Earth the atmosphere also contains a number of natural and man-made pollutants. Natural pollutants include sea salt, dust, etc. and the products of volcanic eruptions, forest fires, decomposition of organic matter. Man made pollutants in the form of gas and particles come from a variety of industrial processes and combustion. Some of these substances, both natural and man-made, are blamed for such phenomena as acid rain, ozone depletion and global warming.

The ultimate source of heat for the Earth is the Sun but the heat is dispersed in a number of different ways. The Sun generates radiation (in the wavelength range 0.15 - 2pm) which to a large extent passes through the atmosphere, although some is reflected by clouds, lying snow etc. and is absorbed at the surface of the Earth. When solar radation reaches the surface of the Earth, heating at a specific location depends to a greater or lesser extent on time of day, time of year, latitude, surface albedo (a measure of reflectivity), surface specific heat capacity, surface thermal conductivity, evaporation, topography, atmospheric stability, wind and turbulence and precipitation. The Earth itself emits radiation (in the wavelength range 5 - 40pm) and some of this in turn is absorbed (and re-radiated) by atmospheric gases such as water vapour and carbon dioxide, leading to the process being described as the greenhouse effect. Cooling also depends on wind strength, cloud cover, water content of the atmosphere, initia.1 temperature, nature of the surface and topography. Heat is also transferred from the Earth to the atmosphere by conduction. Heat is transferred within the atmosphere by convection but the condensation of water vapour, which releases latent heat, also plays significant part. Heat is transported by both atmosphere and oceans away from the tropics (where solar radiation is at a maximum) towards the poles (where solar radiation is at a minimum).

Local heating of the atmosphere will cause expansion and a local reduction in atmospheric pressure. Conversely local cooling will cause a local increase in atmospheric pressure. Air will flow from high to low pressure under the influence of the pressure gradient. (This is not the only cause of pressure gradients.) The winds caused by these pressure gradients are blowing on the Earth (which is a rotating sphere) and an effect called the Coriolis force will cause the wind duection to change (to the right in the northern hemisphere and to the left in the southern hemisphere). In the free atmosphere (beyond the influence of friction) an equilibrium position is reached when the pressure gradient force exactly balances the Coriolis force and this occurs when the wind direction is perpendicular to a line joining centres of hgh and low pressure. This results in winds which blow clockwise (anti- clochse) around centres of hgh pressure in the northern (southern) hemisphere and anti-clockwise (clockwise) around centres of low pressure in the northern (southern) hemisphere. Near the surface of the Earth the frictional effect exerted by surface features results in winds spiralling in towards centres of low pressure and out from centres of high pressure. There is a direct link between temperature gradients, pressure gradients and wind speed over the Earth whlch results in many of the large scale weather features which have significant effects on offshore enpeering. Large scale weather features such as temperate latitude depressions involve strong winds over large areas resulting in large waves, surges and currents. Smaller scale features such as squalls, thunderstorms etc. may involve strong winds but generally do not last long enough to have a profound effect on the ocean.

2.3.2 Large scale weather systems

Temperate latitude depressions These storms generally referred to simply as depressions or lows are areas of low atmospheric pressure which become most prevalent and severe during the winter months when the thermal gradient between temperate

f in& wirt& Trdc tv~nds m t y tca l of tropical crceans ad represent the passage af air from sub-troptcal high pressure beits (the htxsc latitudes) tntvards the Equator where thc pressure 1s lotvcr fn rhc nortltcrn (soilihcrn) hetnisphmc trade \ m d s blow {ram the nod^ (south f easl and are called the north (south) cast trades Trade wnds are pcrsistcnr. r ~ ~ d e r a i e isarnct~nes strong] ~ i t l d s which blow at all times of the \car In the Arabian Sca. Ray of Bengal and Chtna Seas the vadc wnds are suppfuntcld b? thc monsoon n~nds

infemo)pical cortvcqmce ; m e (I TC'Z) und the I)o?(Ir~ims Thc fTCZ 1s a belt of's ar~ablc and ill-defined exrcnt. sornetirncs nssoclatcd wth heay ram and thunderstoms. wl~ere lradc stnds con! e r g Ttte Doldnlrns is the name gitcn to essentiatly the same region but implies lrght wmls and was dreaded dunng thc days of sadlng slups because ttfthc danger of bccorntng becalmcd The I'TCZ rs not a fcaturc which can bc plotted ilom da) to da: and IS nat n from comparable with the fronts associated 1~1th temperate latttude dcprcssions but 1% 1s thc botmdar?, between tropical air and other air OII its pole-ward sides

2.3.3 Small scale weather systems

T%m i l r~ a large number of smaller scaic wsther systcrns whtch v,hiIc not importam on a global scale can have a sigtlficant local impact

2.3,4 The glabal wind climate

The env~ronrnent 2-1 1

M'xinc Climatic Atlas of the World (Department of the Navy). Space will not allow a similar treatment here but Table 2.2 and Figures 2.1 to 2.3 distil some of the information available. Another valuable source of general ~nformation are Pilot Charts (Department of the Navy) and Routing Charts (Hydrographer of the Navy). This information is now becoming available on computer accessible media.

North Atlantic Ocean: Temperate latitude depressions form at any time of year but are most frequent and intense during the winter months. Tropical cyclones affect the Caribbean, the Gulf of Mexico and eastern coastal waters of the USA and Canada.

North Pacifzc Ocean: Temperate latitude depressions form at any time of year but are most frequent and intense during the winter months. The western parts of the North Pacific region experience a monsoon climate. From Japan southwards to the Equator, the winter (northeast) monsoon can cause strong winds whereas the summer (southwest) monsoon is generally less intense. Tropical parts of the North Pacific region (both west and east) experience tropical cyclones with Japan, the China Seas and the Philippine area particularly prone.

North Indian Ocean: The whole area experiences a vigorous monsoon climate. The summer (southwest) monsoon causes strong winds particularly in the Arabian Sea. The winter (northeast) monsoon is less intense. Tropical cyclones can occur in most months between April and December, with the Bay of Bengal particularly at risk.

Southern 0ceans:Temperate latitude depressions form at any time of year which together with persistent and strong westerly winds in middle latitudes (the 'roaring forties') generate large waves which are experienced as swell over much of the region. There is some reduction in wind speeds during summer months but not on the same scale as in the northern hemisphere. Tropical cyclones occur to the east of and along the northern coasts of Australia and also in the Indian Ocean. The South Atlantic is unique among ocean basins in not experiencing tropical cyclones.

Ocean Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

- - -

North temp D D D d d d d d d D D D Atlantlc trop t t T T T t

N East temp D D D d d d d d d D D D Pacific trop t t t T T t

N West temp . DM DM DM d dm d m d m dm dm D D M D M Pacific trop Mt Mt mt t t mt mT mT T MT MT Mt

North temp Indian trop m m m t mt Mt Mt M mt t mt mt

South temp d d D D D D D D D D d d Atlantic trop

South temp d d D D D D D D D D d d Pacific trop t T T t t t

South temp d d D D D D D D D D d d Indian trop T T t t t

Table 2.2 The monthly variation of large scale weather types in each ocean basin.

Key latitude band trop = tropical, temp = temperate temperate latitude depressions D = frequent andlor intense; d = occasional, moderate intensity monsoons M = strong; m = moderate tropical cyclones T = frequent andlor intense; t = occasional, moderate intensity

2-1 2 Floatmg structures a gu~de for des~gn and analyh~s

Figure 2.1 Areas of the world where gales (winds of Beaufon 7 or more) are likely in January are shaded. Note that in addition strong winds will occur during squalls, thunderstorms and tropical cyclones outside these areas

Figure 2.2 Areas of the world where gales (wind of Beaufort 7 or more) are likely in July are shaded Note that in strong winds will occur during squalls, thunderstorms and tropical cyclones outside these areas

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20 40 60 80 100 120 140 160 180 160 140 120 100 80 60 40 20 0 20 80 80

60 60

40 40

20 20

0 0

20 20

40 40

60 60

80 80 20 40 60 80 100 120 140 160 180 160 140 120 100 80 60 40 20 0 20

Figure 2.3 Areas of the World subject to tropical cyclones. Regular occurrences occur within the solid lines with intermittent occurrences within the dotted lines. The tropical cyclone seasons are defined by the months shown for each area

Figure 2.4 Major ocean currents are shown qualiitively. Note that in the Indian Ocean and South China Sea current direction reverses with the monsoon season

2.3.5 Global wave climate

AS waves are caused by winds the distribution of wave height over the globe has a similar pattern to that of wind speed (see Figure 2.5). However an important exception to this general rule (particularly in the context of floating structures) concerns the incidence of swell. Swell waves are originally generated by the wind but with the passage of time they have either moved away from the area where the wind was blowing or else the wind has changed

2-34 Floatmg structures a gu~de for des~gn and analysts

ducction or fallen Ilght. Swcll is gcncrall!~ ~hought of as ha\,& a longer pcriod than othcr waves and the reason for t h~s is that the long penod waves decay less rapidly as thev travel than the short period waves; shorter, steeper waves are more prone to whte-capping (wave energy converted to current energy) and air resistance. Non-linear wave-wave interaction also results in a progressive reduction of short wave energy. All sea-states are likely to consist of both locally generated waves and swell with a spectrum of frequencies and direction and this composite nature of any sea-state is often depicted two or three dimensionally as a spectrum of wave energy.

Swell waves are found in many parts of the world but some areas are particularly susceptible. Most coasts exposed to oceanic waves from the west will be subject to swell and although in temperate latitudes the longer swell waves may be overshadowed by shorter, locally generated wind waves the low frequency oscillations associated with swell may still be felt. In tropical latitudes swell can represent a large part of the total wave energy and th~s is particularly true in areas such as West Afhca. The persistent winds experienced during monsoons make swell an important consideration in the Arabian Sea and China Seas. Trade winds can also generate low swells on the east coasts of Australia, Afnca and South America. Swell can travel huge distances over great circle routes (e.g, southern ocean swell has been identified in Alaska).

2.3.6 Global current climate

Although surface currents are driven by the wind, the resulting global circulation is complicated in several respects. The realisation of the important role that ocean currents play in the distribution of heat around the world has led to considerable recent research into the mechanisms involved. Persistent features of the global atmospheric circulation are the subtropical high pressure belts which lead to the trade winds on the equator-ward side (see above). The effect of wind stress on the surface of a body of water is to generate a depth averaged mean current which has a direction to the right (left) of the wind direction in the northern (southern) hemisphere due to the Conolis effect whch is in turn due to the rotation of the Earth. This leads to what is called Ekman transport and a convergence of water towards a centre of anticyclonic atmospheric circulation. Currents are generated as the water flows down-slope but once again the Coriolis effect changes the current direction so that an anticyclonic oceanic circulation (or gyre) is formed. These gyres tend to be asymmetrical with centres displaced westwards leading to much stronger currents on the western sides of oceans than on the east.

In low latitudes the trade winds cause water to flow from east to west and as the Coriolis effect is small near the Equator (being a function of latitude) a slope in the water level from west to east results. Water flows back down the slope from west to east near the Equator where winds are light (see doldrums above) and forms the equatorial counter currents.

In general the major ocean currents are persistent and change little from month to month although eddies and local winds may cause temporaq changes in strength andlor direction. However the exception to this is in the Indian Ocean and Chma Seas where the monsoon climate does lead to reversals in current direction during each season. Thls effect is particularly noticeable near the coasts of Somalia on the western side of the Indian Ocean and near the coasts of Vietnam on the western side of the South China Sea.

See Section 2.6 for more types and details of currents and water levels.

2.3.7 Global distribution of sea ice

Sea ice comes in many forms and its extent varies considerably from month to month. Comprehensive atlases esist whlch show the average, maximum and minimum extent of pack ice and icebergs by month or season. The mformation is typically more comprehensive for the Arctic than for the Antarctic. Superstructure icing is caused by a combination of low temperature and high winds andlor waves and information about these occurrences is available. Methods exist whch allow calculations of potential superstructure icing to be performed (Overland et al., 1986). The distribution of land masses has a considerable effect. on the nature of ice effects which results in significant differences between the northern and southern hemisphere ice characteristics.

The env~ronment 2-1 5

Northern hemisphere Thcrc is no land mass at the North Pole but the effect of contmental land masses, which become very cold during thc winter months, can result in sea ice extending as far south as 45% near Newfoundland and Nova Scotia in Canada and also near Hokkaido, Japan. Ice may form over parts of the Baltic Sea, Black Sea, Caspian Sea and Bohai Bay. In addition ice may form along the North Sea coasts of northwest Europe, the northern edge of the Sea of Japan and the northwestern edge of the Gulf of Alaska. Icebergs are almost entirely restricted to the North Atlantic Ocean and most of them come into existence (or calve) on the east coast of Greenland where valley glaciers meet the sea. Ocean currents tend to transport the icebergs south and west from Greenland and many approach the Canadian coast.

Superstructure icing occurs when the air temperature is cold enough to freeze sea water and the wind speed or wave height is high enough to cause spray whlch freezes on contact. Such conditions can occur anywhere near the ice edge or cold continental coastline (before very cold Arctic or continental air is warmed by an underlying sea surface) and areas subject to superstructure icing include the Black Sea, Caspian Sea, Baltic Sea, Norwegian Sea, North Atlantic, North Pacific, Bering Sea, Sea of Okhotsk, Sea of Japan and Yellow Sea.

Southern hemisphere The Antarctic continent itself is the only land mass south of 55'' S so that sea ice does not extend as far away from the pole in the southern hemisphere as it does in the northern hemisphere. Pack ice generally extends to about 60' S in winter and melts almost completely by the end of the summer allowing some navigation to the Antarctic for a limited period. Southern ocean icebergs are formed by the break up of shelf ice in the Ross and Weddell Seas and many more icebergs are calved than in the Arctic. Such icebergs are generally flat and can have huge areas estendmg to hundreds and even thousands of square kilometres. Carried by ocean currents these icebergs usually move from west to east once free of the shallow waters of the Antarctic shelf seas but occasionally some can threaten eastern coasts of South America.

Superstructure icing will be a problem near the edge of the Antarctic pack ice but information on frequency of occurrence is sparse compared to the Arctic.

2.3.8 World climate change

Over the past few years prominence has been given to mankind's influence on the environment and the question of whether his activities can introduce sipficant changes in the world climate. The existence of 'global warming' has been prdcted as a result of the 'greenhouse effect', and some have claimed to have detected such effects in meteorologcal measurements. There is hsagreement about what the effects of global warming might be on other weather parameters such as wind speed and wave height.

There is no doubt that the world's climate can be subject to major changes over long periods of time, even without the help of man. The evidence of past ice ages demonstrates this, but the existence of long term trends in temperature, or other meteorological parameters is extremely difficult to identify, except in retrospect, and over long periods of time. For most purposes, therefore, the world climate is usually considered to be a stationary process.

However, it has been noticeable that wave heights in the northeast Atlantic have been increasing over the past decades. Carter and Draper (1 988) and Barratt (1 99 1) have both presented convincing evidence of an increase in the mean wave height, and Van Hooff (1 994) has sumrnarised the present understanding and the potential implications for offshore engineering. However, it is interesting that this indisputable increase in mean wave height is not accompanied by a matching increase in local wind speed (Hogben, 1995), indicating that the underlying reasons are more complex than a simple increase in the severity of the global wind climate.

A comprehensive review of storms to affect Northwest Europe from 1703 to 1990 by Lamb (199 1) has shown that, while there have been some severe storms in the recent past, there have also been other periods, notably in the late 19th centwy, when a number of severe storms also occurred. He also relates the work of Jenkinson

2-16 Floating structures a gwde for des~gn and analys~s

(unpublished) whlch shows that the number of days with gales over the North Sea was at a h ~ g h level in 1880-89, declined to a minimum during 1930-39, and has now reached another maximum comparable with 1880-89.

With regard to the implications for the offshore industry, since much of the data on which design criteria have been based have been collected during what appears to be a period of historically high storm activity, this should give some cause for reassurance. Nevertheless the fact is that high quality data of sufficient duration is just not available at present to permit a detailed understanding of these long term variations in climate. As ever, caution should be exercised in the manipulation of environmental data, and the best quality advice obtained.

2.4 Types of environmental data available

A catalogue of data sources is provided in the annexes to this chapter. The purpose of this section is to enable the reader to make better use of the data available, and to review the available methods of data acquisition and their respective roles in meeting engineering design requirements in rather general terms.

2.4.1 Instrumental measurements

The term instrumental will here be understood to include 'in situ' and 'remote sensing' (mostly satellite-borne) measuring systems.

'In situ ' measurements Most data can be acquired in the form of records from 'in situ' instruments. Data derived from such records, moreover, are widely regarded as being the most reliable. In general, however, deployment is restricted to fixed locations and practical considerations such as cost limit the a\.ailability of data in both spatial extent and duration. For these reasons, 'in situ' measurements are particularly well suited for use in design of fixed structures, especially if they are to be located in mature areas of offshore activity such as the North Sea which are well endowed with reliable instrumental data (Metocean Consultancy Ltd, 1994).

However, when the design and operation of floating structures is considered, the need may arise for knowledge of condtions over relatively large areas including, in some cases, shipping or towing routes. In such cases other methods of data acquisition, as discussed below, may be better suited.

These comments apply with particular force to data from wave records and, to a lesser extent, from wind and current records. It may thus be helpful to illustrate them by reviewing some of the practical constraints on availability and use of 'in situ' wave and wind records.

Consider first wave records. As noted in Annex 2A, The British Oceanographic Data Centre (BODC) formerly the Data Banking Service of IOSIMLAS (Institute of Oceanographic Sciences / Marine Information Advisory Service) has a formal responsibility assigned by the Inter-governmental Oceanographic Commission for knowledge about global availability of 'in situ' wave records. It has accordingly undertaken global cataloguing of records in addition to banking of data on a more localised basis. A published catalogue was issued by IOS/MIAS in 1982, and whilst no new revised version has been issued in paper form, the up-to-date catalogue is available as part of the UK Digital Marine Atlas (British Oceanographic Data Centre, 1991).

From these catalogues it may be found that globally there is now quite a large number of data holdings and that they have been collected by many different agencies, for many different purposes, using many different types of instrument rangmg f3om simple wave staffs to sophisticated directional buoys (see also Section 2.7.2 and 2.7.5). Also, although data &om shp-borne recorders are included, they have all been derived from ships on fixed station such as light vessels or weather ships.

The env~ronrnent 2-1 7

As a result. the data availability and quality are subject to thc following constraints :

. Though the total number of recording stations is quite large, they are mostly concentrated in near shore and continental shelf areas with high levels of offshore engineering activity.

. The reliability and accessibility of the data is vel-p variable. In some cases only raw chart records are held, in others fully processed data may be a~railable but there may be uncertainties regarding the validity of the analysis. Wave period data are, for example, notoriously vulnerable to distortion by variations in analysis procedure. Also, even in the case of the generally high quality data collected by the offshore industry, the periods of years covered (often only 2 or 3 years) are mostly rather short to yield reliable estimates of extreme height for the long return periods (50 or 100 years) commonly specified.

Much of the data collected by the offshore industry and of particular interest to designers is subject to commercial confidentiality restrictions. These are, however, generally lifted after some specified period of years. In the case of data collected by the UK offshore industry these are mostly held by BODCI IOSIMIAS who make them available to authorised users.

Turning now to wind data, the sources are documented in Annex 2A and it may be seen that responsibility for archving is undertaken by national agencies of the WMO (World Meteorological Office). Here again there are similar constraints on availability and reliability.

. Globally there are a very large number of recording stations but most of them are land based. Some data are collected from anemometers on ships of passage, but the records are difficult to interpret. Availability of reliable marine wind records is thus, as in the case of waves, mostly restricted to fixed stations in specific near shore and continental shelf areas.

. The reliability of anemometer wind data can be very variable because of sensitivity to interference effects resulting from unsuitable siting of the instrument. Also, in the case of ship-borne anemometers, readings can be distorted by roll~ng motion.

As in the case of wave data, some of the records collected by the offshore industry are subject to confidentiality restrictions. Most of the UK data, however, are banked at the UK Meteorological Office (UKMO) and are made available to authorised users.

'Remote sensed' measurements Satellite imagery has long been in routine use in the field of weather forecasting, and in recent years the range of parameters for which data can be derived by remote sensing from satellite has been greatly extended. It is now, in fact, possible to derive most of the types of data listed in the annexes in this way.

Satellites tend to be fitted with a large range of instruments, but those of most interest in the context of the ocean environment are:

Radar altimeter - A downward looking radar which measures the distance from the satellite to the water surface. Sigmficant wave height can be ~nferred from the slope of the leading edge of the radar return pulse, and the wind speed can be inferred from the cross-section of the backscatter. Other information derived from the altimeter pertains to the geoid (overall geometry of the earth's water surface) and small-scale anonlalies (such as may be caused by sea mounts, trenches, ocean currents, and fronts). Scatterometer - A sideways looking radar system designed to measure wind speed and direction by precisely measuring the backscattering cross-section. The system is rather prone to errors introduced by the satellite attitude and communication noise. . Synthetic Aperture Radar (SAR) - A powerful and versatile side-looking radar which has the capacity to form very high resolution 2-dimensional images. Might be used to detect areas subject to internal waves and ocean fronts. Ma~7 be developed to measure surface currents.

2-18 Floatmg structures a gu~de for des~gn and analys~s

Rao et al. (1990) and Srokosz et a1.(1993) provide good summaries of weather satellite techniques, and also summarise the various missions that have been accomplished.

Figure 2.5 Global mapping of significant wave height from GEOS 3 (after McMillan, 1981),% of time that Hs > 2.5m

The key advantage of 'remote sensed' data, in contrast to 'in sltu' records, is that in principle global coverage can be achleved (see Figure 2.5), but there are problems in obtaining reliable data close to coastlines or within island chains. However, the availability of data and extent of engineering usage is dependent on the design of relevant satellite missions and the effectiveness of the validation and management of the massive quantities of data generated.

Figure 2.6a GEOSAT tracking: 17 day cycle for UK waters (after Carter, 1993).

M e a s u r e m e n t s i tes e Severa l years of da ta @ A f e w years o f da ta

Figure 2.6b Comparison of 50 year significant wave height. UK HSE (1995) and GEOSAT (Carter, 1992)

Parameter Mission Duration Publication

Waves 1 GEOS 3 1975-1978 McMillan 198 1 (Data Atlas) Winds 1 GEOSAT* 1986- 1989 Born et al., 1987 Currents 1 Carter et al., 1992

Fu et al., 1987 Ice and snow ) NIMBUS 5 1973-1976 Parkinson et al., 1987 (Data Atlas) Temperature } NIMBUS 7 1978-1987 Milman and Wilheit 1985

* Data archived on magnetic tapes available from NOWNESDIS (see Annex 24.

Table 2.3 Some published results from satellite missions.

At the time of writing, global archives have been acquired covering all the data types listed in the annexes, but the extent of engineering use is still somewhat limited because confidence in reliability and adequate user accessibility and friendliness has not yet been widely established. The situation is evolving however, and Table 2.3 lists some of the data archives already available and associated publications relating to the important parameters. The publications cited include assessments of reliability based on comparisons with 'surface truth' data from buoys which show quite good agreement and offer promise of much wider engineering usage in the future. Figure 2.6b (from Carter, 1993) shows contours of 50 year return value of significant wave height for UK waters derived from GEOSAT data, in comparison with corresponding data from the UK Health & Safety Executive Guidance Notes (UK HSE, 1 995).

More recently Young (1994) has compared wave statistics obtained from the GEOSAT satellite with those derived from wave buoy data and found good agreement.

2-20 Floating structures. a gu~de for design and analys~s

2.4.2 Visual observations (from ships)

The term visual obsewations is here used to refer to the data reported from ships in normal service world wide under the auspices of the WMO, although some of the parameters covered, such as temperature, are measured using instruments. The visual observations are made in accordance with an international code of practice, last defined in 'UK Meteorologxal Office, Met.0.509, (1 977), though most of the parameters have been reported for much longer (reporting of wind speed began in 1854). They are archived by national meteorological agencies of designated WMO member countries includmg the Meteorological Office in the UK (Shearman, 1983). The ships making these observations are known as the Voluntary Observing Fleet (VOF).

The parameters reported cover most of the data types listed in the annexes. Though the observations are, in general, individually much less reliable than measurements, they have the advantage of providing global coverage spanning a very long period. Also, due to the very large sample sizes, the reliability of derived statistics is adequate for many engineering purposes. They are thus widely used for cases where suitable measured data are not available, and clearly they are most plentiful on shipping routes.

A brief review of the relevant available data follows:

Waves Provision is made for reporting of the height and period of waves in each of two wave groups (sea and swell) and the direction of the swell: the direction of the sea is assumed to be the same as that of the wind, reported separately (see below). In most cases only one group is reported.

Derived data are normally presented in terms of 'scatter tables' representing the joint probabilities of occurrence of height and period for specified directional classes.

A considerable number of published atlases of such data are available. The most comprehensive of these is 'Global Wave Statistics' (Hogben, Dacunha and Olliver, 1986) which presents tabular data for 104 areas worldwide. It includes assessments of reliability based on comparisons with measured data and a catalogue of other data atlases. More recently t h ~ s data has been made available on computer disk, and a new database covering the northern European Continental Shelf with 30 new sea areas has been added (BMT, 1990).

Indwidual observations of wave height are not generally considered to be very reliable, but when a large number of these observations are processed to yield wave climate statistics, they have been shown to agree very closely with instrumental measurements (providing those measurements were of sufficient duration to obtain a good climatic average). Reliability is therefore generally regarded as reasonably good for statistics of wave height, though estimates of extreme height tend to be somewhat higher than those derived from measured data. Bitner- Gregersen and Cramer (1994) have compared 'Global Wave Statistics' visual wave data with instrumental measurements at six widely spread locations around the world and concluded that agreement is best in the North Atlantic.

It is widely accepted, however, that the visual observations of wave period are unreliable. For this reason the wave period data in 'Global Wave Statistics' are based on modelling of the joint probability with wave height, without any use of visually observed periods.

Winds The parameters reported are wind speed in terms of the Beaufort Scale and direction. The Beaufort Scale (see Table 2.9 in the Glossary) is a long established code based on experience from the days of sail. For each code number it defines a range of wind speed and reasonably objective criteria relating to the appearance of the sea surface for estimation. Deri~~ed data are commonly presented in tenns of so called 'wind roses' displaying frequencies of occurrence graphically along respective directional rays.

The env~ronment 2-21

As in thc case ofwaves, a number of published atlases are available, notably the US Navy Marine Climatic Atlas of the World (US Navy publication in five volumes issued in revised form between 1974 and 1979, also now available on CD-ROM).

Regarding reliability, various studies have been made including Graham, A.E. (1982) and Quayle (1984). Experience at the UKMO inQcates adequate reliability for most engineering purposes. It has been found, in fact, that visual observations of wind speed are more consistent in quality than instrumental measurements which are so prone to serious discrepancies (mostly due to unsuitable anemometer siting and errors in correcting for the speed and headmg of the shp) that they are routinely excluded by quality control procedures. This problem with anemometer readings has more recently been confirmed by Cardone et al., (1990) and by Kent et al., (1991).

Currents Parameters relating directly to currents are not reported, but the relevant data on speed and direction of surface drift can be computed from information given about the ship's position, course and speed as explained, for example, in Ochi et al. (1 982).

The idea of extracting information on the speed and direction of surface currents from ships logbooks was developed by Lt. Maury of the US Navy in the middle of the nineteenth century, and in 1845 he published the first of a series of 'Wind and Current Charts'. The practice has continued over the years and more recently has been encouraged by a plan for international exchange of sea surface current data, approved by the WMOICMM (Commission for Maritime Meteorology) in 1976. The UKMO, for some years, played a leading role in this field and has accordingly been formally designated by the CMM as the 'International Surface Current Data Centre' (ISCDC).

Regardmg availability of published data, mformation on speed and direction of surface currents is included in the US Navy Marine Climatic Atlas of the World, and in Pilot Charts and Sailing Directions.

Ice Parameters relating to ice are reported in two separate categories. The first is concerned with ice accretion on the ship structure and covers the type of ice (e.g. from rain, from fog or from sea spray) and the thickness and accretion rate.

The second is concerned with sea ice and includes a number of coded descriptions of its configuration and development.

Information on ice accretion is given in Dunbar (1 964) and Mertins (1 968) and data on the climatology of sea ice is included in the US Navy Marine Climatic Atlas of the World. Reference may also be made to an excellent review of data on icing relevant to shlp structure design in the proceedings of the 5th ISSC (Walden et al., 1973).

Temperature Measured readmgs of air and sea temperature are reported, and relevant data are included in the US Navy Marine Climatic Atlas of the World.

General A recent study by Kent et al., (1 991) has stuQed the accuracy of ship's meteorological observations and compared them with results fiom the UKMO fine mesh atmospheric forecasting model. The study analysed the observations from 45 selected vessels traversing the North Atlantic over a period of about 12 months. It identified important biases in air temperature and humidity predictions from the numerical forecasting model, and biases in sea temperature and air temperature due to different types of instrument used on the ships. In addition wind speeds from fixed anemometers were higher than those from visual Beaufort estimates, and there were numerous errors in correcting anemometer wind readings for the ship velocity. Whilst the study concentrated on the biases and discrepancies, and will lead to recommendations for improved observational and reporting procedures, the tremendous value of the data generated by the VOF cannot be overestimated.

2-22 Float~ng structures a gu~de for design and analysis

2.4.3 Hindcast data

The principle of hindcasting is to use archived weather records in combination with numerical models to create a long-term time-hstory for the environmental parameter of interest: usually wind speed, wave height and period, current speed and water level. The input is usually atmospheric pressure which is used to create an estimate of the wind fields whlch in turn are used to estimate wave heights etc.. The main attraction of hindcasting is that long records can be created covering large areas of ocean (the only real limitations being the archive of synoptic data available, and the computing resource available). Once the long records have been created they can be analysed to produce statistical wind and wave climate data and estimates of extreme values.

Hindcasts rely on a good primary archive source of atmospheric pressure data covering the area of interest and the period of interest. They also require several numerical models: to convert the pressure fields into wind fields; to convert the wind fields into wave heights; to convert wind and pressure fields plus tidal effects into currents and water levels. In some cases where wind field data already exist (for example from the UKMO's Numerical Weather Prdction Model NWP, or from the European Centre for Medium Range Forecasts ECMWF) then only the later steps are required. The numerical models used for hindcasting are very similar to, and in some cases the same as, the numerical models used by the various meteorological agencies for weather and sea-state forecasting.

The wave height at a given point in space at a given time is dependent on the wind fields over the large surroundmg area and over a sipficant period of time. The wave generation process is quite complex and waves can travel large &stances (arriving as 'swell'), and so the calculation of the waves must take account of both local wind generation, and the propagation of energy fiom remote storms that occurred perhaps several days beforehand (see Section 2.7.1 below). In coastal or shallow water areas the process is further complicated by effects of refraction, bottom friction, wave brealung and sheltering. Windtwave models tend to be classed as either 'spectral models' or 'parametric models'. Examples of such models are HYPA (Gunther et al., 1979), UKMO (Golding, 1983), SWAMP (The SWAMP Group, 1985), WAM (The WAMDI Group, 1988), JONSWAP (Hasselmann et al., 1976). Recently NESS (1987) has found that more advanced 'third generation' wave models perform better in certain types of extreme storm.

Those interested in learning more about these models are particularly directed to Khandekar (1989), the proceedmgs of a Techcal Conference of Ocean Waves (WMO, 1990), the proceedings of other conferences in this series and NESS (1 997).

Although the numerical modelling processes have been extensively developed, most hindcast projects have made use of a considerable amount of manual intervention, particularly in the development of the wind fields. The atmospheric pressure information is normally in the form of point measurements (usually at 6-hourly intervals). Weather forecasters tend to convert these into synoptic charts using other information (e.g. from satellite images on the location of fronts etc.), using their extensive experience of weather patterns in the process. It is very difficult to automate this process on a computer and so most hindcast projects have included a great deaI of manual intervention by experienced meteorologists. Some projects have used manually generated but digitised synoptic charts as the initial pressure field input.

Although some hindcast projects have concentrated on analysing specific storms, most hindcasts, to be of statistical value, must cover a long period of time (say 10 - 30 years) and it is usually impractical to have manual intervention for all pressure and wind fields for the whole record Attention therefore normally tends to be focused on the more severe storm events. The normal procedure is to compare the hindcast winds with any instrumental wind measurements available for the area and period of interest, and adjust the wind field until a reasonable agreement is found. Ths ensures that the wind fields for the more severe events are as realistic as possible. (Peters et al., 1993.)

The uncertainty in the wind fields are crucial to the accuracy of wave hindcasts and Cardone et al., (1985) and Teixeira (1 993) have investigated the influence of these uncertainties on the prediction of wave height. An x % error in wind speed is found to lead to errors of about 2x % in wave height. Attention is also drawn to the effect of the relatively wide spacing of wind speed estimates in time (usually 6 hours or greater) leading to the analysis

The env~ronment 2-23

missing shorter bursts of high wind speed and thus underestimating peak wave heights. Consequently extreme wind speeds and wave heights estinlated by means of hindcasts contain a significant element of uncertainty in relation to their definition - particularly in terms of the averaging period assumed for these parameters.

So whlst hmdcasts have the advantage of generating long time histories of data from which long term statistics can be derived, they are not without problems of interpretation, accuracy and reliability. Particular areas of difficulty are associated with the relatively coarse spatial and temporal resolution of the models, and the associated interpolation procedures, whch can lead h d c a s t models to overlook the more severe local events, and so their application to the estimation of extreme events must be in some question. One published example of the estimation of extremes by this method is that due to Panchang (1 990).

Hindcasts have become increasingly popular in recent years as cheap computing power has become more readily available and a number of major hindcast projects have now been carried out. Some of these are; the Spectral Ocean Wave Model SOWM (Pierson, 1982), Global Spectral Ocean Wave Model GSOWM (Clancy et al., 1986), Wave Hindcast Study (WHIST) and HYPAS Demonstration Exercise (HDE) (both UKMO, 1987) the North European Storm Study (NESS), (Peters et al., 1993 and NESS, 1997), The Gulf of Mexico Storm Hindcast of' Oceanographic Extremes (GUMSHOE), (API RP2A-WSD, 1993), and others performed for New Zealand (Laing, 1992), the Medtenanean and Adriatic (Cavaleri et al., 1991 and 1989), Eastern Canada (Cardone et al., 1985), Beaufort Sea (Murray and Maes, 1986) and West Africa (Cardone, et al. 1995). There have been many others.

Although a number of major hindcast studies have been performed, the results are by no means all published or generally available (the exception being those around Canada for which much data exists in the public domain). Many are commercially confidential to the project participants. However, as the participants of such projects usually include offshore operators, the data can sometimes be made available for appropriate project purposes. For esarnple, in the case of the NESS project, the project reports and data are confidential to the participants until 2001, and the participants included 9 major oil companies. Some results have, however, been published (e.g. Peters et al., 1993, and Zitman et al., 1992).

The NESS project initially simulated wind, wave; current and water level conditions at 3-hourly intervals in the North Sea and North West Atlantic for 25 'winter' periods from 1964 to 1989, each period being 6 months (October to March). In addition, three 6-month 'summer' periods were derived for 1977- 1979, and a further 50 summer storms were analysed. Surge height and depth-integrated surge and tidal currents were also derived for 250 storms whlch occurred during the 25 winter periods. Later extensions of the project include the six years from April 1989 to March 1995 and the rerunning of the entire data with a third generation wave model.

Some organisations offer a hmdcast data service, one example being the UKMO Wave Model Archive. This and other sources are listed in Annex 2A. However, it is perhaps worth drawing attention to the differences between true hmdcast projects (such as NESS) and the archwing of wave forecast data such as that offered by the UKMO. The wave forecasting modellers are continually improving their prediction methods, and consequently these archived data sets tend not to be homogeneous in quality with time. Also the wind and wave forecasts have generally not had the benefit of comparison and modification using instrumental measurements of wind speed. True hindcast projects, by contrast, use measured data wherever possible to improve the reliability of the modelling, and also apply consistent modelling techniques over the whole duration of the data set. They should therefore be statistically and deterministically more reliable than the forecast archives.

Some hmdcast data sets have been collected into published Atlases (e.g. US Government Printing Office, 1983).

2.5 Wind

2.5.1 Introduction

The atmospheric processes that are the origins of winds are described in Section 2.3.

2-24 Floatmg structures. a gu~de for design and analys~s

Winds may be characterised as having the following key features which are described in more detail in later sections:

A mean velocity Averaged over a given period of time (most commonly 1 hour or 10 minutes, but many averaging periods are used for various different purposes). The mean velocity must also be referenced to a standard height (usually 10 m).

A mean speed profile The velocity of the mean wind increases with height due to the friction associated with the flow over the surface of the land or sea (the atmospheric boundary layer). Thls increase with height is normally known as the mean wind speed profile.

Turbulence or gusts The speed of the wind in the atmospheric boundary layer is not constant. The atmospheric mixing processes, and the friction with the Earth's surface both introduce random turbulence covering a wide band of frequencies and length scales.

Figure 2.7 illustrates the main features of the atmospheric boundary layer.

Constant mean

w ~ n d speed I Free

atmosphere

- Variation of - E

L mean wind o

speed w ~ t h r O 0, r,

Mean .- Atmospher ic

height L w l o wmd - boundary 0 direct lor layer X .-

Sur face roughness porarneter

" A / - I U ~ s t r e o r n fe tch

Figure 2.7 The atmospheric boundary layer (Barltrop and Adams, 1991)

In discussing the properties of the wind it is helpful to consider the various influences the wind can have on a floating system. These may be sumrnarised as follows.

Firstly there are the forces and moments caused by the wind:

Mean wind loads on the complete body, Fluctuating wind loads on the complete body, Mean wind loads on structure components, Fluctuating wind loads on structure components,

However, in addrtion to the forces caused by the wind, there are other influences of the wind environment which are often of importance in the design of offshore floating systems:

. The wind effect on the environment for personnel working on the floating system, . The influence of the wind on free ventilation and on the performance of forced ventilation systems (including the possibility that exhaust gases from gas turbines might be ingested), . The influence of the wind on the ingress of smoke or the dispersion of gases following an accidental fire or hydrocarbons leak,

The envtronrnent 2-25

Thc wind flow around thc platfonn helideck and its influence on the safety of helicopter operations.

Considerations of maximum wind loads (for maximum overturning moment or maximum component loads) obviously requires information about extreme storm wind conditions (most design requirements consider the 50 or 100 year return period wind speed).

Considerations of fatigue or wind induced vibration, however, require information about the whole population of wind conditions that can occur in terms of their speed, direction, and turbulence levels and spectra etc.

Consideration of the wind environment requires the whole range of possible wind conditions to be taken into account. For esample, ventilation and gas dispersion aspects may need to focus most closely on the absence of wind as the most critical case.

As indxated above, floating systems can respond to wind in several ways. Firstly they can respond to the mean wind. An example of h s is the angle of heel experienced by a semi-submersible when subjected to a steady wind overturning moment (see Stability, Chapter 4). Such rigid body motions can also be dynamic and even resonant. Additionally the flexibility of the structure can permit the structural components themselves to respond to the wind. An example of this is the dynamic response of a flare tower to wind turbulence. The latter category of structural responses, and the wind turbulence structures that drive them, are much the same for fixed and floating structures: and they are described in Section 3.7.4 and in Barltrop and Adams (1991).

The following sections briefly discuss the structure of the wind, atmospheric stability, wind speed profile and turbulence, and the problems of wind measurement at sea. The application of some of the different wind speed definitions in wind load and response calculations are then outlined, and some of the main wind environmental effects of interest to floating system designers discussed.

Recently a Joint Industry Project initiated by Statoil has studied the nature of this airflow at two Norwegian coastal locations. This work has lead to the recommendations in the I S 0 for offshore structures (to be published).

2.5.2 Measurement of wind

Wind has been routinely observed at sea for a considerable period of time, and consequently there are good databases of wind speed and direction available, but these databases are not as extensive as those available on land. Indeed, data on the structure of the wind over the sea (speed profile, turbulence spectrum etc.) is extremely rare, there having been few detailed studies.

The measurement of wind in the marine environment poses some special problems. Wind measurements can normally only be made from a fixed structure or by a passing ship, or from a purpose built data buoy or weather ship.

Wind speed has been estimated visually by interpreting the surface texture of the sea since the days of sail (see Section 2.4.2) and the Beaufort Scale has proved a very successful medium for wind speed estimation and reporting (see Table 2.1 1).

Wind speed measurement at sea using anemometers has become the norm in recent years, although as will be seen below, this has not necessarily improved the reliability of the wind speeds reported.

By far the most common form of anemometer is the cup anemometer. This device responds equally to wind speed from any horizontal dmction. It does not measure direction, and is therefore usually installed in conjunction with a simple vane direction meter. The only other type of anemometer in common use is the propeller type. This device uses a tail to steer a propeller intvthe wind direction, and consequently also incorporates a directional measurement output.

2-26 Floating structures a g u ~ d e for d e s ~ g n and analys~s

The propeller type anemometer is generally accepted to be lcss reliable in light winds, whcn there is insufficicnl wind force to keep the propeller reliably pointing into the instantaneous wind direction. Cup anemometers, on the other hand, have a tendency to overestimate wind speed in strong gusty conditions because the cup system is quick to accelerate in response to a gust, but tends to continue to spin fast for a while after the wind speed has dropped.

The main difficulties of anemometer wind data are:

Poor siting of the anemometer in the accelerated wind flow around the ship or structure leads to significant differences between the measured wind and the true free-stream wind. Measured wind speeds are often higher than true wind speeds. Incomplete ~nformation about the height of the anemometer, and whether data have been corrected to the standard height above sea level (usually 10 m). The need to correct the measurement for the speed and heading when measurements are made from a moving ship. Ship roll motions tending to increase the wind speed observed by the anemometer. Local wind speeds on buoys in large waves are affected by the waves themselves. The varying averaging methods used by observers watching an anemometer display. . Poor maintenance.

Anemometers mounted on fixed platforms only suffer from the first two of the above difficulties, and many fixed platforms have quite sophisticated oceanographical data capture and analysis systems so that long term mean speed averaging methods are well defined.

In some cases wind tunnel tests are performed to estimate corrections for the first effect when the accuracy of the measurements is important, for example for wind structure measurements made on the West Sole platform in the UK North Sea (Wills et al., 1989).

2.5.3 Atmospheric stability

The stability of the atmosphere influences the wind speed profile and turbulence. A stable atmosphere is one where the temperature reduction with height is less than the adiabatic lapse rate (the adiabatic (no heat transfer) air temperature/pressure relationship). If a block of air is displaced vertically in a stable atmosphere the buoyancy forces will tq to return it to its original level. An unstable atmosphere is the reverse, and a block of air displaced vertically upwards will experience an increased buoyancy force tendmg to make it continue to rise. An atmosphere that is neither stable nor unstable (i.e. the buoyancy forces are negligible) is said to be neutral.

There are a number of ways of classifying atmospheric stability and Davies and Singh (1985) describe several. However, measurements of temperature grahent often show that the real atmosphere refuses to obey such simple classification, and stable and unstable sub-layers are often present at different heights at the same time.

Over the sea the simplest measure of stability is the difference between the air temperature and the sea temperature A, = T, - T,. If the sea temperature is less than the air temperature (4 +ve), then the conditions can be expected to be stable. If the sea temperature is greater than the air temperature (A, -ve), then the conditions can be expected to be unstable. Wills et al. (1 986) used a criterion of I A,/ < 2" C to define neutral conditions, where the air temperature T, was measured at 80 m. They plotted their mean wind speed profile measurements against A, and showed a great deal of scatter, but a clear trend of a flatter velocity profile between the heights of 10 m and 80 m in the less stable conditions.

It can normally be assumed that the atmosphere is neutral in high wind conditions (say > 20 4 s ) because the strong large-scale turbulence ensures that the atmospheric boundary layer is well mixed. Thus for wind loading calculations the extreme wind forces ge&rated on offshore platforms can be assumed to be caused by a neutral atmosphere wind profile.

The env~ronment 2-27

Pasqu111(1974) has classified atmospheric stability classes over land against wind speed and the level of solar radiat~on. but these are not particularly relevant to the atmosphere over the sea. Wills (1992) has presented wind spectra for dfferent atmospheric stabilities over the sea, and has explained some of the features which influence thc lower ii-equencies (see Figure 2.8). The effect of atmospheric stability on the mean wind profile is discussed In Wills et al. (1986).

C s tab le 0 01

Figure 2.8 Measured wind spectra in stable, neutral and unstable conditions (from Wills, 1992) For notation see Section 2.5.6

In the context of the aerodynamics of floating systems, probably the most important influence of stability is its effect on the low frequency energy in the gust spectrum, which excites surge, sway and yaw natural frequencies. In a strongly stable atmosphere there is a tendency to damp out low frequency turbulence and, at the same time, to depress the mean velocity. In an unstable atmosphere the mean velocity and the large scale low frequency turbulence structure is accentuated as the unstable layers 'tumble' over each other.

With regard to the other environmental effects of the wind, the stability properties of the atmosphere tend to be swamped by the local effects caused by the flow around the offshore platform itself. The platform accelerates the flow and sheds vortices, and it is these flows and their associated pressures generated on the platform superstructure which dominate the local flows, while the influence of the atmospheric stability is weak.

2.5.4 Mean wind speed profile

The variation of the mean wind speed with height is known as the speed profile, and at the heights of interest to the floating platform designer can be assumed to be of the following form (Harris and Deaves, 198 1):

where: -

v 2 mean hourly wind speed at height z ( d s )

z height (m) Z, surface roughness parameter (m)

2-28 Float~ng structures a gu~de for des~gn and analysls

h height of boundary laycr = u.lbJ;. (m)

./: Coriolis parameter = 2Q sin 4 (radls) Q angular velocity of the earth = 72.9 x 1 0-6 radk 4) angle of latitude of site (deg)

At lower heights (<loom) the second term is small (h > > z) and so this is usually simplified to:

The key d o w n in the above is the roughness length z, which represents the roughness of the terrain over which the wind is blowing. At sea th~s roughness depends on the height of the waves, which in turn is dependent on the mean wind speed. A commonly used expression for z, is that due to Charnock (1955):

where c is a constant =: 60

As both z, and u. are unknown this must be solved iteratively. The resulting relationship between z, and V,, is shown in Fig 2.9. (see also Section 2.6.6).

ESDU (1 982) has proposed the following relationship:

Wills et al. (1 989) has compared a number of different espressions for 2,.

The draft IS0 (1996) gives a relationship which avoids the calculation of surface rcughness:

Where:

The speed profile can also be approximated as a power law. The following relationship for the mean 1 hour wind speed at height z being from API-RP2A (1 993).

where z, is a reference height

The environment 2-29

.This powcr law rclatlonship can be very easy and convenient to use, but the log-law profile given in equations 2 1 or- 2.2 abovc is more precise for normal neutral stability atmospheric conditions, and has the further advantage

~ h c roughness length z, has a physical relationshp to the roughness of the terrain (or sea) over which the wind is blowing. This is not true of the exponent in the power law formulation which is for marine locations only.

0

' 13-6 I 1 1 I I -

0 10 2 0 30 4 0

V,, (Mean hourly w m d speed a t z = l o r n ) ( m / s )

Figure 2.9 Variation of z, with V,, for ocean sites (Barltrop and Adams, 1991 )

The log law formulation is llkely to yeld a lower mean speed at large values of z than the power law relationship.

In non neutral wind condrtions the wind profile formulation in equation 2.2 can be modified with the addition of a term involving the Monin-Obukhov stability length parameter L.

where:

Well-documented expressions for @,, and $,, for both stable and unstable conditions are given in Panofsky and Dutton (1984) pp 134-136.

Due to its non-steady turbulent nature, wind speeds must be averaged over a period of time, normally 1 hour or 10 minutes. Averages over longer periods of time will exhibit lower extreme values because they smooth out the gusts. When the maximum values of mean wind speed are being quoted it is important to quote the averaging time.

With certain assumptions about the amount of turbulence present (see Section 2.5.5 below) it is possible to convert extreme values based on one averagmg period to those for another. For example the Table 2.4 (UK HSE, 1995) gves 50-year extreme wind speed values for a number of different averag~ng times.

2-30 Floatmg structures a g u ~ d e for d e s ~ g n and analys~s

Extreme wind speed (~nls) with an averaging time of:

(hour) (mins) (secs)

Table 2.4 Extreme wind speeds for different averaging times (UK HSE, 1995)

2.5.5 Gusts

When observed at a point, the wind speed is seen to vary with time. This is due to the turbulence or gusts which are an inherent feature of the atmospheric mixing processes and the surface friction to which the wind flow is subject. The wind flow contains turbulent structures or eddies. Due to the physical dimensions of these eddies, the wind speed is seen to vary in space as well as time (see Section 2.5.7).

The non-steady nature of the wind speed can be described in a number of ways. The most comprehensive is by means of a power spectrum (see Section 2.5.6).

Other simpler definitions of the variability in the wind speed are the gust factor and the turbulence intensity

Gust factor The gust factor can be used to calculate the speed of a given duration of gust from the hourly mean wind speed, and can be defined as (API, 1993):

where:

@A t second mean wind speed at height z (mls)

G(t, z) the gust factor for gust duration t seconds at elevation z the turbulence intensity (see below).

and the factor g(t) is given by:

g(t) = 3.0+ln[(3/t)0.6] for t < 60s

Turbulence intensity The turbulence intensity is the standard deviation of the wind speed divided by the mean hourly wind speed:

T h e envtronment 2-31

~ 1 ' 1 rccommend the following values for I@):

I(z) = 0.1 5 (z/zs) ' 25 for z < z,y

I(z) = 0 .15(~ /z r ) - ( ' .~~~ jur z >za

where: z , the thickness of the surface layer ( taken to be 20 m)

The draft IS0 (1996) recommends:

2.5.6 Wind gust spectra

The frequency dstribution of the wind speed fluctuations can be described by means of a spectrum. Unfortunately there is no universally accepted spectrum shape, nor a standard presentation method. Probably the most

- con~entional form of presentation is to plot In ( f S( f ) / V Z 1 against In i f zlV 1, a dimensionless frequency

parameter. Both ases are then dimensionless permitting the results for different wind speeds to be plotted on a

single cum. Often the variance = (standard deviation)' of the velocity: P is used instead of F2, to normalise

Xf-1.

Some of the most commonly used spectrum shapes are now outlined

The Deaves and Harris (1 978) spectrum has been widely used. It is a form of the von Karman spectrum and can be written as:

where: f S ( f

frequency spectral energy

f l l F

value of n at peak of the c w e a constant a characteristic length dimension mean wind speed standard deviation of (fluctuating) wind velocity

Kaimal(1972) noted that, although the Deaves and Harris (1978) curve fitted measured data well at the frequency extremes of the available data, it was too peaky near the maximum of the curve, and so he suggested instead:

(RP2A, 1993) recommends the Kaimal spectrum and recommend an average value of the peak frequency&, given by:

2-32 Floatmg structures. a gulde for des~gn and analys~s

where:

-6 frequency of the peak in the non-dimensional spectrum = nm I

There are a number of other spectral formulations, most of which have been developed from extensive wind measurements made on land. The dfferent formulations often vary widely in terms of the gust energy they contain at low frequencies. Research work by Eidsvik (1985) and Wills (1986), on measurements made over the sea, has shown there to be more energy at low frequencies than might have otherwise been expected. Furthermore, it is hown that floating systems can in principle be excited in a resonant manner by such low frequency energy (Rowe et al., 1984; Standing et al., 1991)

Figure 2.10 Modified Kaimal spectrum compared with West Sole measurements (Wills, 1992)

Wills (1 992) modified the Kaimal spectrum to improve the fit to low frequency data (measured at West Sole) because of its potential importance to floating offshore systems. The so-called 'Modified Kaimal' spectrum (Figure 2.10) is:

where:

n 100f l J (100 m was chosen as the length scale)

n "I - 0.06 V mean velocity at height considered ~2 variance of the of the fluctuating speed C 0.66

The constant value of C = 0.66 was chosen by Wills to give the best fit of the West Sole data to the lower frequency part of the spectrum, it being considered that this was the most important part of the spectrum to reproduce accurately.

Figure 2.10 from Wills (1 992) compares the modified Kainlal spectra with measurements of wind spectra made at West Sole.

The env~ronrnent 2-33

The rorm of spectrum in the draft I S 0 (1996) is:

Where a and b are functions of mean hourly wind speed and or height, c = 0.468.

2.5.7 Spatial correlation

I t has been noted above that wind speed varies in space as well as with time. In simple terms the frequency spectrum of the turbulence depends on the size of the turbulent eddies and the wind speed. Locations close together in relation to the eddy size will experience substantially the same wind gust speed at the same time, whilst locations that are distant will experience un-correlated speed variations. This means that larger bodies, such as a platform superstructure, will experience a range of different speeds at the same instant of time, and the integrating nature of the large body will cause the variations in the total force experienced to be significantly less than those experienced by a smaller component of the system (say a flare tower).

The spatial correlation can be defined mathematically in terms of a cross correlation function or cross spectrum. See Barltrop and Adams (1991) for a detailed treatment.

The dunensions of the eddies in the flow direction can be simply estimated by dividing the mean wind speed by the turbulence frequency of interest. The eddies tend to be stretched out in the direction of the flow, and so their dunensions in the transverse and vertical directions can be expected to be a lot smaller (say a third). Components that are somewhat closer together than the dimensions estimated by this method can be expected to experience the same wind speeds at the same time, whllst those that are much further apart can be expected to experience un- correlated wind speed fluctuations at this frequency.

However: it is important to appreciate that much wind force coefficient data is obtained from wind tunnel tests on models. Steps should normally have been taken in such tests to ensure that the speed profile and turbulent structure of the wind is correctly modelled in terms of frequency distribution and length scales. Where this is the case, the steady and fluctuating force coefficients obtained in this way already contain the eflects of.spatia1 and temporal variation in the wind, and coefficients expressed in terms of the mean speed at the reference height can be used in design without correction. However, In many cases it is not possible to represent the lower frequency (large scale) turbulence motion in the wind tunnel, and these may be important for floating systems with very low natural fkequencies. In such cases it will normally be acceptable to perform a quasi-static correction based on full- scale spectral data to represent the low frequency forcing. The physical models themselves may be rigid or flexible. If a r i ~ d model is used then the dynamic response will have to be accounted for by suitably processing the wind tunnel results.

2.5.8 Gust speeds used in static or quasi-static analysis

Gust speeds are required in design for overall global wind loads (e.g, for stability and mooring analysis), and for component design (e.g. for the wind load on a flare boom).

It is quite common to use short term gust wind speeds (e.g the 3-second gust) in a static or quasi-static wind loadmg analysis. This is usually intended to be a conseniative approach because the wind speed selected in this way is a high one, and is considered in the analysis to be a steady wind. In practice. a floating system will only

2-34 Floatmg structures. a guide for des~gn and analysis

be able to respond to lhis high speed short-term gust in a dynamic way, and will not have the time to exhibit the response predicted by a quasi-static analysis.

The 10-minute mean wind speed is often specified for quasi-static mooring analysis codes; e.g. DNV (1989), and NMD (1986). The natural period of a floating system on its mooring system is usually in the range 1 - 2 minutes, and the IO-rninute mean wind speed is therefore a reasonable average wind speed to use, especially when the load generated by this wind speed is also taken together with first and second-order significant or maximum wave forces and excursions, and so there is an element of conservatism in assuming that all occur at the same time.

However, there is a general move towards greater use of more sophisticated dynamic analysis, and the current API recommended practice for mooring systems for floating production systems (1 99 1) now recommends either; static analysis using 1-minute mean wind speed, or dynamic analysis using the 1 hour mean wind speed and an appropriate wind specbum shape. The use of the 1 -minute mean for the static case is more onerous than current practice for mobile floating units, and indicates a desire to choose a more conservative value if the more rigorous analysis is not performed.

The logical selection of wind gust speeds is therefore dependent on the type of analysis envisaged, and on the natural period of dynamic response of the system being studied. It may be surnrnarised as follows:

Static Analysis Select a wind gust speed which represents a value to which the system can respond statically (e.g. V,, where x = 5 T,, , where T,, is the system natural period).

Dynamic Analpis There are a number of different dynamic analysis possibilities:

Discrete gust

Random gust

Select a wind gust speed that will maximise the transient dynamic response of the system (e.g. a gust that might be sustained over a half cycle of the system ie V, , where x = 0.5 T,,).

Select a random series of gusts conforming with the expected distribution and determine the mean response (as sometimes applied to ship stability, e.g. as described by Wills, 199 1).

Spectralfrequency domain A wind spectrum or cross coherences can be combined with a linear RAO of e.g. a tanker to determine the surge response to the wind.

Spectral time domain Choose an appropriate wind spectrum shape and perform a fully dynamic analysis (e.g. using time-domain computer simulation. For example Rowe et al. (1 984) considered the response of a semi-submersible to wind turbulence, including the non-linear effect of roll and pitch on wind loading).

2.5.9 Wind environmental effects

Apart from wind generated forces and responses, there are a number of other more general effects of the wind environment that must be considered in the design of both floating and fixed offshore installations. These concern the way in whch the wind influences the working environment around the platform, and plays an important role in safety in relation to ventilation and to the dispersion of smoke and gas in the event of an accident.

The environment 2-35

Free ventilation It IS common for offshore installations to have process plant areas or modules where, owing to the risk of a leak of hydrocarbons, it is appropriate to keep them open to the outside environment in order to ensure that any leaked gases can be freely and quickly dtspersed. Unfortunately these areas also need to be protected from the strongest wmds and fiom water spray in order to protect equipment and provide a reasonable working environment for staff. Consequently there is a design conflict between ensuring free ventilation and providing a reasonable working environment under all conditions.

The ventilation of these areas therefore poses a design problem which needs to be addressed with a knowledge of the day to day wind environment around the platform and a prediction of the ventilation flows that will be Induced by these conditions. Where there is any doubt that sufficient ventilation will be provided, the ventilation flows are usually modelled in a wind tunnel, or using Computational Fluid Dynamic (CFD) techniques. A common ob~Ktive is to ensure adequate ventilation for 95% of the time (i.e. under 95% of wind conditions experienced).

The degree of ventilation is normally defined in terms of the number of air changes per hour, or in terms of the time required to dtsperse a trace gas to a given dilution. The simplest analysis of the flow through a module will assume an empirical pressure drop coefficient across the module, and estimate mean through-put for a gven external pressure field on the platform as a whole. It can readily be seen that the critical conditions for adequate ventilation are the lowest wind speeds or calm conditions.

Forced ventilation Most areas on offshore platforms will be served by forced ventilation systems but the effectiveness of these systems can be impaired under certain conditions by an adverse external wind environment. If ventilation inlets and exhausts are poorly positioned, it is possible for strong winds in adverse directions to generate sufficient pressure differential to stall the system or generate reverse flows. It is also possible for fumes from gas turbine exhausts or flare stacks to be ingested into the forced ventilation system.

These potential problems need to be addressed at the design stage and care taken to ensure that each element is sited in such a way as to make such forced ventilation problems unlikely to occur over the full range of anticipated wind conditions at the location.

Gas and smoke dispersion Consideration of the dispersion of gas leaks or smoke from fires now plays an important element in offshore safety case preparation for oil development areas under the UK Health & Safety Executive regulatory jurisdiction (HSE, 1992). This was one of the important changes following the Piper Alpha Disaster (Cullen, 1990).

To demonstrate the safety of a floating or fixed installation following a serious gas leak or fire, it is usually necessary to postulate various emergency scenarios and then use physical modelling (in a wind tunnel) or CFD techmques to study the consequences.

The key objectives in studying the consequences of a gas leak will usually be to: determine the dynamics of a boundary of a flammable mixture within the gas cloud, ensure sensible positioning of gas detectors to obtain the earliest warning, estimate the risk of a flammable mixture reaching an ignition source before systems can shut down safely.

All of these will be influenced by the wind environment outside the platform, and so representative wind speeds and dmctions will need to be selected for each emergency scenario. These conditions must be selected with care to ensure that the combination of these wind conditions with the circumstances of the emergency represent a realistic credible risk.

Helidecks The wind environment around a fixed or floating platform also represents a potential hazard for helicopters which use the helideck. The main influences on helicopter flight operation safety, related to the wind environment, are: wind turbulence, vertical components of wind velocity, and hot gas plumes in the approach path.

2-36 Floating structures: a guide for design and analysls

The wind conditions over the helideck, and on the landing approach or departure paths, are influenced by the:

wind speed and direction at the time. * shape of the platform, and the distortions this introduces in the wind flow.

location of any hot gas plumes from flare booms or gas turbine exhausts. location of the helideck in relation to the platform topside and the wind direction.

The most important feature of a good helideck siting on an offshore platform are:

Height Generally, the hlgher the helideck is above the surrounding platform topsides, then the better the wind environment for the helicopter.

Air Gap under the helideck A reasonable air gap between the helideck and the module underneath ensures smoother and more horizontal wind flow across the deck.

The siting of helidecks and the requirements for good quality air flow across them are covered by the UK Health & Safety Executive 4th Edition Guidance Notes (1 995).

On structures or vessels where the helideck is in close proximity to a large superstructure, it is normally necessary to perform wind tunnel model tests in order to demonstrate compliance with the turbulence and vertical wind speed certification requirements under all likely wind speed and direction combinations.

2.6 Tides, currents and water levels

2.6.1 Introduction

Currents are the sources of sigmficant loads, particularly on moored vessels and structures. In addition the way in which the current load is distributed through the water column is important because, if the highest current speeds correspond co-linearly with the highest wave orbital velocities (i.e. at the sea surface), then the combined drag load at the surface is sigmficantly increased compared with that due to waves alone (see Section 2.7.6). Other aspects of currents whch may be of importance for a particular structure or location are scouring and deposition at the sea bed, increased corrosion, transverse oscillation, modification of wave effects, impacts from floating material such as flotsam, ice etc. and the effect on construction from currents andlor water levels.

There are a number of hfferent currents including oceanic currents, thermohaline currents, wind driven currents, tidal currents, surge currents and inertial currents. Forcing agents include the wind, atmospheric pressure, heat, evaporation, gravity and motion (of the Earth and the Moon).

2.6.2 Oceanic currents caused by winds

The global current climate was briefly described in Section 2.3.6. The role of Ekrnan transport was mentioned whereby when averaged over depth, water is transported at approximately 90 degrees to the right (left) of the wind direction in the northern (southern) hemisphere. This leads to a convergence of water at the centre of a high (atmospheric) pressure system and a hvergence of water from the centre of a low (atmospheric) pressure system whch is the opposite of what might be expected if consideration was restricted to atmospheric pressure alone. Anomalous water levels so caused lead to flows of water and the Coriolis effect tends to divert flows once more leadmg to large anti-cyclonic subtropical circulations in each ocean called gyres. It is a feature of these g y m that current speed is much greater on the western side of the ocean ( e g Gulf Stream) than on the east and the reason for thls is vorticity.

For horizontal motion in the oceans or atmosphere the conservation of angular momentum requires that in the - absence of external forces such as wind or friction the absolute vorticity remains constant. Fluid moving on the Earth's surface possesses vorticity about a vertical axis as a result of the Earth's rotation if it is anywhere other

The environment 2-37

than at the equator. Ths is the planetary vorticity and its magnitude is equal to the Coriolis effect being positive (anti-clockwise) in the northern hemisphere (negative in the southern hemisphere). A fluid may also possess vorticity with respect to the Earth which is called relative vorticity and is positive for cyclonic (anti-clockwise) rotation in the northern hemisphere. The sum of planetary and relative vorticity is known as the absolute vorticity and conservation of angular momentum requires that this quantity is a constant. Thus we have:

When applied to a subtropical anti-cyclonic rotating gyre with anti-cyclonic wind stress acting on the water surface such as the Gulf Stream system in the North Atlantic, the effects on the western and eastern sides of the ocean will be different. On the western side northward motion will result in the water moving into an area of increased planetary vorticity as latitude increases which must be offset by an increase in negative relative vorticity (i.e. a tendency towards clockwise or anti-cyclonic rotation). On the eastern side the reverse effect will produce a tendency towards anti-clockwise rotation. As the anti-cyclonic winds are acting to produce clockwise rotation there is 'a combined clockwise driving force on the west but opposing forces on the east. One further consideration is hction which acts on the Gulf Stream, slowing it down and effectively reducing clockwise rotation. Friction is proportional to the square of the current speed and an equilibrium condition is reached if the current speed in the west is about ten times that in the east.

The total volumes of water moving north and south in an ocean must be equal. In the North Atlantic Ocean this requirement results in the narrow Gulf Stream, whch is on the western side, acting over a considerable depth while the currents on the east, whlch are spread over a broad area, are mainly restricted to a much shallower layer.

Westward setting North and South Equatorial Currents are found in both the Atlantic and the Pacific Oceans with the South Equatorial Currents in general a little stronger than the North Equatorial Currents. The Equatorial Counter Current (briefly mentioned in 2.3.6) reaches a maximum speed between 5 O N and 10 O N and it may be below the surface as happens with the Guinea Current off West Africa. These counter currents serve to restore the sea surface to an equdibrium position p e n the persistent trade winds which drive the water westwards. Note that because all these currents, as the names suggest, occur very close to the equator there is very little if any planetary vorticity involved. Additionally because the trade winds blow without rotation there is also very little relative vorticity so that the equatorial currents tend to flow in straight lines, backwards and forwards across the oceans. Equatorial currents also occur in the Indian Ocean but speeds, direction and location are influenced by the monsoon winds whlch are very prevalent in the region. Equatorial currents can be as strong as the sub-tropical gyratory currents.

2.6.3 Thermohaline currents

Where horizontal temperature and salinity variations exist in the ocean they lead to baroclinic conditions in which the isopycnic (equal density) and isobaric (equal pressure) surfaces intersect and motion is depth dependent. Density gradients which are not parallel to the direction of gravity inevitably produce motion in a fluid. In the simplified atmospheric model the differential heating leads to convection and with Coriolis forces to the cyclonic and anticyclonic winds; similar structures can exist in the ocean. However these 'baroclinic' currents tend to become unstable so that eddles form. Examples of areas where eddies are of importance to the offshore industry are the waters off Norway and in the Gulf of Mexico.

Large scale meandering in the Norwegian Current can be caused by a sudden outflow of brackish water from the Baltic into the North Sea. Thls can occur following the end of a period of strong westerly winds (I. S. S .C., 1988) and the moving water of different density from that of the North Sea generates eddies with diameters up to 100 h. Current speeds w i h the eddy exceed 1 m/s and may arrive suddenly without warning The eddies associated with the Loop Current in the Gulf of Merrico are due, at least in part, to variations in temperature and density and surface currents associated with one such eddy have been measured with speeds up to 1.4 m/s (Schaudt et al.. 1991).

2-38 Floating structures: a guide for design and analysis

2.6.4 Tides

Tidal forces result from a combination of gravitational force (due to the Earth, Moon and Sun) and centrifugal force due to the motion of the Earth in space. Because the Earth, Moon and Sun are all moving in relation to each other and because the Earth is not of uniform shape, the resultant tidal force varies with time and location but it is predictable.

The equilibrium tide is often used as a starting point in the descriptions of tides. Such a lunar tide would represent the state of equilibrium which would be reached between the gravitational pull exerted by the Moon and the centrifugal force due to the rotation of the Earth about the centre of mass of the Earth-Moon system. It would be represented by an ellipsoid with one bulge closest to the Moon and the other on the opposite side of the Earth. However such a situation could never exist in practice because these bulges would have to travel right round the Earth in 24 hours 50 minutes whlch is the period of rotation of the Earth related to the Earth-Moon system. Given that the speed of long waves is proportional to water depth this would require water to a depth of about 20 lulometres all round the Earth at the equator and also the absence of continents preventing the passage of such waves. A sirmlar solar tide can also be thought of but with a period of 24 hours. Given that both tides have two crests the fundamental periods associated with tides may be calculated to be 12 hours and 12 hours 25 minutes. Coincident crests lead to higher tides called spring tides while coincidence of crests and troughs lead to lower tides called neap tides. Despite its smaller mass, the Moon, being much closer to the Earth than the Sun, exerts the greater force so that the crests of the lunar equilibrium tide are higher than that of the solar equilibrium tide.

The dynamic theory of tides takes account also of the shape, depth and relative positions of ocean basins, the Coriolis effect and fiction of the seabed. All basins have natural periods associated with them (see Section 2.6.7) and the forces mentioned in the description of the equilibrium tide serve to enhance oscillations whch have the same natural periods. Tidal waves interact at 'arnphidromic' points resulting in zero amplitude. Tidal rise increases with increasing distance from amphidromes and the times of high water propagate around them. Tidal currents vary in strength and direction during the tidal cycles and, if plotted hourly as a point in polar coordinates of speed and direction, the resulting pattern of points will resemble an ellipse.

If the rise and fall of sea level or the ebb and flow of current is analysed harmonically a number of coefficients may be determined whch represent partial tides such as the principal lunar and solar effects discussed above. Using knowledge of the motions of the Earth and Moon with respect to each other and the Sun; tidal heights, tidal current speeds and the times of maxima and minima can be predicted for the future. Such predictions are published annually in tide tables. That part of the change in sea level or current which is not explainable in terms of harmonic constituents is called the residual and is unpredictable so that there will always be some difference between predicted and actual tides. During storms a storm surge may occur which may have a dramatic effect on water levels andlor currents (see Section 2.6.6).

Four of the most important harmonic tidal constituents are shown below in Table 2.5

Origin Symbol Speed (Ofhour) Period (hours) ReI. coeff.

Principal lunar semi-diurnal M2 28.9841 12.42 1 .OOOO

Principal solar semi-diurnal 5'2 30.0000 12.00 0.4652

Luni-solar diurnal KI 15.041 1 23.93 0.5842

Principal lunar diurnal 0, 13.9430 25.82 0.4151

Table 2.5 Harmonic tidal constituents

The environment 2-39

Tides may be classified by considering the form factor ( F ) which is defined as

where Hx is the amplitude of the tidal constituent x at some location. Table 2.6 shows values of form factor which define the type of tidal cycle that occurs given certain values of harmonic constituents:

Range of form factor Example M2 SZ KI 01

Semi-diurnal 0...0.25

Mixed, mainly semi-diurnal 0.25.. .1.5

Mixed, mainly diurnal 1.5 ... 3.0

Diurnal 3.0 ...

-

Avonrnouth 4.36 1.51 0.07 0.07

Key West 0.17 0.05 0.09 0.09

Galveston 0.09 0.03 0.12 0.1 1

New Orleans 0.01 0.01 0.08 0.08

Table 2.6 Types of tide and form factor

Where d~urnal tides have approximately one cycle per day and semi-diurnal tides have approximately two cycles per day.

In the deep oceans both tidal rise and tidal currents are generally small but this situation can change dramatically in shallower water. Tidal levels are commonly referred to as 'springs' when lunar and solar tides are in phase and 'neaps' when out of phase. Spring tides occur at around the time of the new and full moon. The harmonic constituents can be related to non-harmonic terms commonly used to describe tidal levels such as shown below. Some of the highest tidal rises which occur are also shown below in Table 2.7.

mean high water springs = z, +(Hm +H,) mean low water springs = z,-(HM2+Hs2) mean high water neaps = zo+(HM2-Hz) mean low water neaps = 2,-(HM2-Hs2)

Location Maximum mean H , Hs2 H,, H,, 2(H*z+Hsz) spring range (m)

- .

Bay of Fundy (Canada) 12.9 5.64 0.83 0.14 0.12 12.94

Avonmouth (England) 12.3 4.36 1.51 0.07 0.07 11.74

Gulf of St. Malo (France) 11.4 3.93 1.53 0.09 0.09 10.92

Puerto Gallegos (Argentina) 10.4 3.93 0.94 0.24 0.24 9.74

Gulf of Cambay (India) 8.8 3.14 0.96 0.76 0.34 8.20

Inch'on (Korea) - 8.4 2.84 1.09 0.39 0.28 7.86

Table 2.7 Examples of large t~dal rises

2-40 Floating structures: a guide for design and analys~s

Table 2.7 illustrates that for many locations in the world an estimate of the mean spring tidal range can be obtained from twice the spring tidal amplitude which is the sum of the amplitudes of the M, and S, harmonic constituents. Such an estimate for offshore locations is likely to be more accurate than coastal sites because shallow waters introduce further terms which complicate the calculation. Values for the amplitudes of the major harmonic constituents can be obtained for anywhere in the world using published co-tidal charts or atlases such as 'Global Ocean Tides' (Schwiderski, 1978- 1982).

Two further commonly used tidal terms are Lowest Astronomical Tide (LAT) and Highest Astronomical Tide (HAT). LAT is the lowest level which can be predicted to occur under any combination of astronomical conditions and occurs once every 18.6 years. LAT is used as the chart datum for many navigational charts being an effective minimum water level although it is possible that meteorological effects may reduce water levels further. There is no simple mathematical way to calculate LAT or HAT for a new location, although they can be inferred by comparing the ratios of LAT to MLWS ( mean low water springs) and HAT to MHWS (mean high water springs) at a port which has a similar tidal cycle. The most accurate way to calculate LAT and HAT is to predict tidal levels for 18.6 years using the harmonic constituents derived from a period of water level analysis and to choose the lowest and highest water level respectively. In recent years the highest and lowest tides occurred on 10 March 1993.

2.6.5 Tidal currents

The currents associated with the tidal cycle are analysed in very similar ways to tidal levels except that since currents are vectors having both magnitude and direction it is necessary to resolve them into u and v components. Tidal currents are associated with the passage of tidal waves and in deep water are insipficant but in shallow water a dramatic change takes place whch, when combined with the effects of topography, can result in very high currents. If speed and duection are plotted on polar coordinates each hour, the consecutive plots will describe an ekptical shape (whch in rivers and channels will have only one axis). In fact each harmonic constituent of current may also be plotted and will appear as an ellipse, although the axes of each constituent may not be parallel. For most practical purposes the tidal current is often dominated by the M, component. For the U.K. Continental Shelf the direction and speed associated with the maximum and minimum amplitudes of the spring tidal current are published (OTH 89 299, 1990) which allows an ellipse to be visualised and any difference in tidal current direction, from the directions where other environmental loads are expected, to be noted. For other parts of the world tidal stream atlases may be available and in some cases tidal current information is printed on navigation charts.

The change in tidal current speed with depth is normally taken as having a 117 power law decay:

117

(z is positive upwards)

The value of the depth averaged current will actually only occur at about 0.32 h (where h is the total water depth) and the surface current will be about 1.07 times the depth averaged value. Thus if this theoretical model is reproduced in practice a current meter should be set at a height above the seabed equal to 32% of the total water depth to record directly the depth averaged current. The reduction in current speed is due to the frictional effect of the seabed and thls will vary according to the nature of the seabed. In addition the depth of the mixed surface layer, any stratification of the water column and the local topography may all exert an influence on the shape of the profile.

The maximum tidal currents will occur with the highest tides i.e. the spring tides and the highest tidal currents of all are likely to occur at around the time of HAT and LAT. The value of current speed will vary in a similar way to the values of tidal height so that the ratio of the amplitudes HATIMHWS may be applied to the maximum value of current speed at spring tides in order to estimate the maximum value of current speed at HAT.

The environment 2-41

Tldal currents can be extremely high in channels, near shoals and around headlands. One of the worst places is the Pentland Firth between Duncansby Head, (Scottish mainland and South Ronaldsway (Orkney Islands) where currents of 12 knots (6 m/s) are shown at spring tides in the Admiralty Tidal Stream Atlas (1986).

2.6.6 Storm surge

Surge is the name given to changes in water level due to meteorological forcing which is the combined effect of wind and atmospheric pressure. Storm surge is the surge associated with a storm and 'storm tide' has come to mean the combined effects of storm surge and astronomical tide. During a storm event, varying surge levels will occur over large areas and some locations may actually experience negative surges which can be important when navigating in shallow water. However, the most dramatic examples of the storm surge phenomenon occur in association with the landfall of severe tropical cyclones at landfall and famous examples have occurred in the Gulf of Mexico, the Bay of Bengal and Japan. A short review is given by the World Meteorological Organisation (1978) in which the maximum storm surge associated with hurricane 'Camille' in the Gulf of Mexico in 1970 is given as 7.4 metres and that associated with a Bangladesh cyclone, also in 1970 is gven as 7.2 metres. These huge increases in water level cause widespread damage and loss of life on land, with the 1970 Bangladesh cyclone being responsible for more than 200,000 deaths. However such disasters occur at the coastline while offshore the effects on water level are not as dramatic although strong currents will be of importance.

The effect of reduced atmospheric pressure allowing a local rise in sea surface and that of wind stress on the sea surface are difficult to separate in any particular storm. Local effects are complicated by basin shape, size and water depth and computerised numerical models are used to predict the effects of a particular storm. The inverted barometer effect is a hypothetical response of the sea surface to changes in atmospheric pressure and is given approximately as an increase in sea level of one centirnetre for each one millibar fall in atmospheric pressure. This s ~ p l e situation d l not occur in practice because the sea is a dynamic system that cannot immediately statically equilibrate the changing atmospheric pressure and the Ekman transport acts in the reverse direction as noted above in Section 2.6.2.

where 6 = surface and elevation and C,= (0.63 +0.066~,,)10"

The effect of wind, particularly in a basin, is more tractable as described by Pugh (1 987): Substituting a wind speed of 30 d s , assuming a fetch of 200 krn, a water depth of 30 m, air density p, = 1.25 kg/m3and water density p = 1027 kg/m3, results in an increase in water level of 1.9 metres. This expression also emphasises the increased effect whch occurs over shallow water.

The currents associated with storm surge are still under investigation using a variety of measuring and modelling techmques. One of the major -culties associated with the problem is to ascertain the current due to wind stress at the sea surface in the presence of waves. A logarithmic near surface layer has been suggested, of the form:

l h s is basically the same form of expression as used for profiles of wind speed with height, with in this case a reduction m speed below the surface. The value of u, (current speed at the surface) is taken to be approximately

I i 3% of the mean wind speed: vlo at 10 metres above mean sea level (MSL). The values of r, (surface roughness) I I and u. (hction velocity of the water) have proved to be difficult to define. Although a wlde range of values seem i to have been used (OTH 89 299, 1990): the value of z, can be calculated according to Cook (1985) as: I

2-42 Floating structures: a guide for des~gn and analysis

An expression for u. (friction velocity of the water) is given by Heaps and Jones (1987):

where zis the surface stress due to the wind, p is the density of sea water (= 1027 kg/m3) and p, is the density of air (= 1.25 kg/m3). For practical purposes u.(water)= 0.00 12 ? .

The logarithmic profile discussed above will have limited vertical extent unless large values of surface roughness are used. The effect of other parameters such as waves and tidal current will induce turbulent mixing of the surface layers of the water column spreading momentum throughout. Other factors which may also affect the magnitude of wind induced current are wind speed, fetch, duration, water depth and stratification.

The theoretical profile over the bulk of the water column is also still a matter for debate. Some authorities specify a sheared current reducing with depth while others favour a block profile. The theoretical profile is based on the Ekman spiral which is a consequence of the relationship between speed of the water mass and its deflection by the Coriolis effect. This deflection increases with decreasing speed so the surface current, with a lower speed than the wind which is causing it suffers a greater deflection than the wind itself. The surface layer exerts a stress on the underlying layer whch moves at a slower speed and suffers more deflection and so on. In deep water, with constant eddy viscosity (a measure of turbulence), the lowest affected layer moves in a direction opposite to that of the wind although this has never been observed in practice. Theoretically the sum effect is a current at 90' to the wind direction (on the right in the northern hemisphere) although local conditions and water depth will influence h s . Wind driven currents exist in the mixed layer where turbulent mixing due to waves and tidal flow will spread the momentum of wind driven flow. The depth of this mixed layer is quite small in calm weather, particularly when surface heating causes expansion and buoyancy of the upper layers but maybe 100 m during severe andfor prolonged storms. The magnitude of the wind driven current at depth will be in the range 1% - 3% of hourly mean wind speed with the actual magnitude dependent on local factors. Recent research and measurement campaigns suggest a block profile in the mixed layer as the most realistic. (e g. Vyas et al., 1988, and API RP2A, 1993).

2.6.7 Seiches and other low frequency oscillations

Standmg waves or basin oscillations known as seiches can occur in bays and enclosed lakes. For standing waves to develop, the resonant period of the basin must be equal to the period of the wave (or a small whole number of multiples of it).For an enclosed lake the wavelength = lake length (L) x 2/n ( n = 1,2,3.. . .). If the ratio of water depth to wavelength of the wave is less than 1 to 10 then the wave can be considered as a shallow water wave with a penod (8 and the period of the oscillation is related to the length of the lake and the depth of the water in it by:

The standing wave will consist of a node (with no vertical motion in the centre) and anti-nodes with alternate maximum displacement at either end.

In the case of bays or harbours the node is found near the entrance with the anti-node at the closed end which results in a wavelength = bay lengthx 4/(2n - 1) and for shallow water waves gives natural periods of

The environment 2-43

In order for seiches to begin and continue there needs to be some sort of forcing mechanism and of course the cffccts of the Moon and Sun are the most important, resulting in tides as discussed above (see Section 2.6.4). However other mechanisms can trigger a seiche such as a squall or an earthquake (note that the incorrectly named .tidal waves' associated with earthquakes are properly called tsunamis and these waves are generated by submarine landslides and not the earthquake itself). Horizontal water velocities will be greatest at the node locations and although currents may be small, horizontal displacement may be appreciable and have a period similar to that of a floating structure.

Other oscillations may be due to stratification of the water column with internal waves forming on the boundaries between layers of different density. Such waves may be related to tides or have higher frequencies. Changes in temperature and density can also occur horizontally giving rise to fronts which are marine equivalents of atmospheric fiontal systems. Such currents have dmctions along the fronts and are usually very localised. Inertial currents are those whlch persist after the forcing mechanism (e.g. a wind blowing) has ceased to operate and with little hction such a current can last for several days. The moving water will be influenced by the Coriolis effect which will introduce a circular path and an angular velocity:

where Q = angular velocity of the earths rotation and $ = latitude.

2.6.8 Currents in deep waters

As oil exploration and production moves into deeper waters such as west of Shetland, tides and storm surge currents become proportionately less important but the total current may still be very significant, particularly on a shelf edge where the bathyrnetry constrains currents to move in particular directions.

There may be a persistent oceanic flow such as the Gulf Stream or North Atlantic Drift which in the vicinity of islands can split leading to eddies. In the Faeroe-Shetland Channel cold water from the Nonvegan Sea sets southwest below warmer water setting northeast leading to stratification and strong vertical shear between the two bodies of water.

At the boundary between two bodies of water with Qfferent densities, internal waves can form which also produce signtficant currents. These currents can arise without warning although in other cases may be triggered by tidal effects. Internal waves may be particularly prevalent near shelf edges where stratification exists and occur in the tropics as well as more temperate latitudes.

It is sometimes very difficult to assess the scale of current effects since by their nature certain types of current occur at random or in certain seasons and may not be manifest during a brief measurement campaign (e.g. one month) sufficient to identify tidal characteristics. During drilling, west of Shetland currents were found to be higher than expected even though data had been gathered for some years previously.

2.7 Waves

2.7.1 Wave generation and dissipation

There is a very extensive literature on wave generation but rather less on dissipation. Attention is here confined to wind waves, and only a highly simplified summary of basic concepts can be given. A useful introduction to fuller accounts, with comprehensive reference lists may be found in Tucker (1 991).

Generation Our knowledge of the physics of wave generation by wind still owes much to pioneering theoretical work by Phillips and Miles A more recent investigation k n o w as JONSWAP (Joint North Sea Wave Project) led.

2-44 Floating structures a guide for des~gn and analysis

however, to major advances in understanding which underlie contemporary methods for predicting wave growth in terms of spectral development.

The early theoretical work studied the mechanics of energy transfer from the wind in two stages. Phlllips defined an initial stage starting from calm water with a constant and relatively low rate of height increase often referred to as the linear growth phase. He explained h s in terms of resonant responses of the water surface to the turbulent fluctuations of pressure in the wind boundary layer. Also, as noted below, he defined (Phillips, 195 8) a frequency dependent limit to wave growth imposed by energy losses due to breaking. In the second stage, s t d e d by Miles (1 957), it was assumed that there is an established regular wave train with sufficient height to cause a substantial cyclic pressure variation in the incident air stream. The phase of this cyclic variation is shifted by the influence of the wind boundary layer, introducing a component of pressure fluctuation in phase with wave slope which acts as the generating force. By deriving an expression for this phase shift as a function of the shape of the velocity profile in the wind boundary layer, Miles predicted an exponential rate of growth.

The Phillips and Miles theories were widely accepted as mathematically valid. Prior to the JONSWAP investigation, however, they were generally regarded as yielding unrealistically low estimates of wave growth and were only used in conjunction with large empirical correction factors.

The critical finding of the JONSWAP investigation, which effectively restored the credibility of the earlier theories, was the importance of the role of non-linear interactions between waves of different frequencies in the development of a wind sea spectrum. Analysis of the extensive field measurements made showed clearly (Hasselrnann et al., 1973) that if the growth of a complete spectrum is studied, energy is received from the wind only at the hlgh fiequency end. It is then transferred, by the non-linear wavelwave interaction process, to the lower frequency region in which the peak level of energy is accumulated.

The JONSWAP results indicated that the Phillips and Miles theories are compatible with the more limited role required by this re-interpretation of the energy transfer mechanism. They also led to the derivation of formulae for prdction of spectral growth as a hc t ion of wind field properties expressible in terms of simple engineering parameters. D e a s may be found in Hasselmann et al., (1 976) but it may be useful to cite the following formulae (translated into enweering units) for predicting significant wave height and zero crossing period (H, (m) and T, (s)) as functions of wind speed, fetch and duration (V in knots, F in nautical miles and D in hours respectively).

Fetch limitation

TZ = 0.405 V 0.4F 0.3

Duration limitation:

H, and TZ are defined in relation to spectral properties in Section 2.7.3. In deciding whether to use F o r D it is recommended by Carter (1 982) that fetch limitation should be assumed and Fused if the duration D reaches:

It should also be noted that there are limiting values of fetch and duration at whch the waves reach a so-called 'fully arisen' condtion: when they are in equilibrium with the wind. It is commonly assumed that in this condition the wave spectrum will approximate to the form known as Pierson-Moskowitz (P-M), and Hs and T, are then

The environment 2-45

rclated to the wind speed P'(corrected from the values V,,, measured at a height of 19.5m used by Pierson and Moskowitz (1964), to values Vat the standard height of 10m assuming V/V,,, = 0.93) by:

Carter (1982) suggests that the relevant fetch and duration limits are related to the wind speed by:

and

D = 1.035V

It may indeed be found by substituting these expressions for F and D into the equations 2.3 1 to 2.34 for H, and T, that the P-M equations 2.36 and 2.37 are approximately recovered. For example, substituting F = 0.33.2 P i n equation 2.3 1 gwes:

which agrees quite closely with equation 2.3 6.

The above P-M equations serve to determine the value of a steepness parameter S expressed in terms of H, and a wavelength 31 corresponding to T, which may be regarded as characteristic of fully arisen seas, namely:

It is of fiuther interest to note that in fully arisen conditions the phase speed C, of waves corresponding to the modal (or peak energy) frequency exceeds the wind speed. It may in fact be found that for a P-M spectrum the ratio C, lV (sometimes known as the 'wave age') has the value 1.23 (assuming that C, and V are in consistent units, and that V has been corrected to a standard height of 1 Om).

Dissipation The term dwipation here refers to the loss of energy and associated decrease in height caused by wave breaking and internal friction. It does not include the dispersion of energy which leads to the decay in the height of swell waves as they spread out &om the generating area, whlch will be discussed in the next section. Also excluded here are losses due to wave breaking and bottom friction in shallow water which are covered in Section 2.12.3.

Since internal friction losses in deep water are negligible (Tucker. 199 1) only energy losses due to wave breaking in deep water remain to be considered. Such losses are not easily predicted and it must suffice here to note that most of the theoretical spectral models currently used (see Section 2.7.5 below) define energy as proportional at high frequencies to f i e q ~ e n c ~ - ~ . This ensures compliance with a 'saturation' or 'equilibrium' limit beyond which the input of energy fiom the wind is balanced by losses due to wave breaking. It accords, in fact, with the limiting form proposed by Phillips (1 958) incorporated in the so called Phillips' equilibrium spectrum written as:

2-46 Float~ng structures: a guide for design and analysis

Where S( f ) energy density

f frequency in Hz f, g 1 (2xV V Wind speed a 0.008 1 (sometimes known as the Phillips' Constant)

2.7.2 Wave measurement

Knowledge of the waves is crucial to the design of floating offshore systems, and it is therefore unfortunate that waves are not particularly easy to measure in the ocean. Measurement is not quite so difficult when there is already a fixed or floating structure at the location of interest, but when such platforms are absent it presents sipficant difficulties.

As a result, two basic types of wave measuring device have been developed; those floating on self-contained buoys, and those requiring a platform on which they can be mounted. The latter type mostly measure the instantaneous water elevation directly (by a variety of different principles) whilst the former measure the motions (usually the accelerations) of the floating buoy and deduce the wave height from these. Closely allied with the buoy systems are ship-borne wave recorders whlch measure the motions of a ship, together with hull submergence from pressure transducers, and deduce the wave height.

In adhtion to the above, radar altimeters mounted on satellites, are also in use for the collection of wave height data (see also Section 2.4. I), but the rapid passage of the satellite footprint across the ocean surface means that the data collected is not duectly comparable with point measurements of wave elevation time history made by 'in situ' instruments at a fixed location.

Wave measurements can be of point elevation only, in which case sigmficant wave height and the 'point' wave spectrum can be deduced. If mformation on wave direction and the directional spread of the energy is required, then either additional point elevation measurements are required close by, or alternatively the wave slope must be measured.

Data fi-om the wave measuring device must either be collected and processed in the instrument or transmitted to some remote data logger for storage and analysis.

Once the measurement and storage of an elevation time history (or data from which one can be deduced) has been successfully accomplished it is necessary to analyse the signal to derive the most usual sea-state parameters; significant wave height H, , zero crossing period T, , modal or peak period T,, , and wave energy spectrum S( f) or S(f, 0 8). The derivation of the periods can be particularly sensitive to the analysis procedure, the frequency bandwidth of the instrument and any filtering that has been performed. The derivation of directional wave spectra is particularly complex, there being a number of different methods whose performance varies widely.

Point elevation measurements attached to fixed or floating platforms can operate on a number of different principles. One of the first in common use was the so-called wave-staff. A wave-staff works by detecting the changes in electrical properties as the water level moves up and down it, and it needs to be rigidly attached to a platform leg covering the full wave height and tidal rise and fall. They are therefore not particularly easy to install and maintain, and are vulnerable to damage. More recently systems based on laser light or microwaves reflected off the surface of the sea have found favour because of their greater ease of installation and maintenance (they just need a rigd attachment at platform deck level). They can however be affected by spray, especially if they are

The envtronment 2-47

on the downwind side of the platform. Some of these systems now incorporate motion sensing so that they automatically correct for wave motions when attached to a floating platform or vessel. Figure 2.1 1 illustrates the principle of operation of a number of wave measurement systems.

Rodor altimeter or loser

Wave r ~ d e r buoy 'li i

Downward p o ~ n t ~ n g rodar (or infra- red device)

Radar

Figure 2.1 1 Wave measuring devicies (Barltrop and Adams, 1991 ; after Draper 1970)

Some microwave and radar systems (e.g. MIROS and CODAR) have bsen developed to scan a larger area of sea and return signals that can be analysed to yield directional wave spectra.

In addition to the platform-mounted sensors there are also seabed mounted, or sub-surface buoy mounted systems. Some of these work on the principle of an inverted echo-sounder, whilst others measure pressure. The latter only measure the longer wave components, as the pressures associated with the shorter higher frequency components decay quickly with depth.

The most common wave measuring device has been the Datawell Wavender Buoy which has been in use for many years. The buoy is attached to a mooring system designed to minimise influence on the buoy motions, and the buoy contains a device detecting vertical acceleration, the signal from which is filtered and integrated to derive a wave elevation signal. It is therefore a point elevation measuring device. The signal is usually transmitted by VHF radio to a receiving and recording device installed at a convenient location in the vicinity.

More recently the wave buoy concept has been developed by an number of organisations to measure wave directional properties, normally by detecting the wave slope (or the buoy's response to the wave slope) as well as the vertical acceleration. The size and ease of deployment of these buoys can vary widely.

Wave buoys suffer fiom difficulties in detecting low frequency components (say periods greater than 15 seconds) because their elevation measurements are based on the Integration of accelerations, which must be high-pass filtered in order to prevent drift. The arrangement of the buoy's mooring system is also critical to its performance in large waves, as the buoy can be dragged through the crest of large waves as the mooring pulls tight, or can be subject to resonant rolling and pitching motions large enough to submerge the transmitter aerial.

2-48 Floating structures: a guide for design and analys~s

The measurement device most appropriate to a given application depends on a number of factors including; the presence or othewise of a fixed platform, the ease of deployment, duration of the measurement program, and the need to measure other parameters (e.g. tide, wind). All the above classes of measurement device have their strengths and weaknesses. Any platform-mounted system is potentially prone to distortion of the wave field around the platform legs, some of the optical and radar systems can be confused by the presence of spray in the air, buoy systems tend to be unreliable in severe wave conditions due to mooring and stability problems, and the directional systems can be sensitive to duectional ambiguity and directional resolution difficulties in the analysis. Carter et al. (1986) have described the various advantages and disadvantages of the different measurement systems.

A number of field stuhes have been performed comparing the reliability and accuracy of in situ wave measuring systems, two of the best known being the Atlantic Remote Sensing Land Ocean Experiment (ARSLOE) in 1980, and the Wave Direction Measurement Calibration project (WADIC) carried out in the North Sea in 1983. The results of the WADIC project, a comprehensive comparison between results obtained from seven different wave buoys and a variety of reference instrumentation mounted on the Edda platform are described by Allender et al. (1989). Young (1994) has studied the very limited directional resolving power of pitchlroll buoys, and compared them with spatial elevation arrays.

2.7.3 Sea and swell description

The wave condhons at any point in space and time will usually involve a combination of locally generated wind waves known as sea and waves generated elsewhere known as swell. The development of such mixed conditions should automatically be modelled by numerical hindcasting systems such as those referred to in Section 2.4.3. The present purpose is to discuss the behaviour of sea and swell, and the way in whch they combine in terms of simple descriptive parameters.

Sea The most commonly used descriptive parameters for a sea state are the significant height H,, the zero crossing period T, and the peak period (or period of the mode of the wave energy spectrum) T,. In Section 2.7.1, H, and T, are used in formulae quoted for predicting wind generated sea conditions assuming a JONSWAP form of spectrum with specified fetch or duration. To assist interpretation of these formulae it may be helpful first to define H, and T, and their relation to spectral properties. Originally significant height was defined as the mean value fiom the hlghest thlrd of a sample of wave heights and zero crossing period as the average interval between alternate zero crossings on a wave record. It is now usual, however, to define them in terms of spectral moments, thus :

where:

and: f wave frequency (Hz) S( f ) energy density (m2/Hz)

The envtronment 2-49

On the basis of the above definitions, most of the commonly used theoretical spectra can be expressed as functions of H, and TZ (or related period parameters) as described in Section 2.7.5.

The JONSWAP spectrum is widely used for characterising wind seas, having the advantage of including parameters for describing fetch or duration limited conditions. In addition, as also explained in Sections 2.7.5 and 2.1 3.3, it can be modelled as a directional spectrum.

Swell The origins of swell can be explained by reference to the discussion of wave generation in Section 2.7.1. From this it follows that the energy in a growing wind sea moves towards progressively lower frequencies and correspondmgly increasing crest (or phase) speeds (since crest speed C = gI2n1; see Annex 3A). Thus for a given wind speed V, the sigmficant wave height and crest speed C, (at the modal or peak energy frequency) will grow, as long as the wind persists, up to the lirmt described in Section 2.7.1. As this limit is approached, C, will exceed Vuntil the waves are in equilibrium with the wind, and the sea is then said to be fully arisen. When waves cease to be wind dnven, which may occur at varying stages of development, they continue to propagate and eventually lose height as they spread out away from the generating area.

All waves not generated by the local wind are known as swell. A hstinction may be made however between waves generated by recent or nearby wind action sometimes called young swell, and waves originating from remote unrelated weather systems which may be called old swell.

The decay in the height of swell waves as they propagate away from their origin is not readily predicted by any simple formula but should be approximately modelled by numerical hindcasting schemes. A small part of the decay may be due to energy loss but in deep water it is mainly the result of directional and frequency dispersion.

Directional hspersion may be thought of as a fanning out, and if this occurs at a constant rate the energy density far from the generating area (then seen as approximating to a point source) will decrease as the inverse of the distance travelled. The wave height which is proportional to the square root of the energy density will thus correspondingly decay as the inverse square root of the distance.

Frequency dispersion is the radial spreading out of enerby travelling at group velocity which is inversely proportional to frequency (in deep water group velocity = % (I = g/4?cf; see Annex 3A). This leads to a decrease of energy density as the low frequency waves run ahead of those at high frequency. The corresponding decay in height is not readily prehcted. It is of interest to note, however, that it follows from the above that the frequency of swell waves from a distant storm will increase with time and they may thus be distinguished from sea waves (in a growing sea) whose frequency decreases with time.

Combined Sea and Swell The combination of sea and swell can be modelled as in numerical hindcast schemes in terms of a composite spectrum whlch may have more than one mode (or peak of energy density). This may be achieved either by linear superposition of suitable sea and swell spectra, or by use of some multi-modal forms (see Section 2.7.5). From equation 2 above it follows that when two spectra with significant heights H, and H, are added, the resultant significant height H, for the combined spectrum will be given by:

Th~s formula is indeed used by the UKMO for interpreting visual observations of sea and swell height. It is also used by Hogben (1988) in a modelling of the joint probability of wave height and wind speed (see Section 2.1 1.3) whlch offers a basis for estimating mean levels of swell to be added to predictions of wind sea height. These are found to range from about '/2 m in limited fetch areas to 2 m or more in the open ocean (see Figure 7b of Hogben, 1988).

2-50 Floatmg structures a gu~de for des~gn and analys~s

'. (0) Airy wove: deep woter , srnol l wove s teepness

(b) S tokes wove: d e e p wote r , Io rge wave s teepness

c (c) Cnoidol wove: shal low wate r

(d ) Sol i tory wove l i m i t c u r v e f o r cno ida l wove. when the per iod tends t o ~ n f i n ~ t y

Figure 2.1 2 Some theoretical wave profiles (after Le Mehaute, 1976)

frequency Hz

0 0.05 0.1 0.1 5

400 7 7 Water surface I 1 elevation spectrol density S(f)

n frequency component

10 ,__---,,---- -,-c

Component woves . - - - H

of 5e1ght - w - u - 8 4---vAv-----.

Hn = J 8 ~ ( f ) ~ f zF=+=

7 ,---. ,---. -14 \ -,,-----

5 -uc -+

frequency 3 3 corrponent

n 2

Wovelength A n = g / ( i n f n 2 j

I I 1 I 0 10 20 30

Wove t ~ m e h ~ s t o r y

Figure 2.1 3 Modelling of wave spectra (after Hogben, 1986)

The environment 2-51

2.7.4 Regular waves

The term regular wave refers to a unichrectional train of waves with constant amplitude and frequency, and hence constant length, Ifthe ratio amplitudeAength (known as steepness) is sufficiently small, the waves are said to be linear or Airy waves. As explained in Annex 3A, the surface profile can then be well approximated by a sine wave, and theoretical descriptions of the complete wave motion including the surface and sub-surface kinematics are readily available.

When the steepness is greater, the waves are known as finite amplitude or non-linear. The profile then becomes more peaked at the crests and flatter in the troughs and valid description of the-profile requires non-linear solutions of the relevant equations. Figure 2.12 shows some theoretical profiles including the so called Stokes Wave, commonly used for modelling deep water waves of extreme height (see Sections 2.8.4 and 2.8.5). These involve additional harmonics, which travel at the overall wave celerity and increase in order with steepness, typically up to 5th order.

It is not to be expected that regular waves, either linear or non-linear, will be found in the real environment. They nonetheless both have an important role in computer and laboratory modelling of sea conditions for engineering investigation and are often the basis for design, especially in conjunction with 'spectral' methods of analysis. Care is needed however because important nonlinear effects, which can lead e.g. to ringing and springing (see Section 3.9),are not included.

The key significance of linear waves is that they can be combined by linear superposition to compose realistic models of actual sea conditions in terms of energy spectra as illustrated in Figure 2.13. The figure shows a 1 - dunensional or point spectrum which takes no account of wave direction but is, nonetheless, widely used. It may be seen that each of a series of frequency bands with width Gfcan define a component regular wave train with frequencyf,, energy S(f,)Gf and corresponding height H, and length A, given by :

Thls modehg of a sea state can be translated into a time hlstory describing the complete wave motion including subsurface lanematics by linear superposition of the components with random phase differences E,. Thus a time history realisation of surface elevation 5 may be written as:

The concept is readily extended to directional spectra where the energy density is then a function: S(J0) of frequency, and dxection, and component wave trains can be defined corresponding to cells in thef-0 plane with bandwidths Gf and 60, instead of frequency bands.

An important advantage of spectral modelling of waves is that any responses such as structural loads or motions whlch are linear can be s d a r l y described by spectra derivable from wave spectra by use of frequency dependent transfer functions known as response amplitude operators (see Annex 3F.). The response amplitude operator for each frequency component: moreover, can be determined by computation or experiments in regular waves.

The importance of non-linear descriptions of waves relates mostly to modelling of extreme waves whlch is discussed in Sections 2.8.4 and 2.8.5 and steep shallow water waves.

2-52 Floating structures: a guide for design and analysis

2.7.5 Random waves

Waves in the real environment are sometimes referred to as random or irregular. As explained in the previous section, they can be effectively modelled in terms of energy spectra which describe ensembles of regular wave trains combining in random phase. An important advantage of such modelling is that the complete descriptions of the wave motions including subsurface kinematics, available as noted in Section 2.7.4, for the regular components can be linearly superposed to provide corresponding complete descriptions of the combined wave motion. On thls basis, spectra can be used to compute a wide range of statistical properties, and the formulae for sigmficant lmght and zero crossing period in terms of spectral moments have already been cited (Section 2.7.3). It should also be mentioned that for narrow band spectra (Longuet-Higgins, 1952) the statistics of individual wave height h can be approximated by Rayleigh distributions. Thus the probability density p(h) and exceedence probability Q(h) may be written as:

and

There are methods of description for random waves other than spectra, including use of wave height sequences defined by statistical laws such as those known as Markov or ARMA (Auto-regressive Moving Average) processes (Box and Jenluns, 1970 : see also Section 2.9.4). These are less widely used, however, and attention will here be concentrated on reviewing the forms of spectrum commonly employed for modelling random waves.

One of the available options is to use spectra from the extensive archives now accumulated of instrumental data which have been banked in spectral format as noted in Section 2.4.1. In practice, however, it is often more convenient to use one of the theoretical forms defined in terms of simple descriptive parameters referred to in Section 2.7.3.

General Spectral Form (Pierson Moskowitr and JONSWAP)

Parameter values

Bretschnelder ISSC' Goda"

x (unrts)

aT;+

bTp4

T,

Y

69 IT,

I

Y = I Yields Pierson-Moskowitz spectruma Y ' 1 Yields JONSWAP spectrum Y = 3.3 Y~elds 'Mean JONSWAP' spectrum

" F(y) = 0.0624/[0.230 - 0 0 3 3 6 ~ - O.I85/(1.9 + y)] Note that at correspond~ng y . Goda and ISSC are in close agreement.

Table 2.8 Wave Spectral Formulations (Hogben, 1990-b)

The environment 2-53

A considerable number of such parametric spectra are available (see for example Huang et al., 1990). A selection of widely used formulae which are, in fact, all expressible in terms of the same general spectral form is shown in Table 2.8 cited fiom Hogben (1990-b). The general form quoted at the head of the figure is a parametric version due to Ewing (ISSC, 1982) of the JONSWAP spectrum derived by Hasselrnann et al., (1973) referred to in Sections 2.7.1, 2.7.3, and 2.7.5, and developed specifically for characterising wind generated seas subject to limitation by fetch and duration. It contains a so-called peakedness parameter y with value 3.3 for a Mean JONSWAP spectrum and reduces to a version of the broader earlier form due to Pierson and Moskowitz (1964) when y = 1. The Pierson Moskowitz or PM form was derived fiom analysis of a sample of some 400 spectra measured in the North Atlantic, and is widely used for characterising waves in the open ocean.

The four columns in Table 2.8 define different presentations of the PM (ITTC, 1972 and Bretschneider, 1969) and JONSWAP (ISSC, 1982 and Goda, 1985) spectra with variations only in the units and choice of period parameter. The periods used, together with approximate relationships which connect them, are:

T, = m, lm, .: (1.086-0.005y)TZ (2.53)

and for the Bretschneider spectrum:

Ts = Tp / 1.05

where:

T. peak energy or modal period, T, zero crossing period (see Section 2.7.3), TI average or first moment period (m, and m, are spectral moments as defined in Section 2.7.3), T, significant period defined as the mean period of the hlghest third of all waves, Y JONS WAP peak enhancement factor.

An alternative formulation of the JONSWAP spectrum has been developed by Barltrop and Adarns (1991) expressed in terms of H,, T, and y (for 1 < y 6):

where: k 1.4085 kb 0.327e-0315Y+1.17 k , 1 - 0.285 h(y) a f ( T , , k p ) = e x p [ - ( k , T , f - 1 ) 2 / 2 a 2 ] a 0.07forf<(k,Tz)-'

or a 0.09forf>(kpT,)-'

(T, / T, for y = 1) (T, 1 T, for selected y )

For consistency with Houmb and Overvik (1976):

y = 1 or y = 5.55 (1 74(H,/g T,Z) - 1) whichever is the larger, although other research has suggested that y may be largely unrelated to H, and T,.

2-54 Floating structures: a guide for design and analys~s

The spectra as defined above are unidirectional, but in the case of the JONSWAP form frequency dependent dlreectional spreading can be introduced as described by Hasselmann et al. (1 980) and Mitsuyasu et al. (1 975) and is further drscussed in Section 2.13.4.

The spectra in the table also only have a single energy peak or mode but bimodal forms derived by Ochi (1 978) and Soares (1 984) are suitable for use when sea and swell peaks may need to be separately defined.

The Ochi formula was derived fiom analysis of some 800 spectra measured in the North Atlantic and is illustrated in Figure 2.14 for a case in which the two modes are well separated. It contains six parameters, two values each for (, A and& defining respectively the significant height, spectral width and modal frequency for sea and swell energy lobes, which may often be merged into a single peak.

Soares reviewed about 1000 spectra measured in the North Atlantic drawn from various sources and nearly 6000 from a limited fetch location off the coast of Norway. About 22% of the open ocean spectra (mostly in the lower height range), and 11% of the limited fetch sample were double peaked. He thus developed a procedure for modelling bimodal spectra by linear addition of two JONSWAP forms each defined as in Table 2.8, with y set at 2, and each entered by values of H, and TI computed using formulae given in the reference (note that Soares uses the symbol T, for m,/m, = T, as defmed here). Given bimodal spectra can thus be modelled by use of four parameters.

Torsethaugen, (1993) has also developed a double peaked spectrum model based on the JONSWAP spectrum based on data from the Statfjord field and compared it with measurements from two other locations on the Norwegian Continental Shelf.

Frequency Hertz

Figure 2.14 Sample fithng of bimodal spectrum using Ochi's six parameter formula (Hogben and Cobb, 1986).

However, the problem that is often met in practice, when attempting to use bi-modal wave spectra for design, is an inability to define the spectral shape parameters adequately due to the limited amount of measured spectra available for the location of interest.

The environment 2-55

2.7.6 Wave-current interaction

The interaction between currents and waves is a complicated subject and solutions of the flow kinematics have only been developed for relatively simple cases. T h s section will describe the main issues and list some of the main theories, but the reader is referred to the source documents for details of the implementation of these theories. The reader is particularly ref& to Jonnson, (1990), which gives a good summary of all the issues and the various methods that have been developed.

However, it is first worth noting why this complicated area of fluid dynamics wave-current interaction is of mterest to the designer of an offshore floating system:

The combined effect of current and waves potentially gives rise to the largest instantaneous water particle velocities, and thus the largest fluid drag forces. This is likely to be most important for smaller components of the floating system (e.g. risers). Strong current fields have a marked influence on the properties of the wave which pass through them. Waves can become much steeper, and wave energy can be focused in particular locations, giving rise to waves of much greater steepness and height than might otherwise be expected. The wave-period : wave-length relationship is changed.

The supporting document to the UK Department of Energy Guidance on Design and Construction and Certification - Environmental Considerations (UK DEn, 1989) recommends using a suitable wave-current interaction theory in order to estimate extreme fluid velocities. API also recommend this.

Wave-current interaction measurement and interpretation is made particularly complicated by:

The difficulty in measuring current in fixed (Eulerian) axes in the presence of waves. . The difficulty in distinguishing between measured velocity components due to waves and those due to currents (there is no clear distinction in reality, as they combine to present an integrated fluid flow field, and, except in the laboratory, one cannot switch-off one or the other to see the remaining flow component in its uncontaminated form). Measurements of waves often already include influences due to current (for example in terms of Doppler shift on wave frequencies).

Regular waves Barltrop and Adams (1 99 1) have noted that the wave-current interaction problem is very simple if:

the current is constant with water depth, the water depth is constant, and . the current is steady.

In these circumstances a regular wave simply travels on the current, and all the established wave theories can be used, providing they are applied relative to an axis system moving with the current. This results in an apparent Doppler shift to wave period and a consequent change in the wave period I wavelength relationshp. The stationary observer sees the wave period change from:

T = Llc

to:

2-56 Floating structures: a guide for design and analysis

where: L wavelength T wave period (relative to stationary observer) To wave period relative to current and predicted by zero current theory u, current velocity 6 angle between current and the wave c wave celerity.

In practice, currents usually vary with depth and various methods and theories have been developed to deal with such sheared currents. Barltrop and Adam (1 99 1) suggest a simple procedure for replacing a current profile with a constant current in order to estimate the wave properties, and then adding the sheared profile onto the wave kinematics to obtain an estimate of the combined kinematics.

As will be seen in Chapter 3, Section 3, it is also important that for steep waves, non-linear wave theories (such as Stokes 5th or Stream Function) are used to estimate the wave lunematics.

Eastwood and Watson (1989) and Tournazis and Ahilan ( I 990) have outlined the history of the development of solutions to the wave-current interaction problem, and identified the main theories applicable to non-linear waves and sheared currents. These are those due to Fenton (1985) and Dalrymple (1974), which have both been extensively used. Eastwood and Watson also outline their own analytxal approach, based on that of Fenton, for a bi-linear current. (A bi-linear sheared profile can be made to fit most practical measurements of current profile reasonably well.) Tournazis and Ahilan have compared a number of these different methods and concluded that in most circumstances the results for the fluid lunematics are in close agreement. They also make the following recommendations :

For bi-linear current profiles and Stokes 5th waves they recommend the method of Eastwood and Watson (1989). For less steep waves where Stokes 3rd order is considered satisfactory, the method of Kishida and Sobey (1988) is the easiest to implement and fastest to run. Where the limited range of applicability of the analytical methods becomes a problem, then the numerical solutions of Dalrymple (1989) and Chaplin (1 989) can be used. These solutions are rather complex and demandmg of computational resource, but will find greater favour as computing power increases.

More recently Cummins and Swan (1993) have extended Dalrymple's method to deal with a five layered description of the current profile where each layer has a linear current profile. This makes it possible to model much more realistic profiles.

1- , Equihbrium r a n g e limit f o r U=+2rn/s

Equilibrium range limit fo r U=-2 m / s

Energy dissipated

I I I 1

0 4 0 8 1 2 1 9

ma rad/s

Figure 2.15 Influence of current on a P~erson-Moskowltz spectrum meet~ng a 2mls current (after Hedges 1987)

The environment 2-57

Unsteady currents are not normally considered by the offshore designer, but their influence on waves can be quite unportant. It follows f?om the simple analysis of equations 2.5 6 and 2.5 7 above that waves propagating from still water into a current field will have to undergo a transformation in terms of wavelength, celerity and group velocity.

The change in the group velocity means that the wave height must change in order to preserve the energy flux. The result is that wave heights increase when waves meet an opposing current and reduce when they meet an assisting current. Such effects can cause marked changes in wave properties over quite short distances and in some circumstances very steep waves. The effect is most often seen in inshore waters where current fields (usually tidal) can vary markedly in space and time. However, the effect can also be important where waves interact with a general circulation current, such as off South Africa, where extremely steep waves have often caused damage to vessels. A famous example was the Bencruachan whlch suffered severe damage in May 1973 (anon, 1975).

To illustrate the dramatic changes that can take place in waves, Figure 2.15 from Hedges (1 987) shows the change in the shape of a Pierson-Moskowitz deep water spectrum when the waves encounter (i) an opposing 2 m/s current and (ii) an assisting 2 m/s current in the wave direction.

A wave meeting a current field boundary at an oblique angle will have its celerity component in the direction of the current vector changed and this will give rise to a change in the direction of wave propagation, and the wave will be refracted. It is possible therefore for wave fronts to be diffused or focussed by the action of a non-uniform current field. In Figure 2.16 the dotted curves are streamlines and Fl-F2-F3-F4 are wave fronts. (a) illustrates the spread of wave energy by a flood current and (b) the concentration of energy in the Inlet middle by the ebb current.

The concept of wave rays is useful in analysing the way in which waves are refracted by a current field. A ray has everywhere the absolute wave group velocity as a tangent and the wave relationships are simpler if considered along these curves (Christofferson, 1982, gives a full explanation). Considerable computer software exists to analyse the refraction of waves due to current fields and seabed topography, and these find particularly extensive application in the field of coastal engineering. However, it is generally accepted that these methods require a considerable degree of enpeering judgement in their application.

(0) (b)

Figure 2.16 Wave refraction in a tidal inlet (after Per Bruun, 1978)

Random waves As in Figure 2.15 above, the linear regular wave results can be directly applied to random waves described in terms of wave spectra. Such spectra may be multidirectional, and the changes in the directional distribution of the wave energy can be predxted using the ray -tracing methods. Methods therefore exist for the calculation of linear waves and random waves described by spectra in the presence of varying currents and changing bottom topography.

2-58 Float~ng structures: a guide for d e s ~ g n and analys~s

The fundamental problem with irregular waves is that they can only be represented conveniently by linear spectral methods and tlus prevents the various extensions that have been made of wave-current interaction theory to non- linear regular waves (e.g. Stokes 5th order) being applied to the random wave situation.

The current state-of-the-art in wave-current interaction is well summed up by Jonnson, 1990:

'There are still many gaps to bejlled in our understandmg and capability before it becomes possible toperform accurate computation ofthe combined refraction/diffraction of a random sea with high waves riding on a nonsteady, depth-varying current under the influence of generating and dissipating mechanisms. '

However, the important issues for the offshore designer, whose floating system is to be installed at a fixed location, is to ensure that:

A wave-current interaction theory is used for the prediction of maximum water particle velocities for smaller system components. It will normally be adequate to use a regular design wave approach which will permit one of the non-linear regular wave theories to be used if desired. Any necessary corrections are made to wave data to take account of the influence of current, bearing in mind that: Ifthe wave data being used for design have been based on measurements at the appropriate location and in the presence of the appropriate currents, then the wave spectra and statistics can be used without further correction, but consideration should be given to including the effects of current when determining flow kinematics or when calculating the wavelengths. . Ifthe waves have been measured in a different location, where the current fields are different, then consideration should be gven to adjusting the wave heights and periods (spectra) to compensate. Note that this needs to be done on a direction-by-direction basis for each directional component in the wave climate.

2.7.7 Non-linear wave in te rac t ions

The linear (Any) theory ofrandom waves, described in Sections 2.7.4 and 2.7.5, has become the established basis for analysing shp seakeeping and structural response in a seaway. Non-linear interactions between the linear wave components may, however, become important for lightly damped systems which have resonant responses at particularly hlgh or low frequencies. In the present context the non-linear interaction process itself will be of lesser interest than the way in which these interactions affect the analysis of a structure floating in the wave field.

The conventional h e a r ( A q ) wave theory is based on potential flow assumptions, and represents the first-order terms in a Stokes series, whlch has been expanded in powers of a wave steepness parameters (proportional to HIL, where H is the wa17e height and L the wavelength). Thus the surface elevation [ at location x and time t may be expressed in the form of the power series:

[(x:t) = s <( ' ) (x , f ) + s c ( 2 ) ( ~ , t ) + s p ( x : t ) + ... (2.58)

and other quantities, such as water particle velocities, accelerations and pressures are expanded similarly. The linear solution, represented by the Airy theov, is obtained by substituting expressions of this form into the potential flow equations, retaining only the terms proportional to wave steepness.

Steady-state solutions of th~s type are well known to designers of fixed offshore structures. The Stokes fifth-order solution has been the mainstay of jacket structure design for many years, and is used to represent the extreme indwidual wave in the design storm. It represents a Stokes power series solution with terms up to s5, formulated in a frame of reference moving with t h ~ wave crest, thus allowing time-dependence to be ignored. The Stokes fifth-order wave propagates with no change in its surface profile, and the surface elevation time-hlstory passing a fixed point contains the first five harmonics of the fundamental wave period.

The envtronment 2-59

Note that the harmonics in the Stokes wave are a result of non-linearities associated with large wave height. The llamlonlcs have a particular phase relationshp and all propagate with the velocity of the overall wave. This is very different to the low wave height random sea where the different frequencies all propagate independently and at the velocity associated with their individual wavelengths. A real high sea will contain both phenomena with the nonlinear Stokes type of harmonics occurring particularly in the large wave groups. At present it is not practical to include both effects in a wave theory or wave loading analysis. The designer therefore has to choose the most important effect and possibly make some allowance for the other effect. For a fixed structure responding quasi- statically to extreme wave loading the higher velocities predicted by the Stokes non-linearity are the most important effect. For a fixed structure responding resonantly in smaller sea states and for many types of floating structure, the spread of frequencies from the random sea are the most important effwt and so LRWT will commonly be chosen. These theories will not however model TLP springing or ringing behaviour which is dependent on the higher order terms.

Linear, first-order theory has a number of convenient and useful properties Firstly, the wave motions in an irregular sea state may be represented as a linear sum of sinusoidal regular-wave motions over a range of angular frequencies o (= 2nf), using the so-called principle of linear superposition. The properties of this irregular wave history may then be expressed in terms of power spectra (see Section 2.7.4), and the statistics are usually described in terms of the equally well-established theories of Gaussian and Rayleigh processes. Secondly, in a regular sinusoidal wave of amplitude a and frequency o , any quantity which is linearly related to the surface elevation, such as the water particle velocity and acceleration or the vessel's motion, has an amplitude linearly proportional to a and varies sinusoidally with the same frequency o. This means that, for every o , the relationship between a typical response X and the wave amplitude may be expressed in terms of a complex transfer function HAW) :

where the response amplitude operator 1 HAw) / is the ratio of the amplitudes of the response and wave elevation, and the argument 6, of HX(o) represents the phase lag between the response and the wave. The response spectrum S,(o) is then related to the wave spectrum S(o) by the simple expression:

According to linear theory, motions will only be excited at frequencies where there is sufficient wave energy. Motions may be excited at much hgher or lower frequencies, however, if there is some kind of non-linear mechanism. It is known, for example, that moored shps in waves tend to take up a mean offset position, and tend to surge, sway and yaw at their own low natural fiequencies. These steady offsets and low-frequency motions can be explained in terms of second-order, difference-frequency effects. Similarly the high-frequency springng motions of large ships and of tension leg platform motions can be caused by second-order, sum-frequency effects (as well as first order effects when natural frequencies and wave frequencies coincide).

The expression second-order will be used here to describe terms that are mathematically of second order in a Stokes-type series expansion in powers of wave steepness, and are therefore proportional to .r2. The process by which two first-order quantities interact to produce second-order sum and difference frequency responses may be illustrated very simply as follows. We consider an irregular first-order surface elevation history consisting of N superimposed cosine waves at angular frequencies o, for j = 1,2, 3 . . . N:

together with two linearly related first-order quantities X(" and Y ( I ) :

2-60 Floatmg structures: a gu~de for destgn and analys~s

Then the second-order product of these two first-order quantities is:

(2.63) To second-order the product may be written in complex form:

' a { Q J ; ~ ~ - J + ~ - I -

J - 1 k - 1 + QJ; exp - i [ (a J - o,) r - cJ + ek ] } where the complex quantities Q,,' and Q,,' represent quadratic transfer functions analogous to the linear transfer functions H,,, H,, applying to the first-order quantities. In particular it should be noted that the amplitudes and phases of the quadratic transfer h c t i o n s characterise the relationsiup between the second-order quantity and component pairs of waves with amplitudes a,, a, and corresponding fiequencies o, o , in a manner whch is analogous to the linear transfer function relationships.

The above second-order expressions contain two types of terms:

components at the dgeerence frequencies (a, - o ,), representing a source of low-frequency forcing, whch extends down to zero frequency (when oJ = o,). and thus contains components at frequencies well below those contained in the wave spectrum itself; and:

components at the sum frequencies (o, + o,), representing a source of high-frequency forcing, whch extends up to 2 0 ~ and thus contains components up to twice the maximum frequency contained in the wave spectrum itself.

It may be seen that the second-order excitation at a particular sum or difference frequency (causing a resonant response at that frequency) depends on all of the wave components present in the wave spectrum. A wave model with a very small number of components may therefore cause either excessive or insufficient forcing at the natural frequency.

Second-order forces may result fiom interactions between several different first-order quantities: from first-order pressures acting over the first-order varying ~mrnersed surface of the structure, from the first-order velocity

The env~ronrnent 2-61

squared term in Bernoulli's equation, from interactions between first-order structure motions and first-order forces. or as a result of second-order interactions within the wave field itself. The relevant components of the second-order force will be described in detail in Chapter 3. Components which involve products of first-order quantities may be obtained directly from the linear wave diffraction solution. Those that involve interactions uitlun the wave field itself, however, require the solution of the much more complex second-order wave problem.

Mathematical solutions describing the second-order surface elevation and velocity potential in an undisturbed lrregular wave field (i.e. in the absence of a structure to cause diffraction) have appeared in several publications. Longuet-Kggms (1 963) obtained the solution for second-order interactions of short-crested waves in deep water. Hudspeth (1975) and Sharma and Dean (1979) extended the theory to water of finite depth. Bowers (1 976) obtained the low-frequency component of this solution in long-crested waves. Kim and Yue (199 1) and other authors have subsequently used these solutions to represent the second-order incident wave when solving the second-order diffracted wave problem. Forristall's (1985) paper reproduces the Sharma and Dean solution in a convenient and readily accessible form, but seems to contain misprints. Because of the likelihood of errors in these fairly complicated analytical expressions, caution is advised before using published solutions.

It is noted that several related or alternative formulations exist. Power series expansions using parameters other than wave steepness (e.g. similar to the steady-state cnoidal wave) may be more appropriate than the Stokes solution in shallow water (see Dean and Dalrymple, 1984) Dogliani and Cazzulo (1992) describe a formulation of the second-order irregular wave problem involving a solution of the Korteweg de Vries equation. Fully non- linear, numerical models are now being developed as the basis for representing a numerical wave tank, analogous to the laboratory wave basin. Examples may be found in papers by Chan and Calisal(1993) and by Skourup et al. (1992).

Statistics of first-order processes, includmg the surface elevation, wave forces and structure response, are usually described by means of Gaussian probability distributions. The various frequency components in a linear model do not interact, and their phases are randomly related. The resulting Gaussian distribution then has the characteristics that its mean value and skewness are zero, and the distribution is symmetric. Second-order interactions cause the phases of the various second-order components to be inter-related; the probability distribution is then asymmetric with non-zero mean and skewness. Longuet-Higgins (1 963) derived an expression for the skewness of the distribution of deepwater second-order random waves, and showed that t h s could be used in conjunction with a Gram-Charlier type series to estimate the probability density function of surface elevation. Bitner (1980) demonstrated important non-linear effects in the statistics of shallow-water waves, and found that a Gram-Charlier series with terms up to fourth-order moments agreed well with measured data. Langley (1987) presented an alternative formulation based on a Kac-Siegert type of model. Numerous other papers have appeared in recent years describing the statistics of second-order processes, often based on Gram-Charlier or Kac-Siegert type models. Naess (e.g. 1986, 1992) has published a notable series of such papers, using a variety of methods.

Dalzell (1986) derived formulae for statistical parameters describing quite general second-order processes in short-crested random seas, expressed in terms of their quadratic transfer functions and the wave spectral density. These expressions include the mean response, whlch has a particularly simple form, and higher order moments of the spectrum.

Low frequency interactions Moored vessels have long been known to experience long-penod surge, sway and yaw motions. Hsu and Blenkarn (1 970) and Remery and Hermans (1 97 1) found remarkably good correlation between predictions based on a simplified second-order theory and model test data, confirming that second-order processes are an important source of low-frequency motion, see Section 3.7. Later work by Pinkster and others showed that second-order forces could often be predicted quite well by a suitable second-order extension of three-dimensional wave diffraction theory.

DBerence frequency components arise from interactions between every pair of frequencies present in the wave spectrum. If the wave is represented as a s& of components at discrete frequency mtervals 6f; then the frequency resolutions of the second-order wave and force spectra are the same. Care is needed if the natural frequency of the structuref, and its damping ratio 5 are very low, in order to ensure that the frequency resolution is fine enough

2-62 Floating structures: a guide for design and analys~s

to represent the very narrow-banded and peaky response spectrum adequately. Dacunha et al. (1981) recommended, as a minimum, that the frequency resolution should satisfjr the criterion:

in order to obtain a stable estimate of the standard deviation of response. An even finer frequency resolution, or an equivalently longer simulation period with a non-repeating wave sequence, may be required in order to obtain stable estimates of extreme responses (see discussion by Standing, 1991).

As noted in the previous section, there is an important distinction between modifications to kinematics and hence forces arising from second-order interactions w i t h the wave field and second-order forces caused directly by products of first-order quantities. The analysis of a conventional spread mooring or station-keeping system generally requires only the surge, sway and yaw components of the second-order force and moment. These components can often be calculated quite well using the first-order product terms only. Second-order wave interactions do not contribute at all to the mean horizontal forces, and are small at low wave difference fi-equencies. Thls means that if the natural frequencies of the moored system are low, and the water is deep, then second-order wave interactions can generally be ignored. Thls is fortunate because:

relatively few wave diffraction computer programs take adequate account of the second-order interaction process, and relatively few laboratory wave basins take precautions to represent the second-order interaction process correctly.

It may nonetheless be prudent to consider second-order wave interactions when evaluating low-frequency surge, sway and yaw forces, moments and motions in the following circumstances:

when the water is of fairly shallow depth, especially in relation to the vessel's draught, rn and, at the same time, the natural period of the moored structure is relatively short.

It is d~Ecult to gwe precise guidance on when these circumstances are likely to arise. Bowers's (1 976) simplified theory showed that the low-frequency force on a moored s h p in head waves involved a term proportional to (1 - Dld), where D is the vessel's draught and d is the water depth. The second term represents the second-order wave interaction process, whch is important only if Dld is of order 1.

Systematic calculations by Kim and Yue (1991) on a vertical cylinder of diameter 15 m, draught D = 60 m, in water of depth d = 120 m, using a Pierson-Moskowitz spectrum with significant wave height H, = 6 m and mean period T, = 8 s, indicated that the horizontal drift force spectrum became sensitive to the manner in which the second-order wave interaction process was represented when the wave difference frequency (or the frequency of any resonant motion excited by it) was hlgher than about 0 1 rad/s, or 0.0 1 6 Hz (i. e. T < 1 min) . The second-order wave interaction process seemed to be insignificant, however, at lower difference frequencies

Kun and Yue found, moreover, that second-order wave interaction terms were important at all frequencies when determining low-frequency vertical motions. Such might be true, for example, of the low-frequency heave, roll and pitch of a very large semi-submersible or deep-draught floater. In such circumstances care should be taken over the way in whichthe second-order wave interaction process is represented.

Hydrauhcs laboratones have shown part~cular concern about modellmg second-order waves correctly in shallow- water conhtions. The second-order, low-frequency wave is often known as wave set-down. because it represents a depression m the water surface m a regon of hlgh wave activity, and a relatlve raising of the surface m a regon of low wave activity The set-down wave tends to travel with the first-order wave group pattern Wavemakers m model basms are designed to simulate the first-order wave spectrum correctly. but usually make no attempt to represent second-order effects As noted by Bowers (1976), the fluld partlcle motions at the wavemaker do not represent the second-order boundary conditions correctly. and the consequence is that the wave pattern contains not only second-order Interaction waves, whlch are naturally bound to the first-order wave pattern, but also

The envtronrnent 2-63

spurious free waves at the same low frequencies. These spurious free waves travel more quickly than the bound wave pattern, and may either increase or decrease the low-6equency force acting on a model installed in the basin. Bowers (1993) cited an example where the motions of a moored ship were overestimated by 40% when no correction signal was applied to the wave paddle in order to remove the spurious free waves. Recent research has shown that, in both long-crested waves (Bowers, 1980; Barthel et al. 1983) and short-crested waves (Bowers, 1993), it is practical to provide an additional low-frequency signal to the wavemaker, which exactly cancels the spurious fie wave, leaving the correct second-order set-down wave only. These precautions are often necessary in shallow-water conditions, but are not generally considered worthwhile in deep-water conditions, where the second-order wave interaction process is less important.

The discussion above suggests, however, that precautions may be necessary when modelling low-frequency heave and pitch motions of very large semi-submersibles, even in deep-water conditions.

Bowers (1976) noted that in many harbour models the wave paddle is placed in water which is much deeper than that at the harbour jetty. This has the effect of reducing the error caused by the spurious free wave component, because the bound second-order component increases in proportion to (lld)" as the waves propagate into shallow water, where n is near or greater than 1.

Wave set-down has also been put forward as the cause of a low-frequency wave phenomenon known as surf beats, which can be trapped by the coastline in the form of edge waves. Surf beats have been explained in terms of reflection of the set-down wave from a beach (Longuet-Higgins and Stewart, 1964), and are also implicated in cases of harbour resonance (Bowers, 1993). Harbour resonance can cause a vessel moored inside a harbour to experience large low-frequency resonant motions when its natural surge, sway or yaw frequency happens to be close to one of the natural seiche frequencies of the harbour itself. Similar phenomena may occur, intentionally or otherwise, at beaches in laboratory wave basins.

High frequenq interactions Second-order, high-frequency effects are likely to be of engineering significance in circumstances where the structure has a natural frequency above the range of the wave spectrum. This is true for example of the vertical heave, roll and pitch motions of a tethered TLP, or the longitudinal flexing motions of a large ship. Both phenomena are known as springing, and the mechanisms will be discussed in later chapters of this book. Jensen and Pedersen (1 979) found that up to 30% of the maximum longtuhal bending moment in a large container ship came from second-order, sum-frequency forces.

As with the corresponding low-frequency motions, a distinction needs to be drawn between the second-order, sum-frequency forces which arise directly as a result of interactions between first-order quantities acting on the structure, and second-order interactions w i t h the wave field itself. Second-order wave interaction, a major contribution to the vertical force on a TLP, come from a deeply-penetrating and slowly-attenuating component of the second-order pressure, acting on the lower surfaces of the TLP columns. This mechanism involves interactions between the incident and reflected waves, which cause a partial standing wave pattern. The process is analogous to that described by Longuet-Higgins (1 950) as a possible cause of so-called microseisms in deep water. Such forces are likely to be most significant in situations where:

the diameter of the TLP column is large enough in relation to the wave length to cause significant wave diffraction, the draught of the TLP is large enough in relation to the wave length so that the resulting second- order force is significant in relation to the more rapidly attenuated first-order pressure.

Recent studies (e.g. Kim and Yue, 1991; Chen et al., 1991) showed that this particular second-order mechanism can make a major contribution to TLP tether loads, and that interactions between the diffracted wave patterns caused by the TLP legs are of major importance. Few existing wave diffraction programs have the capability to calculate these forces adequately, although possible approximate calculation procedures are under development (e.g. Newman, 1990; Chen et al., 1991).

2-64 Floating structures: a guide for design and analys~s

2.8 Extreme value analysis

2.8.1 Exceedence statistics

The calculation of extreme values of the various environmental parameters which are important to the design of structures is one of the most important problems in applied climatology. Extreme value analysis was first forrnalised by Fisher and Tippet (1 928) and greatly elaborated by Gumbel(195 8), although it is only much more recently that the particular problems of offshore engineering have been addressed.

The major problem with any extreme value analysis is the quantity and type of data available. Theoretically any meteorological or oceanographic variable can be measured continuously over a long time period thus making it possible to identi@ the maximum (and minimum) occurrences of the variable. The values of the parameter arranged in a standard way represent what is called the parent distribution of the variable and typically samples are taken from the parent distribution (e.g. all values measured in one year) and the maxima from each sample extracted. If only one value per year is to be used and some minimum number of data points is specified for the extreme value analysis (e.g. 10) then it immediately becomes apparent that data measurement must be started many years in advance of the date when the design criterion based on the data is required. In the vast majority of cases thls time penalty is unacceptable making it necessary to use proxy data, hindcast data or to use a method of defining criteria whch is not classical extreme value analysis. In many cases, when data is unsuitable for extreme value analysis, extrapolation is used in which case a statistical distribution function is fitted to the data and the curve representing the function is extrapolated to a point corresponding to a small probability of exceedence where a value for the parameter is defined.

The measurement of wave height is designed to supply sufficient information for spectral analysis using Fast Fourier Transform (FFT) so that wave height data is often sampled at half second intervals 2" times (totalling 17 minutes 4 seconds) every 3 hours. This enables values of the spectral moments to be estimated from whch can be calculated various wave height and period parameters including significant wave height and zero up- crossing period (see Section 2.7.3). However this process does not allow the maximum individual wave height in the three hour sea state to be identified and such waves are normally estimated using statistical relationships commonly based on the Rayleigh distribution. This predicts a most probable maximum value of 1.86 times sipficant however, the maximum individual wave height in a three hour sea state is typically found to be a little less e.g. 1.7 times the sigmficant wave height associated with the sea state.

Wind speed is normally measured continuously although observations may be recorded only once every one, three or six hours. Modem instruments can calculate maximum p s t s of various durations but generally the gust values associated with a particular wind speed averaged over one hour or 10 minutes are estimated using empirical formulae.

Current velocity is the vector addtion of a number of independent effects such as tides, wind drift, ocean currents etc. and it is normal practice to separate the total current velocity into tidal components and residuals since tidal components are not random and may be predicted deterministically.

Extreme values may be derived either by analysis using extremal distribution functions fitted to distributions of maxima obtained from independent, identically distributed samples of the parent distribution or by extrapolation of dstribution functions fitted to the cumulative frequency distributions of the data. Independent and identically distributed implies that data should all be derived from the same population whch means not mixing hurricane generated winds and other winds for example. It also means that months or seasons should be analysed separately and that sequential storm events should be independent. Outliers should not be discarded without good reason.

2.8.2 Distribution types

With both extreme value analysis and extrapolation it is necessary to model the variation in the data using a mathematical function. Standard functions are familiar to other workers, behave in a predictable way and have

The environment 2-65

\veil know properties. I f X is any random variable (e.g. the wind speed measured at a particular place), then for ;~1\, real number x and the event 'Xtakes a value less than x' there exists a probability P(X5x) of that event which is hefined on the interval [0 ... 11. The probability P(X<x) is obtained from the (cumulative) distribution function of X denoted by F(x). In the context of extreme value analysis and extrapolation the random variables and corresponhg distribution functions are generally continuous in which case differentiating F(x) will result in the probability density function denoted byxx).

The theory of extreme values has established that for sufficiently large parent sample size there exists only three possible extremal distribution functions which are shown below.

The Gurnbel or Fisher-Tippett type 1 distribution:

The Frechet or Fisher-Tippett type 2 distribution:

The Fisher-Tippett type 3 distribution:

However Jenlunson (1955) showed that these three distributions can be expressed in one generalised form which is commonly called the General Extreme Value (GEV) distribution:

F(x) = 0 x < a + b l c : c < O = exp[ -[I -c(x -a)/b] "'1 (2.70) = 1 x > a + b / c , c > O

Another distribution which is in common use is the Weibull distribution (Weibull, 195 1):

The Weibull distribution has a number of different forms such as 2 parameter Weibull distribution (a = O), Rayleigh distribution (a = 0, c = 2) and exponential distribution (a = 0, c = 1). Figure 2.17 shows some example distributions. Other distributions may be useful in certain applications but space does not permit a complete dmxxion here. A more complete catalogue of distributions and attributes may be found in Carter et al. (1986).

The domain of attraction of an extreme value distiibution is the set of all parent distributions which have that extreme value mstribution as their limiting type. In general it has been found that most of the distributions used in the analysis of winds, waves etc. come w i h the domain of attraction of the FT- 1 distribution. However if the GEV is used the problem of decidmg which distribution to use disappears. Considering the FT- 1 alone the term:

2-66 Floattng structures: a gu~de for des~gn and analys~s

is called the 'reduced variate' (where reduced is a mistranslation of the French word for standardised). Here a is called the mode and b is called the dispersion of the extreme value distribution which correspond to the mean and standard deviation of the parent distribution.

Cvmulotive p robob~ l i i y

0

Cumulotive probability

X

Figure 2.1 7 Fisher-Tippett and Weibull extreke value distributions

The environment 2-67

2.8.3 Design criteria

A brief overview of the fitting and extrapolation techniques commonly used to obtain design criteria from data follows.

The data available are usually frequency distributions of wind speed and wave height derived from:

visual observations (see Section 2.4.2), . computer models (see Section 2.4.3) also called hindcast data.

Visual observations are normally made from a moving platform (e.g. a ship) preferably every six hours although often the time interval is longer, and in any one area the interval between observations may be many days. Consequently the data will not contain a number of maxima and is not suitable for extreme value analysis. Weather forecast data may be for fixed locations and is continuous albeit with rather long time intervals (3,6 or 12 hours) between values so that extreme value analysis is possible with care but extrapolation may be more reliable.

Tow route criteria A typical approach, using visual observations, is to recognise that conditions along the route will change with the seasons and to divide the route into a number of sectors. Statistical distribution functions are fitted to monthly or seasonal data for each sector and design criteria calculated such as the 10-year return value for the worst sector of the route (Lynagh, 1991). An alternative is to consider the risk of exceeding a certain threshold value in each sector and weight the risk associated with each sector according to the expected duration of the voyage in each sector. The weighted risks for all sectors leads to an accumulated risk for the whole route (Van Hoorn, 1991). Methods exist for considering the effects of tropical cyclones (Vermersch, 1990).

The risk of encountering some extreme condition with event duration n and with a return period N in a lifetime L (for L, N )) n) is given by:

The overall risk for a tow route with m segments is the product of individual segment risks:

Location reports In many cases, particularly associated with exploration, reports are required based on minimal or broad scale data. In these cases extrapolation is used because insufficient data exists to conduct extreme value analysis. Examples of some of the techques employed are described in publications available from HSE (OTH 89 299; 1990, OTH 89 300, 1990). Typically methods such as least squares or the method of moments are used to fit distributions to data.

Zn the case of least squares fitting, a cumulative frequency distribution is constructed and probabilities associated with values of the random variable X. As a linear regression model is normally required the distribution function must be linearised (usually by talung logarithms) to define the axes of the regression line. Referring to the version of the Weibull distribution shown above by taking logarithms twice an expression is obtained of the form:

ln(-ln(1 -F(x))) = c ln(x -a) - cln(b) (2.75)

whlch can be plotted as a straight line g~ven suitable axes with slope c and intercept -cln(b).

2-68 Floating structures: a gu~de for des~gn and analysts

The method of moments uses values of mean and standard deviation derived from the data to estimate distribution function parameters. As an example the parameters of the FT- 1 distribution are given by

mean = a+yb (y = Euler 's constant = 0.5772) (2.76)

standard deviation = nb l f i

When mean and standard deviation are known, values for a and b can be estimated. The fit to the data of the chosen distribution function should be checked before using for extrapolation.

To obtain some return period value from the distribution function it is necessary to calculate the probability associated with such a value. Thls may be done by assuming that the extreme event lasts a period of time n (wically 1,3 or 6 hours) and that the extreme event occurs once on average during the return period of N years. Thus the probability associated with the return period value is given by:

To calculate a value x from a FT- 1 distribution requires an expression of the form:

If n=3 and N=50 then x=a+l1.892b. These methods are quite simple to apply and can give good results but it is dangerous to use them in isolation. Checks should always be made of the quality of fit of the distribution function to the data and they should not be used for estimation of very long return period extremes. A method similar to this has recently been used with satellite data to give preliminary estimates of 50-year extremes of sigmficant wave height over the northeast Atlantic Ocean (Carter, 1993).

Design values Extreme value analysis (ie. analysis of maxima ffom a parent distribution) is normally preferable to extrapolation of a function fitted to a limited sample data but in many cases insufficient data exist for extreme value analysis. Research has been conducted to increase the quantity of information which can be extracted from the parent distribution such as analysis of monthly rather than annual maxima (Carter and Challenor, 1979) or the analysis ofmaxima fiom indwidual storms (Cook, 1982). Reviews of methods available have been published (Muir and El-Shaarawi, 1986; Farago and Katz, 1990) and the special problems associated with hindcast data have been considered (Canadian Climate Centre, 199 1 ; Peters et al.; 1993).

If an initial assessment of extreme values is required it may be advantageous to plot the data on Gumbel probability paper where the vertical axis corresponds to -In(-Mp)) so that extreme values fitted by a Gumbel hstribution will lie on a straight line. The mode and dispersion of the Gumbel distribution can be calculated by measuring the line. However if the data is fitted by a FT-2 distribution the data will be better fitted by a line curving downwards and if it is fitted by a FT-3 mstribution the data will be better fitted by a line curving upwards. The coordmates of the points to be depicted on the Gumbel probability paper are ( X , p ) , j = 1,2, ... m where the

! . J X, are the observed maxima ranked in ascending order and the p, represent the empmcal estimates of the values of their distribution function. These plotting positions are often defined in different ways but it is important to define them correctly so that goodness of fit tests are accurate (Carter & Challenor, 1983). The formula given by (Gnngorten, 1963) is:

The env~ronment 2-69

If using a computer to carry out the extreme value analysis then it is recommended that maximum likelihood methods are used to define the parameters of the GEV distribution and methods of estimation are given in the Flood Studies Report (NERC, 1975). Software is available. Another method is given by Hosking et al. (1 984).

The goodness of the fit of the distribution to the data should always be checked if only by visual inspection of a plot of the data and distribution. Normally the GEV distribution will fit the data adequately and the purpose of goodness of fit tests may be to ascertain whether the FT- 1 will suffice. These tests are described by Farago and Katz (1990) while others are reviewed by Muir and El-Shaarawi (1986).

2.8.4 Design wave height and period

The methods of extreme value analysis and extrapolation, described above, applied to significant wave height will yeld estimates of extreme sigTllficant wave height. The normal requirement is to associate a wave period or range of wave periods to the extreme sigmficant wave height to define extreme sea states and to calculate the maximum individual wave height and associated period, given that the extreme sea state persists for a number of hours (normally taken as 3 or 6). Given that floating structures may be particularly susceptible to wave energy at a particular eequency, design criteria should specify wave height and period pairs over the whole range of period hkely to be experienced at a particular location. Such information will normally be calculated from data measured at the location or modelled using a computer model of wave generation.

In the absence of such data, or as a means of checking it when it exists, a number of relationships between wave height and period have been developed. Wave steepness is defined as a wave height parameter divided by a wave length parameter and wave length can be calculated in deep water as 1.56(TJ2 where T, is the zero up-crossing wave period (also denoted by T,,,). The spectral peak period Tp is the inverse of the frequency of the peak of the wave energy spectrum (assuming a single peaked spectrum). The relationship between T, and Tp (for theoretical spectra) is not constant being 1 : 1.286 for the mean JONSWAP spectrum and 1 : 1.4 1 for the Pierson-Moskowitz spectrum.

The report of committee I. 1 (ISSC, 1979) proposed a range of Tp as:

but emphasised that the recommendation was not based on oceanographic criteria alone. This range is still used Gequently today for tow route criteria.

Values of sigmficant steepness in deep water are given by:

For wind driven seas this parameter has a practical lower limit of about 1/20 (e.g. for a Pierson-Moskowitz spectrum it has the value 1 h9.7). For fixed structures a range of sipficant steepness of 11 1 6 to 1 /20 is suggested for U.K. waters (HSE, 1995). However when swell waves form a significant part of the design storm wave energy then lower steepnesses are possible. For very short fetches (down to 10 km) it is demonstrated (Carter et a1.,1986) that significant steepnesses to about 1/11 are possible and an effective upper limit is normally taken as 111 0.

Having decided on extreme sigmficant wave heights and periods it is possible to estimate extreme individual wave heights and associated periods. Maximum individual wave height is often calculated as 1.86H, although a wider range such as 1.7H,.< H,, < 1.9H, may be considered. The ratio H,JH, = 1.86 is based on the assumption that the Qstribution of individual waves in a sea state (lasting 3 hours with 1000 waves) may be fitted by a Rayleigh Qstribution. In most real sea states the ratio is reduced due to the imperfect correlation between wave crests and

2-70 Floating structures. a guide for design and analysis

wave troughs (i.e. the highest crest is rarely followed by the lowest trough). The reduction in the ratio has been found by many experimenters to be about 10% so that a good estimate of H,,,, in a constant sea state (lasting 3 hours with 1000 waves) is 1.68 H,. However an extreme indwidual wave height with a return period of 50 or 100 years whlch is to be used for design may occur in a sea state which has a lesser return period. Investigators have shown that taking account of this aspect results coincidentally in a ratio of 1.86: 1 for extreme individual wave height (or design wave height) : extreme significant wave height (OTH 89 300, 1990). In shallow water the familiar relationships tend to change. The relationshp between H,,,, and H, in shallow water can be estimated using models due to Glukhovskiy (Bouws, 1979).

The period range associated with the maximum individual wave height is recommended (ISSC, 1979) as:

again this range is not based on oceanographical considerations alone.

2.8.5 Design wave profile

Unlike the real ocean, regular wave theories assume that waves are periodic and uniform with common period and height. Some of the wave theories commonly used in offshore design are linear or Airy wave theory, Stokes fifth order wave theory and Deans stream function wave theory. Figure 2.18 indicates the regons of applicability of wave theories dependent on water depth and wave steepness. Figure 2.19 illustrates the variation in crest elevation whlch is predicted by the various theories as wave period, steepness and water depth change. Wave theories are also discussed in Annex 3A of this volume and in many other books (e.g. Section 6.7: Barltrop and Adarns, 1 99 1). Chakrabarti (1987) discusses the simulation of wave profile from wave energy spectra.

Deep water breoking l imit

Shollow woter

or streom

funct ion 3

St ream funct ion

Linear/A~ry or

stream funct ion

0 0001

0 00005

0.001 0.002 0.005 0.01 0.02 0.05 0 1 0.2

G L - I

Woves: Shallow water lntermedioie depth Deep water

The boundaries given are approximate and depend on the purpose o f the onolysis being per formed

I t is accepted thot re f rac t ion and d~ f f r oc t i on ana lys~s will usually be based on linear theory

Figure 2.1 8 Regular wave theory selection diagram: log scale (Barltrop et at., 1990)

The environment 2-71

Deep woter breokir ig 11rr11t H /L=0 .14

Shallow water breokiny limit ~ / d = 0 . 7 8

4 Y '

k -- Woves: Shallow water In te rmed ia te dep th Deep water

Figure 2.1 9 Ratio of crest height above mean water level to wave height (Barltrop et al., 1990)

2.8.6 Design sea state

The statistical properties of random waves in a sea may be assumed to be approximately constant for short periods (e.g. one to three hours). During thls time the 'sea state' which exists may be modelled by a frequency spectrum of water surface elevation which may include information by direction. A spectrum may be defined by sigmficant wave height and zero up-crossing wave period (Sections 2.7.3 and Barltrop et al., 1990: Section 6.5). The long term chstribution of sea states may be represented by a scatter diagram inchcating the relative frequency of various combinations of height and period. Measured spectra often exhibit complex shapes which may include more than one peak. Theoretical spectra are inevitably simpler although a bi-modal model does exist.

Commonly used spectra include the Pierson-Moskowitz spectral form:

and the JONSWAP spectral form:

Mathematical spectrum models are reviewed in Section 2.7.5 and by Chakrabarti (1987).

2-72 Floattng structures: a guide for design and analys~s

2.8.7 Breaking waves

For a given water depth and wave period there is an upper limit to wave height at which the wave becomes too steep and breaks. The Stokes criterion for wave breaking is that the water particle velocity at the crest equals the speed at which the wave is moving forward. In deep water the theoretical limiting wave steepness is 117 but in practice 1/10 is observed. In shallow water regular waves have a limiting height of approximately 0.78 times the water depth over a level sea bed but considerably higher than this over a sloping sea bed. Breaking waves are of great importance near beaches and for coastal engineering design but information for use in offshore locations is scarce. Most of the research into breaking waves is confined to wave tanks and it is not clear that breaking waves in deep water caused by winds, currents and wave-wave interaction have the same lnematic properties as waves breaking due to shallow water. There are reviews of the problems involved in publications such as Barltrop et al. (1990); ISSC (1988); Torurn and Gudmestad (1990) and Easson (1997).

2.8.8 Large waves

Large waves are often referred to as 'freak' waves which implies that no explanation can exist. However although explanations for such waves may not be readily available this has more to do with lack of information. Large or freak waves are so defined lf they exceed twice the sigmficant wave height in a sea state. In fact individual waves exceeding 2.5 times the sipficant wave height have been measured as reported by Sand et al. (1990). Large waves are llkely to be caused by: topography (refraction, diffraction, reflection); wave-current interaction (see Section 2.7.6); interaction between weather systems; combinations of wind-sea and swell; and turning wind fields. Additionally the highest wave in a sea state is a variable that can only be described statistically. This is because it depends on the superposition of waves arriving from different directions and waves of different frequencies. Therefore unusually high waves should be occasionally expected.

2.9 Down-time and operability analysis

Down-time and operability analysis is the estimation of lost working time (down-time) or probabilities of occurrence of weather windows for given operations. Such information is important for assessing the economic viability of a system at the design stage as well as for operational planning when in service.

For many purposes it is most convenient to use 'persistence statistics', which are derived from time hstory records. For other purposes it is necessary to retain the time domain format. Ideally measured time histories should be the preferred source, for both forms of data, but because of the limited availability and high cost of the long runs of record needed, methods have been developed for synthesising both frequency and time domain data from available information.

A brief review of data formats and methods of synthesis is gven below. A fuller account of such methods and their application may be found in Standing (1989)

2.9.1 Persistence analysis

Persistence analysis is concerned with the durations for which specified conditions prevail. A common requirement is for data defining frequency distributions of durations for whch the severity of conditions remain above (persistence of storms) or below (persistence of calms) specified threshold levels. In Figures 2.20 and 2.2 1, sipficant wave height is the index of severity, but the concepts are the same for wind speed or other severity parameters. Figure 2.20 shows a short sample of a wave height time hlstory to illustrate the definition of the relevant durations. Shown are the durations in hours above and below the two threshold levels: H, = 1 m and H, = 2 m. Those above are storm durations and those below are calm durations. Durations of storms are usually denoted by z, (g denotes greater than) and durations of calms by t, ( I denotes less than).

The env~ronment 2-73

I I I I I I I 0 1 2 24 36 4 8 60 72

t (hour)

Figure 2.20 Definition of durations of storms and calms (after Hogben, 1990-a)

Persistence of storm:; -winter

1 5 10 50 100 300

Duration in hours

Figure 2.21 Sample data presentation (after Fortnum and Tann, 1 977)

A widely used form of data presentation is illustrated for persistence of storms in Figure 2.2 1. It may be seen that there is a set of seven curves corresponding to seven threshold levels of H, as marked. Each curve defines the exceedance frequencies for a population of durations T , as defined above, expressed as numbers of occurrences in a gven total time span often of several years (in thls case an average winter from six years of data). Persistence of calms may be similarly presented as exceedance frequencies oft,.

An alternative convention sometimes used is to express the exceedance as a percentage of the total time span rather than as numbers of occurrences.

In interpreting persistence data such as the curves in Figure 2.2 1, it is important to appreciate that conventionally the counts of short durations do not include the sequential occurrences combining to form longer durations. Thus counts of 3 hour duration do not, for instance. include the groups of 4 x 3 hours intervals combining to form the 1 2 hour durations.

It should be noted that the persistence statistics defined here and in the following sections may not be of direct help if operability and down-time are to be estimated for specific operations which contain tasks with different

2-74 Floating structures: a guide for design and analysts

weather restraints. In such cases it is necessary to simulate the operations with realistic weather time histories (see Sections 2.9.2 and 2.9.5).

2.9.2 Use of measured time histories

As noted earlier, time hstories may in some cases be needed for use in their origmal time domain format. Such cases would include, for example, analysis of down-time or operability involving criteria dependent on more than one parameter when it may be necessary to employ hour by hour Monte Carlo type computation (Standing, 1989). For most purposes, however, it is preferable to use data transformed into the frequency domain format known as persistence statistics described in 2.9.1 above.

In either case, measured time histories which are to be used for persistence analysis must cover long time spans, ideally without interruptions (which can distort the duration sequence). In practice, unfortunately, measured time histories covering sufficiently long periods (usually a year or more) are not very widely available. Those that do exist, moreover, tend to contain a considerable number of gaps. This means that when processing measured records for use in persistence analysis, the first stage must be to locate and fill the gaps.

Three possible procedures for filling gaps have been compared by Kuwashima and Hogben (1986) and found to yield similar satisfactory results. Figure 2.22 illustrates one of these which involves folding of real data from either side of the gap to meet in the middle as indicated by the arrows.

I Doto r e c o r d 1 % / inf i l led. 1 w i t h I with

befor-e o f te r

Real data r e c o r d --. 1 a 1 -&%- 1 - Real d o t o record

Figure 2.22 Infilling gaps in measured time histories: folding method (Kuwashima and Hogben. 1986)

When all the gaps have been filled, measured records can be used for deriving frequency domain persistence statistics such as those described in Section 2.9.1. The first step is to count all the durations for each chosen threshold level into populations of T, (or t, ) values as defined above. The respective curves of exceedance frequency for these populations which comprise the persistence statistics can then be computed in the usual way.

The env~ronment 2-75

Figure 2.23 Synthesis of persistence data: illustrative diagram (Hogben, 1990a)

2.9.3 Synthesis of persistence statistics

Because of the relative scarcity of suitable measured time hstories noted in the previous section, and the high cost of acquiring and processing such data, methods have been developed for synthesising persistence statistics using more readily available source data. The basis of two such methods, due to Graham, C. (1982) and Kuwashima and Hogben (1 986), are briefly outlined here. Fuller accounts may be found in the references.

In principle these methods are applicable to data for any severity parameter and the references describe development and validation of procedures for synthesis of wind speed as well as wave height persistence. For simplicity, however, the explanation given here will refer only to wave height.

For thls case both methods use exceedance probability Qstributions Q(HJ of significant height as the source data. These are widely available, and the Kuwashima and Hogben analysis has been shown (Hogben and Dacunha, 1985) to gve reasonably reliable results using data from the global archives of visual observations described in Section 2.4.2. Also, in both cases it is assumed that the persistence curves to be derived (see Figure 2.21) can, as illustrated in Figure 2.23, be expressed in the form of two parameter Weibull distributions :

Q(T) = exp[-c(t/ 7 )"I (2.85)

where t may correspond to t, (duration of storms) or T, (duration of calms) as defined in Section 2.9.1. The synthesis procedure thus requires determination of the three parameters 7, c and a (7 is a mean duration serving as a norrnalising factor and c and a are the two Weibull parameters) by reference to a given curve Q(H, ) of height esceedance.

2.9.4 Synthesis of long weather time histories

It has been explained in Section 2.9.2 that down-time or operability analysis may sometimes need to be undertaken in the time domain using time h s t o ~ y data. Since, as also noted, measured time history data are costly and relatively scarce; methods have been developed for synthesising them from more accessible sources. Three such methods are now briefly reviewed: and references to fuller accounts cited.

Markov process modelling The Markov process is a well established concept in statistics (see for example Box and Jenkins, 1970). It may be defined as a class of time series in which the value of a variable at any one of a sequence of time steps determines the probability of transition to the next value. Thus, given an initial value and a suitable matrix of transition probabilities, a continuing sequence of values compliant with this definition can be generated. This approach to modelling of weather time hstories has been used by Springett and Abramowch (1 977) and Standing (1 989), and the following brief description is based on the latter.

2-76 Float~ng structures a gu~de for des~gn and analys~s

Assuming the weather variable to be significant height H,, the source data used are probability distributions for H, in the form of probability densities p (or probabilities of exceedance or non-exceedance, Q or P respectively, which are derivable fiomp), accompanied by persistence statistics for storms and calms for a sequence of height thresholds H,.

Since the persistence statistics can, as described in the previous section, be synthesised from Q, it is possible to apply h s method using only exceedance probabilities which, as noted earlier, are widely available as the source data.

Startingnow with an initial H, in the height class H,., to H,, the transition probabilities that the class of the next height will be above, the same or below are written as a,, b, and c, respectively, and when these are known an indefinitely continuing series can be generated. Since a, + b, + c, = 1, it is in fact only necessary to determine a, and c, whch may be computed from relations defining the number of crossings of the threshold H,, thus for a long record:

upcrossings = a m p m = downcrossings = em+, pm+, = Nm (2.86)

where:

P,, probability that Hm-, < H, I H, N number of durations for storms or calms as defined in Section 2.9.3 for the threshold height H,.

Hence:

a, = Nm /Pm

and N, (or N,-,) may be derived either directly Gom persistence curves as the number of occurrences exceeding the shortest duration or computed using the method cited in the previous section from :

(assuming unit time steps):

where: P, probability of exceeding H, - z, mean storm duration for the threshold H,

L

Auto-regressive moving average (ARMA) modelling Llke the Markov process, ARMA modelling is a well established statistical concept (Box and Jenkins, 1970) In

%

~ t s most general form it defines a variable z, (with zero mean) as a functlon of a series of earlier values at time a;

d steps (t-n) using a combinahon of an auto-regressive process of order p, AR(p) and a movlng average process of order q, M(q) whlch may be written as: -4

9 k

where: a, and Y, are constants to be determined, and a, is a white noise process.

O'Carroll(1984) has used auto-regressivemodell~ng of weather records for analysis of offshore operations. Much $ of the computation described in the reference is concerned mth normalisatlon to remove seasonal bias which need not be d~scussed here For the auto-regressive modelling he used a process of order 1. AR(1) requmng ?;

The env~ronment 2-77

determination only of the coefficient 0, which he estimated from analysis of measured time history records. The formula for computing 0, from a given record z, is :

where E denotes expected or average value of the product in brackets taken over the complete record.

Thls formula may be derived from the earlier equation for z, in the case p = 1, q = 0 noting that since a, is white noise, E [ z,, a, ] 0.

For higher orders (p > I), the earlier equation yields a set of p linear equations for 0, which can be solved by matrix inversion (Box and Jenkins, 1970). A disadvantage of ARMA modelling for the present purpose is the requirement for measured time histories for determining the coefficients. Also it is not specifically aimed at matchmg given persistence data.

Building brick method Unlke the previous two models, the building brick method is not a well established statistical procedure. It was developed by Hogben and Standing (1987) specifically for use in offshore operational analysis, and a krther account of its application in comparison with other methods is given by Standing (1 989). Like the Markov method it uses persistence frequency statistics as the source data which, as explained in Section 2.9.3, can be synthesised from wave height probability distributions which are very widely available.

Population of durations H,=8n1 r = 1 , 1

6m I = 7 , 7 . 6 4rn I - = 3 2 , 3 , 1 2m r = f i 7 , 1 3 , 1 1 . 1

67 1 1 L I I I I I I I I I I

10 20 30 40 50 60 70 80 90 100

3 haul ~n tervn ls

Figure 2.24 Synthesis of time histories: Building Brick Method (Hogben and Standing, 1987)

In concept it is a procedure for constructing a time sequence for whch derived persistence statistics will match the Bven data. The first step is to translate each persistence c w e which may be denoted by the exceedance probability Qm (t 2 t,) for the threshold height Hm into a frequency distribution nm(rr) of individual durations t,.. This may be done using the finite differencing process defined by :

The second stage is illustrated by Figure 2.24 in which the relevant durations for a short sample sequence are identified by heavy horizontal lines. It involves arranging the durations in their respective layers by a process whlch may be llkened to the buildmg of a brick wall using members of the populations n,(r,) as bricks. There are only three rules of construction :

The bricks in the first layer are arranged at random along the total time base.

The bricks in succeeding layers are arranged at random subject to the condition that each must rest on a brick of the previous layer without any overhang.

As far as possible, all bricks should be used as this will ensure that the given persistence statistics are identically matched.

2-78 Floating structures: a guide for design and analysis

The third stage is then to simulate the required time history curve in such as way as to pass through all brick comers without any intermediate threshold crossing as shown in the figure. In this final stage there is scope for introducing piece-wise use of Markov or ARMA modelling.

Choice of method Regarding choice of method, this will, in practice, depend on many factors including data availability, reliability requirements and cost. Reference may be made to Standing (1 98 9) for comparative assessments of the Markov and buildmg brick methods. Broadly it may be said that the Markov method is particularly well suited for generating relatively long sequences when it is much more economical to run, and offers good matching of gwen source data.

For shorter runs the building brick method offers better matching of given persistence statistics and, though less economical to run, may sometimes be preferred. ARMA methods are also economical for long runs once the relevant coefficients have been determined, but are not specifically aimed at matching given persistence data. A &sadvantage is that the source data are measured time histories which are relatively scarce and costly.

2.9.5 Operational simulation techniques

Operational simulation means the simulation of a complete operation or activity, as opposed to the simulation of, for example, the dynamic responses of a floating system in waves. The latter may form the basis of one aspect of the operation and may be crucial to the determination of the weather limits on the activity, but this weather limit will normally need to be derived before the operational simulation is performed. Figure 2.25 shows the relationship between operational simulation and hydrodynamic simulation for a tanker off-loading system.

The motive behmd such simulation may be simply to determine the extent of any weather down-time, or it may be to examine the interrelation between the different tasks or activities in order to optirnise the operation (in this context for floating offshore systems, weather will normally be one of the factors to be included). Simulation is often the only practical way of studymg such systems because they are too complex, and have too many non-linear interactions, to make them tractable by purely statistical techniques. Powerful modem personal computers have also made such simulation relatively easy to perform. Rowe and Woodyard (1 993) describe the application of this type of simulation to oil transportation from a floating production system by shuttle tanker, whilst White et al. (1996) describe the application of similar techniques to the simulation of all the weather-dependent activities in an oil production operation.

The objective of the simulation is to generate performance data for a complex system. If one considers, for example, the case of transporting oil to shore by shuttle tanker from a floating production system, then the main components of this system and their properties that influence the performance of the system as a whole are:

Component Main properties

The Floating Production System Oil production rate, Storage capacity (if any), Weather limits on production (if any).

Loading buoy/ tanker mooring. Weather limit for connecting to buoy, Time required to establish oil flow after connection: Loading rate, Weather limit for disconnecting.

Shuttle tanker fleet/ delivery route. Ship product capacity, - Number of ships in fleet,

Transit speed (and dependency on weather conditions): Distance to delivery port.

The environment 2-79

IV'eather (at the FPS or for route) Waves, wind, current and / or other factors which influence the operation, Probability of esceedance of wind speed / wave height etc., Persistence probabilities for storms / calms.

An operational simulation will normally include a mixture of different activity types or tasks. Many of these tasks udl be dependent on the completion of other tasks, and the tasks may each have different weather constraints. For example, loading of oil cannot commence until the shuttle tanker has connected to the loading buoy, and this connection task normally requires better weather than the loading operation itself.

The nature of the weather influence on different tasks is also important, some tasks being capable of suspension lf weather gets worse and continuing as soon as there is a there is an improvement. Other tasks may have to be completely cancelled if weather intervenes and re-started from scratch when there is an improvement (the shuttle tanker connection task is an example of one of these). In some offshore construction and heavy lift activities a long string of tasks may have to be re-started from scratch, or may not be able to start until there is a long forecast penod of good weather. It is also possible to include other deterministic influences or random influences such as the occurrence of mechanical failure. All these influences can be built into a simulation by framing logical rules which determine the progress of the tasks.

Hydrodynamic onolysis/simulot ion

Input Wove, wind, current condi t ions

Output : Vessel mot ions Mooring hawser loods Stot ion-keeping per for rnonce e tc .

Marine experience:

Est imate weather l imi ts for disconnect,' reconnect

1 o r 1 ~ p e r o t i o n 1 o ~ t i o n o l 1 s tat ist ics synt hesis simulat ion s tat is t ics

( t ime domoin)

Figure 2.25 Relationship between operational and hydrodynamic simulation: An example for a tanker off-loading system

It is usually necessary to perform simulations for long periods of time in order to obtain statistically sipficant data on the operation. For a tanker loading operation the simulation may have to run for several decades in order to meet sufficient different weather situations to give an accurate picture of the operational down-time. As noted in Section 2.9.4, it is unusual to find long enough measured records for these simulations, hence the requirement to use the weather time series synthesis techniques outlined in that section. Sometimes hindcast data (see Section 2.4.3) may be available and suitable.

Simulations of b s type are normally performed in the event domain (as opposed to the time-domain commonly used for other non-linear problems). This is because the progress of the activities withm the operation can normally conveniently be described in terms of changes of state or events (an event in this context might be the

2-80 Floating structures. a guide for des~gn and analysis

starting of a particular task, or the occasion that the significant wave height crosses an operating criterion threshold). Performing a simulation by tracking discrete events can be an extremely fast computing process permitting many decades of simulation to be performed in a few minutes on a modest personal computer.

Extensive use has been made of this simulation technique in operational research, and Mitchell (1972) gives a good introduction.

Prior to a simulation, the long weather time history to be used as input (perhaps synthesized using one of the methods described in Sections 2.9.3 or 2.9.4) can be processed to determine the time/date of each occurrence of the crossing of a weather criterion threshold value. The weather time history can then be discarded, just keeping the chronologmd sequence of weather events. The simulation progresses by processing each event and evaluating the consequences of each event according to the rules which have been framed to describe the way in which the operation proceeds (e.g. if the weather has just improved so that a criterion down-crossing event has been processed, then there is probably a task that can start or re-start, or continue).

As the simulation progresses, data is collected on the performance of the operation (e.g. totalling the down-time, accumulating the produced oil, counting the number of shuttle tanker trips etc.). It is the summary of this data which can be examined at the end of the simulation to evaluate the operational performance and to gain an insight into the way the operational tasks interact with the weather and with each other.

Key steps in framing and running any simulation of this type may be sumrnarised as follows:

. Analyse the main activities which go to make up the operation and identify the critical weather influences. Add in any mechanical breakdown issues (e.g. SPM hawser failure), perhaps characterised by a mean time between failure and exponential or normal tlistribution. . Identify the inter-dependencies between the various tasks and activities. Simpli@ the activities and the inter-dependencies as much as possible whilst retaining sufficient realism (it is always better to start with a simple simulation and add greater complexity later if required). Determine what are the key measures of operational performance. This might be the number of barrels of oil shpped, or it might be a number of different revenue and cost drivers which can form the input to a complete economic analysis. . Configure the simulation so that the necessary statistics on these parameters are being collected for examination (and perhaps further processing) at the end of the simulation run. Run the simulation and examine the results for the key operational measures of performance. Try changmg an input parameter and re-running the simulation to see how sensitive the results are to it. Ths enables the realism of the simulation to be probed, and also permits the operation to be optimised. Trade offs between additional capital expenditure or running costs (e.g. more expensive technology to reduce dependence on weather and increase total oil production) can be examined.

2.10 Long term statistics for fatigue analysis

Fatigue is the tendency of structures to suffer structural cracking due to the accumulated damage associated with many stress reversals (see Section 7.2). In the ocean the strongest and most obvious source of stress reversals or cyclic loadmg are the waves, but wind turbulence can add to the slow dnft oscillations of a moored vessel and may also be a problem for superstructure components. Dunng the life of a floating system it will experience an almost infinite number of dfferent wind, wave, and current conditions some severe, some moderate, and some mild. The aggregate effect of all these different conditions, from different directions and with different intensities will be to accumulate fatigue damage, and the designer must ensure that his design will be able to cope with this duty without structural damage or failure during the design life.

Obviously one cannot p r d c t or model in a deterministic manner the entire history of wind and wave action that a vessel is going to experience, so the problem is to define a series of weather conditions that can be used to characterise the large range of Merent condtions that the vessel will experience during its life. A fatigue analysis

The environment 2-81

call then be performed that will calculate and accumulate the fatigue damage associated wlth each of thesc collditions to arrive at the total damage accruing from one typical year of operation, and hence over the design life.

Fatigue analysis can be performed in three main ways normally referred to as the deterministic method, semi- method and the spectral analysis method. The deterministic method is based on an analysis of

individual waves and takes no account of the spread of different periods at which a wave of a given height may occur. It is therefore unsuitable for floating systems where dynamic, and sometimes resonant, response is often an important feature. The semi-probabilistic method is also based on individual waves and, although it deals with a range of wave periods for each wave height, it does not take proper account of the dynamic response of a vessel

I 1. to irregular waves. The spectral method will normally be most appropriate for floating systems and is now

recommended for all structures as standard practice by some authorities (e.g. API RP2A-LRFD, 1993). However, for completeness the environmental input data for each type of analysis are outlined here.

potthurst (1988) gwes a description of fatigue correlation studies performed on semi-submersible platforms using the semi-probabilistic and spectral methods.

Because of their basic similarity, the deterministic and semi-probabilistic methods will be dealt with together.

2.10.1 Deterministic and semi-probabilistic methods

European Database

S i g AREA No 20 Dec - Feb West = 17 69% Obs Hgt 124 347 328 149 42 9 2 0 0 0 01000

(m) - >14 0 0 0 0 0 0 0 0 0 0 0 0

13-14 0 0 0 0 0 0 0 0 0 0 0 0 12-13 0 0 0 0 0 0 0 0 0 0 0 0 11-12 0 0 0 0 0 0 0 0 0 0 0 0 10-11 0 0 0 0 0 0 0 0 0 0 0 1 9-10 0 0 0 0 0 0 0 0 0 0 0 1 8 - 9 0 0 1 1 0 0 0 0 0 0 0 2 7 - 8 0 0 1 1 1 0 0 0 0 0 0 4 6 - 7 0 1 3 3 1 0 0 0 0 0 0 9 5 - 6 0 2 6 6 3 1 0 0 0 0 0 1 8 4 - 5 1 6 1 4 1 1 4 1 0 0 0 0 0 3 8 3 - 4 2 17 32 21 7 2 0 0 0 0 0 81 2 - 3 7 4 8 6 9 3 7 1 1 2 0 0 0 0 0 1 7 5 1- 2 28 124 124 49 11 2 0 0 0 0 0 339 0 - 1 86 146 77 18 3 0 0 0 0 0 0 331 (m)

4- 5 6- 7 8- 9 10-11 12-13 To ta l < 4 5- 6 7- 8 9-10 11-12 >13

Zero Crossing Per iod ( s )

Figure 2.26 Example joint probability distribution of significant wave height and zero crossing period (BMT, 1990)

The principle of the semi-probabilistic method of fatigue analysis is to determine the stress range levels for a shgle wave of given height and period, and accumulate the fatigue damage that results from the passage of this single wave. This process is repeated for a large number of different individual waves which are representative of the waves anticipated at the location over the design life. (See Section 7.2.3 for a full description of the method.)

Consequently the requirement for wave input data for the method is the number of individual waves that will be experienced, with a gwen height and period, during a given duration of exposure (usually one year). This is a joint

2-82 Floating structures: a guide for design and analys~s

eequency distribution of individual wave heights and periods. It can be expressed either in terms of frequency (number of occurrences in a given period of time) or in terms of probability. Fig 2.26 is an example of such a distribution. In most cases, due to the directionally sensitive nature of response, it will be necessary to obtain separate scatter diagrams for each directional sector.

In some cases, where wave measurements have been made for a long period of time, these individual wave scatter tables may be available directly from measurements. More often, however, it will be necessary to derive them from other data, usually from the joint probability distribution of significant wave heights and periods. Thls is a distribution of sea-states (each lasting, say, 3 hours) and should not be confused with the distribution of individual waves referred to earlier. Confusingly, both these different types of distribution are often referred to as scatter diagrams or scatter tables.

The most common method of deriving the individual wave distribution for a given sea-state significant wave height and period is using the Longuet-Higgins (1983) formula:

where: R = HIHrms H,, = H,lJ2 S = TIT, T, = m,lm, v = (T,21T,Z-1)'

L( v) = 2[1 + (1 + v2)-"I-'

This non-dimensional expression for individual wave heights and periods permits a population of individual heights and periods to be created for a gwen sea-state. It can be repeated for each sea-state in the H,, T, joint probability distribution and then summed in the proportions of that probability distribution in order to arrive at a population of individual waves characteristic of the desired period of exposure.

The deterministic fatigue assessment method is similar in many respects to the semi-probabilistic method but simpler. Instead of using a range of wave periods for each wave height, this method just assigns one period to each height. Consequently the input data requirements are just the individual wave height distribution and a characteristic period for that height. However, the choice of this period, in order to be rigorous, requires access to the scatter dagram mentioned in the previous section, and so for most purposes the environmental data input requirements can be considered to be the same as the serni-probabilistic method.

If suffcient indwidual wave observations are not available, the frequency distribution, or probability distribution, of the individual wave heights can be obtained using a negative exponential distribution (UK HSE, 1995) as follows:

where: h = wave height

N, = the number of waves exceeding h in a year D = the distribution parameter, with value depending on the location.

N, = the total number of zero up-crossing waves expected in the location in a year.

Values of D and N, for the UK Continental Shelf are given in UK HSE (1 995) Equivalent values are also given "4

for the Gulf of Memo in API ( w ~ A - L ~ D . 1993) whlch illustrate the lncorporatlon of two separate populations X B

of waves (one due to normal waves, and the other due to hurricane conditions) - see Figure 2.27.

The envlronrnent 2-83

Sum of n o r m a l and hurr icane cornpanents

Normal c o m p o n e n t

1 10 N Number o f waves e x c e e d ~ n g H (cycles per 100 yrs)

Figure 2.27 Cumulative frequency distribution of individual waves (from API RP2A-LRFD, 1993)

2.10.2 Spectral method

The spectral method is a more rigorous form of fatigue analysis which determines the dynamic response stresses, and consequently the fatigue damage, in each of a population of sea states which characterise the environment at the location of interest. It is also the only method that can take account of the directional spreading in a sea state. It is therefore more appropriate to the study of floating systems than the simpler methods described earlier. Here the primary environmental input data is the Joint Probability of Significant Height and Period mentioned earlier (e.g. Fig 2.26). Each cell in this distribution represents a sea-state with a given probability (or frequency) of occurrence.

The spectral method assumes that:

The effects of different wave frequencies in a sea state can be combined by linear superposition, For any gven wave frequency and direction w i t h a sea state, the load effect is linearly proportional to the wave amplitude or height.

These assumptions may not be valid in very steep waves or in very shallow water.

Whereas in the semi-probabilistic method it was necessary to derive the distribution of individual wave heights and periods, in the case of the spectral method it is necessary to provide a wave spectrum shape that can be used as input to the wave motions and dynamic structural analysis which will be used to calculate the stress levels and accumulated fatigue damage (see Section 7.2.3).

In some locations where instrumental wave measurements have been made for a long period of time there may be measured wave spectra available that can be used in the analysis. However, it is more usual for this data not to be avdable, and it is therefore more common to assume one of the established empirical spectrum shapes. This will often be Pierson-Moskowitz for open ocean, or JONSWAP for limited fetch conditions. In some cases it may be appropriate to use spectra which deal separately with sea and swell components (e.g. those due to Ochi et al., (1976) or Guides Soares (1984)) - see Section 2.7.5. llus is hkely to be particularly appropriate in locations (such as, for example, the west coast of Australia) where there is always a strong swell in addition to a wind driven sea.

The wave spectrum chosen may be assumed to be uni-directional (i.e. all the wave energy in the sea-state is approachmg from one discrete direction), or a spreading function may be employed to define a distribution of wave energy about the primary direction axis (see Section 2.7.5).

2-84 Floating structures: a gutde for design and analysis

The fatigue damage associated with each discrete sea state is accumulated in the analysis in proportion to the frequency of occurrence of the sea state as given by the sea state scatter diagram.

2.10.3 Directional considerations

Many floating systems experience quite different responses to waves depending on their direction of approach, and so it is usually necessary to take this directional@ into account in the fatigue analysis. Permanent installations which cannot rotate with the weather will obviously have a fixed heading with respect to the wave climate. And even mobile systems such as semi-submersible drilling vessels will usually moor pointing into a preferred direction (usually the anticipated direction of the severest weather), and this leads to a directional bias in the weather conditions they experience.

The fatigue analysis needs to take account of the distribution of these wave directions about the vessel axis, and indeed the analysis usually takes benefit from the fact that the waves (and stresses) are not always in the same direction. By the same token, any tendency of the waves to most often approach from a prevailing direction also needs to be taken into account.

The ideal s~tuation is to have wave scatter diagrams defined for each of the directional sectors of interest, however statistical information on the wave climate may be inadequate to derive this directional breakdown if the source measurement program or analysis covers too short a period of time.

Proportion of culrns

Radial lengths indicate I , , , I , , , , I I 1 proport ion o f time 0 5 10 1 5 % 20

Mork~ngs ~ r ~ d ~ c a t e wlnd speed r a n g e 1-5 5-10 10-15 15-20 20-25

Figure 2.28 Example Wind Rose (from Wills, 1989)

In such situations recourse is usually made to the directional distribution of the winds or the Wind Rose (see Fig 2.28). There are usually sufficient wind observations to generate a reliable wind rose (either from the location, or fiom an appropriate recording station in the vicinity). In these cases it may be appropriate to assume that the same probability distribution of wave heights and periods comes from all directions, but that the probability of waves fiom a given dmction are accorchg to the wind rose. An alternative is to predict the directional population of waves using a hindcast model (with the appropriate fetches in the different directions) and finally to adjust the total predicted wave population according to the wave measurements.

In a fat~gue calculation it is always necessary to estimate the proportion of the waves coming from different j headmgs because fatigue damage is an acc&ulation of damage from all waves It would be poss~ble to make the P

assumption that all the waves could come from any direction (the worst direction for any gwen structural detail). E

C

The environment 2-85

but h s would usually be very conservative. (Ths is in contrast with extreme loading calculations where it is often satisfactory to assume that the design wave can come from any direction. Thls may be conservative, but not excessively so.)

Some floating systems have a fixed headmg (e.g. a Tension Leg Platform), in which case the geographic wave direction is important. However, some other floating systems weathexvane, in which case it is the relative directions of sea, swell and the floater's heading that matters. Thls is much more difficult to determine as it requires a knowledge of the weathervaning behaviour of the system and, in the case of thruster-assisted systems, a knowledge of the operational policy on vessel heading that is going to be followed by the crew.

It is simplest and usually conservative to assume that within any sea state all the waves are travelling in the same du-ection. However, for more refined design directional spreading w i t h the sea state (see Section 2.13.3) can be taken into account.

The selection of combinations of wave, swell, wind, and current magnitude and direction for fatigue analysis is a complex problem, whch is made even more difficult for weathervaning or thruster-assisted systems. However, the objective for fatigue analysis must be to create a set of environmental combinations of magnitude and relative headmg whch together form a reasonable approximation to the complete population of weather conditions that the system will experience in its operational life.

Both the estimation of extreme and fatigue response where wave, wind and current are all important may be performed with 'response based methodology' which uses long simulations in hindcast data to determine response statistics (Section 2.1 1.7).

2.10.4 Current

Although it has been stated above that the main driving force behind fatigue loading of floating systems is waves, current forces can also play an important role in the fatigue loading cases. Although current is normally a reasonably steady fluid flow, whlch in itself does not nonnally give rise to cyclic loading and hence fatigue damage, the presence of a current can increase cyclic drag loading due to waves. The drag force is proportional to U / U / where the U should include both wave and current components, and the presence of the current will therefore increase the range of Ui U / and hence the drag force experienced.

The UK Health & Safety Executive (1 995) recommends that current should be taken into account if the current maptude is comparable with the wave orbital velocity for those waves that make the greatest contribution to the fatigue damage.

The size of the members will determine the importance of currents on fatigue. Generally currents will be more important for small diameter members (e.g. production risers, or TLP tethers) where they may lead to increases in the Morison loading ranges. Current may also lead to vortex shedding and other dynamic instabilities which can cause sigrdicant fatigue damage. Currents may also beneficially increase damping and so reduce the size of resonant dynamic response.

See Section 2.7.6 for a description of wave current interaction.

2.10.5 Wind

Wind can be an influence on fatigue for floating systems. Wind turbulence, vortex shedding and other dynamic effects can lead to significant fatigue damage to superstructure components (as they can for fixed offshore structures).

2-86 Floating structures: a guide for design and analysis

However, certain floating systems, such as Tension Leg Platforms, can also be subject to dynamic responses to wind at much lower frequencies. These can excite surge or yaw motions which in principle can fatigue the tethers or mooring system. Unfortunately their are few sources of reliable data on low frequency wind gusting. This is because very long continuous records of measurements are needed in order to obtain good estimates of the low frequency end of the wind gust spectrum (see Section 2.5 .6) .

2.1 1 Joint probability of environmental parameters

2.1 1.1 Introduction

Engineering analysis of environmental conditions must o h n assess criteria involving the combined effect of more than one parameter. For this purpose, data defining the probabilities of occurrence of given combinations of parameter values known as joint probability may be needed. Such data are specially important when worst case assessments based on separate consideration of individual parameter values could be seriously misleading and result in gross over design. The approach to identification of worst case probabilities when more than one parameter is involved is explained for the example of wave height and period in Section 2.1 1.4 below. When more than two environmental parameters affect the response and an accurate assessment of extreme response is required then a multidimensional joint probability diagram would be required. These are difficult to determine because a large amount of data is needed, extrapolation is still required and this is difficult in more than two dunensions Instead therefore the offshore industry increasingly applies 'response based methodology' which uses an empirical or simple response model, in conjunction with a long time history of the full environmental data in order to determine the response statistics of the simple model. Deterministic load cases are then selected which are equivalent to the required statistical extremes for the simple model and which should also be approximately the required extreme loadings for the more complicated model (See Section 1 1.7). Nevertheless it is helpful to consider simple relationships in the data because thls assists the engneer to understand the environment the platform is to work in. Before &scussing specific parameter pairings, the formats and notation used for presenting joint probability data are reviewed.

Conditional probabi l i ty ~ (x jy , ) = P ( X X ) / ~ ( Y )

\ Marginal probability

Joint probability p(xy) .%

Marginal probabi l i ty p(x) L I 1. i I 1 I I column p P X Grand

totals totol

Figure 2.29 Joint probability data: format and notation

In practice, it is usually only practical to consider the two parameter case when formats known as scatter diagrams are commonly used. These consist of bivkate tabulations (or in some cases contours) of probability density based on frequencies of occurrence of the respective parameter combinations derived from historical data (see Figure 2.29). The probability density in each cell of such distributions is expressed as number of occurrences or as joint

The env~ronment 2-87

probability p(x ,y ) '100 in parts per thousand. Row and column totals p(y) and p(x) are known as marginal probabilities. Also, each individual row or column, when nonnalised by its respective total, is known as a conditional probability.

Thus in the case of a row (columns are similar), the conditional probability of x given y = y, written as p(x1 y,) is related to the joint probability p(x,yJ by:

Though not Qscussed below, joint probability data covering combinations of the three parameters wave height, period and direction are also available (Hogben et al., 1986). They are presented in the form of an array of bivariate (height versus period) scatter tables, one for each of a set of directional classes. Joint probability is also discussed in the context of directionality and seasonality in Section 2.13.

2.1 1.2 The wave generation process

Before Qscussing joint probabihty data relating to waves in detail, the wave generation process already described in Sections 2.7.1 and 2.7.3, which underlies the development of associated parameter combinations is reviewed. At any gven place and time conditions will, as previously noted, involve a mixture of locally generated seas and swell waves generated elsewhere. For high local wind speeds (W >> 10 knots or 4.5 dsec) , the height of the local wind-driven sea waves will be dominant. It is important to appreciate, however, that its relation to the wind speed may vary widely due to the influence of duration and of directionally dependent changes in fetch. Figure 2.30 indicates the extent of such variation in duration limited conhtions estimated using the JONSWAP based formula cited in Section 2.7.1

u 10 20 30 40 50 60

W ~ n d speed ( a t ? O m ) W (knots)

Figure 2.30 Relation of wave height and wind speed: The influence of swell and duration (after Hogben and Tucker, 1994)

2-88 Floating structures: a guide for des~gn and analysis

The figure also shows that for wind speeds below about 10 knots, the height of the swell waves will usually be dominant and it will depend on the degree of exposure of the site to large fetches. As noted earlier (Hogben, 1988), mean levels of swell height tend to range from about !4 m in enclosed seas, to about 2 m in sites exposed to swell from the open ocean.

For moderate wind speeds when the heights of both sea and swell (H, and H,) may be comparable, the resulting combined height may be estimated as noted earlier using the square law formula:

Since H, tends to be independent of wind speed, thls formula means that it is relatively less important at hlgh wind speeds. Thus, if, for example, H, = 10 m and H, = 2 my H, = 10.2 m.

Understanding of the wave generation process also has a bearing on joint probabilities of wave height and period, as illustrated by Figure 2.3 1 (from Schmied and Cadenet, 1980). This shows time tracks in the Hs - T, plane resulting &om three basic types of weather cycle. The first corresponds to the passage of a local storm in which the relation of Hs and Ts tends to follow an upper boundary corresponding to a limiting value of a steepness parameter S defined by :

The second corresponds to a situation in which nearby winds are stronger than local winds leading to a combination of sea and swell waves with time track lymg slightly below that for the local storm. The swell waves in such cases will have been recently generated within the same weather pattern as the local wind sea, and are thus sometimes referred to as young swell. The third track, lying well below the other two, corresponds to swell waves from a remote storm which may be called old swell. As expected from the discussion in Section 2.7.3, it spans quite a wide range of periods with a relatively low level of wave height.

Over a long time span a joint probability population will develop below the steepness boundary with a density distribution reflecting the relative frequencies of the various types of weather cycle encountered.

2.1 1.3 Joint probability of wind and waves

Engmeers have had a long s t a n h g interest in codifying the relation between wind speed and wave height. Much of th~s interest has arisen because of the widespread use of the Beaufort scale (Table 2.1 1) of wind speed as an index of weather severity, and the need to estimate corresponding wave heights. Various empirical formulae have been proposed (ITTC, 1966 and Scott, 1968) and the WMO description of the Beaufort Scale (UK Meteorologcal Office, Met.0.887, 1977) includes estimates of probable wave height for each Beaufort number. Use is also often made of the JONSWAP formulae (Section 2.7.1) for some assumed fetch or duration.

It has long been recognised, however, that it is unrealistic to assume a simple and unique relation between wind speed and wave height. It must rather be expected, as indcated by Figure 2.30, that in practice there will be a wide scatter due mainly to the influence of swell at low wind speeds and to the effect of variation in duration and fetch at hlgh wind speeds.

The anatomy of this scatter can be well described using the concept of joint probability and associated data formats (Figure 2.32; Hogben (1 969); Shellard and Draper (1 975)). Hogben (1 979) developed a parametric modelling of the joint probability of wave height and wind speed which can be used in various ways (Dacunha et al., 1984). The origmal intention was that it should serve as a predictive tool for translating known probability distributions of wind speed into corresponding distributions of wave height and it has been used in this way. It has, however, been most widely used as a smoothmg process for enhancing the reliability of visual wind and wave data (Hogben, 1988).

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1 2 3 4 5 6 7 8 9 1 0

T s

Figure 2.31 Relation of wave height and period: Mapping of three types of weather cycle in the H, - T, plane (Schrnied and Cadenet, 1980)

Beaufor t wind scole

1 2 3 4 5 6 7 8 9 10 1 1 1 2

Anemomete r wind speed, W (knots) (measured at he ight o f 19 5 metres)

(:) Mean of measurements Total number of

(2) Mean plus s tandard deviation compar isons = 2245

( 3 ) Mean minus s tandard deviat ion selected ot random

( 4 ) Recomrnenda t~on of 1 9 6 6 I n C f r o m years 1 9 5 7 tu 1 9 6 5

(5) H s =(0 0 7 5 w3I2+ 5) feet Scott

Figure 2.32 Measured data for weather station India In the North Atlantic (Hogben, 1969)

The modelling is illustrated in Figure 2.33 from which it may be found that it uses six parameters. The first three (a, n and H,) define a curve through the mean height in each wind speed class Wr:

2-90 Floatmg structures: a guide for design and analysls

Where: H, = aWrn = a mean height of wind sea. H2 = a mean swell height parameter.

The remaining three (b, c and 6) defme a best fit of the associated standard deviation or of the scatter of wave height in the form:

or = b + c W r + d W : (2.99)

p ( W , ) w i n d speed

Signif icant wave h e ~ g h t

H s metres

H2 _, Meon swell

Height

W i n d s p e e d W , Knots

Figure 2.33 Parametric modelling (Hogben et al., 1986)

When the six parameters are known, the complete joint probability &stribution can be modelled by assuming that the scatter of wave height in each wind speed class has the form of a gamma distribution (or other suitable known dstribution), entered by Hr and or as derived above. Thus, using the notation described at the beginning of this section (see Figure 2.29), it may be found that:

where:

and

To use the model in its predxtive mode it is necessary to choose values for the six parameters based on experience for similar sea areas ( e g open oceanr limited fetch; Hogben, 1988). Then, given a known probability distribution

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p ( ~ r ) ~fwind speed. the corresponhg wave height dstribution p(HJ can be computed using the above formulae

* ~n the smoothing mode case, the six parameters are determined by best fitting of a given set of joint probability data such as mght be denved from visual observations. Use of the model instead of the origmal data then offers two important advantages

) Reliability is enhanced by objective suppression of outlying observations. This is specially important when estimates of extreme height are needed, since outliers can lead to serious errors in such estimates.

b) It has been found that reliable sets of parameter values can be derived from relatively small samples of joint wavelheight wind speed data. They can then be applied, to the much larger samples of wind-only data covering much longer time spans, to derive more reliable wave height data (wind observations have been reported since 1854 whereas useful wave heights have only been reported since 1949). This procedure was used in the compilation of the book 'Global Wave Statistics' (Hogben et al., 1986).

2.1 1.4 Joint probability of wave height and period

In discussing the joint probabhty of wave height and period, a clear distinction must be made between two types of data. The first, which is most widely used, describes populations of sea state whlch may cover several years, in terms of characterising height and period parameters such as significant height H, and zero crossing period T, with joint probability of occurrence written as p(H,, T,). The second, less widely used but nonetheless of some importance, describes populations of individual waves in terms of their heights H and periods T with joint probability written as p(H, T ) . (See also Section 2.10).

Mean zero crossing period in seconds

Figure 2.34 Joint probability of wave height and period: Sample for population of sea states p(H,, T, ) from measured data at Sevenstones (Fortnum and Tann, 1977)

In reviewing the interpretation of such data, reference will be made to parametric modelling methods developed to assist the analysis. In addtion, in a separate subsection, qttention is drawn to the special difficulty of applying extreme value analysis to combinations of parameters illustrked by examples involving wave height and period.

sea state populations A sample of this type of data is shown in Figure 2.34. It is widely used because it can describe wave conditions over a time span of several years in a format whxh is concise. but nonetheless, as explained below, contains sufficient information when suitably analysed to meet most engineering requirements.

2-92 Floatmg structures a g u d e for des~gn and analysts

In considering the question of mterpretation, it may be noted that the occurrence frequency or probability density in each cell identifies a number of sea states sharing the same H, and T,. The option is thus available to translate the complete population of sea states into a corresponding representative population of wave spectra using the methods reviewed in Section 2.7.5 for modelling spectra as functions of H, and T, or related parameters.

Such a procedure offers two benefits. The first is that the capability of spectra, to describe all the waves and their associated kinematics and statistical properties in a given sea state lasting several hours and explained in Section 2.7.5, can thus be extended to cover all the waves in a time span of several years.

The second important advantage is that the way is then opened for application of spectral analysis methods such as are described in Annex 3F for computing statistics of structural response. On this basis it is, for example, possible to translate a complete population of sea states via wave spectra into a corresponding population of response spectra which could be used for fatigue analysis (see Sections 2.10 and 7.2.3) or estimation of extreme loads (see, for instance, Hogben, 1990-b).

In undertaking such analysis, it is sometimes helpful to derive a parametric model of the joint probability, as described for wave height and wind speed in Section 2.1 1.3, but using a different form. Such a procedure has been developed by Ochi (1 978) and applied to design studies of ships and offshore structures. A detailed account of Ochi's model, which is based on a bivariate log normal distribution, may be found in the reference.

It must suBce here to quote the formulae used which define p(H, , T,) as a function of h = In H, and t = In T, and of the parameters p,, pn oh, 0, and p which are respectively the means, standard deviations and correlation coefficient of h and t computed from the given data. On this basis:

where: A = 2 n H , . T Z ( 1 -pZ)"uhu, B = 2 (1 - p2) C = (h - pI1) I Oh

D = (t - pt) l o ,

This model and variants of it have been widely used (Hogben et al., 1986) and it generally offers a reasonable quality of fit. However, it cannot accommodate cases which sometimes arise when the distribution is locally hstorted as: for instance: when heavy incidence of swell from distant storms leads to the development of a lobe of low wave height long period waves appearing as a bump on the heel of the distribution. Occasional incidence of freak conditions such as typhoons can also cause local distortion not readily accommodated by the model.

Individual wave populations Data on joint probabilitiesp(H, 7) of the heights and periods of indwidual waves in a given sea state when coupled with correspondmg data on dstributions of sea state p(H,, T, j, as discussed above, offer a basis for very detailed statistical description of populations of indwidual waves covering several years. Such data can be specially useful, moreover, for estimating the periods of extreme waves for design purposes as discussed below.

As noted in Section 2.10.1 : this data is useful for fatigue analysis, but the availability of reliable p(H, 7) data is unfortunately quite limited and, though a number of modelling formulae have been developed, their relative complexity has discouraged widespread use. Extensive analysis and modelling of measured data has been undertaken by Cavanie et al., (1 976) and Goda (1 978) (measured data from Goda (1 978) are shown in Figure 2.35, and mathematical formulae have also been developed by Longuet-Higgins (1983) and others. A comprehensive critical review of modelling formulae in comparison with measured data can be found in Srokosz and Challenor (1987). It should therefore suffice here to refer briefly to the comparison shown in Figure 2.36 between measured data and theory of Longuet-Higgins (1 983) and Cavanie et al., (1 976). The Longuet-Higgins formulae, which are rather simpler than-those of Cavanie et al., are quoted in equation. 2.93 of Section 2 10.1,

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,4s noted by Srokosz and Challenor, both the theoretical formulations are based on the assumption that the correspondmg wave spectrum is narrow banded, and the measured data shown are for such a spectrum. The co- ordinates used are :

1 No = 2593 woves 1 1 r(H,T) = 0 51 2 0.05

1

A2

Figure 2.35 Joint probability of wave height and period: Sample for population of individual waves P(H, 7) from measured data (Goda, 1978)

t = TIT,

where: T, = mJm,

and for a spectrum S(f):

A characteristic feature of the distributions is that, as might be expected, the periods tend to become longer as the wave height increases and this has an important bearing on estimation of wave periods for design waves.

Extreme value anaZvsis Methods of extreme value analysis are reviewed in Section 2.8. Some comment is appropriate here, however, about the special difficulty of interpreting the term extreme in application to a combination of parameters, illustrated here by the case of joint heights and periods.

For many purposes it is to be expected that any assumed extreme condition would involve a wave of extreme height: but the choice of associated period is less clear. Options might: for example, include the most probable period for the height concerned. the shortest period leading to maximum steepness or the longest period leading

2-94 Floating structures: a gu~de for des~gn and analys~s

to maximum depth of penetration. Any of these three choices can be made by reference to the conditional probabhty distribution of individual period given a maximum value for individual height, p(TIH,J (see Figure 2.37). In practice, however, concern is with extreme severity of response and this criterion requires that sensitivities in the response characteristics of the structure in question must be taken into account. On t h ~ s basis, the extreme case might involve waves of some specific critical period or waves of extreme steepness for which the associated height might be relatively moderate.

Measured Longuet-Higgins C a v a n ~ e e t al

Figure 2.36 Joint probability of individual waves heights and periods: Comparison of measured data with theory of Longuet- Higgins (1 983) and Cavanie et al. (1 976)

/\

Figure 2.37 Conditional probability of individual period for individual wave height of 30rn (Arhan et at., 1979)

It is therefore advisable, when investigating extreme conditions for design purposes, to explore a range of periods in association with any given extreme height. A simple empirical rule for guidance in such cases (Hogben et al., 1979) is to choose values of the peak period T, over a range defined by:

This is equivalent to prescribing a range of wave steepness:

0.02 < H51hp < 0.05

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where A, is a wavelength parameter defined by:

\ = (g/2n)~:

For floamg structures wave penod has a large effect on the structural response and on the pitch and roll responses which will affect process equipment, and in extreme cases the overall stability.

Figure 2 3 8 illustrates an approach to such analysis in which contours of the standard deviat~on o of roll angle. computed using ship response data, as functions of H, and T, are superimposed on a tabulation of a jomt probability distribution p(HJ',) (for clarity, the tabulation is only shown in a specific band of a values). By integrat~ng the total probability mass (probability density x cell area) contained within successive bands of a values, an exceedance curve P (0 > o ') can be computed as shown in the figure from whlch an extreme roll angle at any specified risk level can be derived.

I I I I I I I I

0 2 4 6 8 10 12 14

Zero c ross lng per lod TZ 0 4 8 1 2 16 20 24

Standa rd dev lo i ion of ro l l ang le u (deg)

( b )

Figure 2.38 Extreme value analysis of jomt probability data: Estimation of extreme roll response from p(H,, T, )

Thls procedure for translating joint probability data into an exceedance probability for a single severity parameter exemplifies an approach to extreme value analysis which can be applied to other combinations of parameters. In some cases, however, a systematic search of the joint probability space to find the most severe response may be needed.

2.1 1.5 Joint probability of waves and current

It is tempting to consider that waves and current are independent physical phenomena, and can thus be considered to be statistically independent, but there are a number of physical processes which do connect them together. Currents arise from a number of different physical phenomena (see Section 2.6) and the driving forces behind some of these components are correlated with the driving influences on the waves.

These connecting influences between waves and current may be summarised as follows: The wind-dnven component of current is correlated with strong winds, which are in turn correlated with the occurrence of high wave heights.

2-96 Floating structures: a guide for d e s ~ g n and analys~s

Current due to a storm surge will also be correlated in some manner with the passage of a storm, and will therefore be correlated with high wind speeds and liuge wave height. (However, this correlation may be weak due to the strong influences of water depth and proximity to land etc.) Wave-current interaction effects (see Section 2.7.6) can lead to circumstances where the presence of the current increases the height of any existing waves.

These issues therefore imply that some account must be taken of correlation between currents and waves, particularly when considering extreme events. It would clearly not be satisfactory to assume that the extreme current velocity and the extreme wave height are completely independent events. On the other hand, to assume that the highest waves and the hlghest currents will occur at the same time and in the same direction is excessively conservative in most cases.

Unfortunately, it is difficult to make general observations on the joint probability of currents and waves because the current environment tends to be complex, and unique at. each different offshore location. The designer must therefore look for joint probability data on which to base h s design cases, but reliable data on the joint probability of current and waves is quite rare. One of the reasons for this dearth of data is the difficulty in defining a current in the presence of large amplitude waves noted in Section 2.7.6.

Heideman et al., (1989) studied simultaneous measurements of wave height and current at a number of sites on the Nonvegan Continental Shelf as part ofthe Norwegian Ocean Current Data Analysis Project (NOCDAP). The measurements included 38 storms (defined as having peak significant wave heights above 7 m). They plotted the maximum sigmficant wave height in the storms against the maximum equivalent in-line current and showed current speeds at hgh wave heights very much lower than the Norwegian Petroleum Directorate recommend for design in this area.

\ FI 1 Number o f samples 5617 1 1

M c x i r n u m wave height (M)

Figure 2.39 Equivalent current at constant probability versus maximum wave height (Heideman et al., 1989)

One important discovery from these measurements was that, during the course of the storm, the time of the maximum sipficant wave height very seldom coincided with the time of the maximum in-line current. This only happened on one occasion in the 38 storms examined. So, whilst the measurements indicate a clear correlation between higher wave heights and hgher in-line current speeds, assuming that these maxima occurred at the same time in all storms might lead to excessive conservatism in design.

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2.1 1.6 Other combinations

The need for investigation of other combinations of environmental parameters is very much dependent on design of the articular floating system. It is the responsibility of the designer to foresee that a particular combination of external environmental factors may lead to a critical design case for the system. It is difficult to generalise herefore on whlch may be hportant for a particular case. However, the following should be considered for most floating systems: . Combinations of winds, waves and temperatures, . Combinations of snow and h ~ g h winds,

Combinations of water depth, tidal and surge elevation and wave height.

High winds or large waves when combined with low temperatures give rise to icing conditions where it is likely that the floating system may collect large quantities of ice on the superstructure increasing the weight and degrading stability.

Heavy falls of snow or accretions of ice may also significantly increase the wind forces and overturning moments experienced by the vessel.

Extreme water depth variations and wave heights are important in terms of air-gap for fixed structures and for floating structures where the system is not free to float to its own level (e.g. tension leg platforms). Variations in water depth may also have a ~ i ~ c a n t influence on mooring system performance for shallow water systems and so consideration of the dynamic response to the most extreme wave conditions in the extremes of water level is likely to be necessav.

One approach is to assume that the extreme conditions for each parameter occur simultaneously. For example, assuming that the 100 year wind and the 100 year coldest temperatures can occur at the same time. However, this approach may be unduly conservative (in the North Sea, for example, the strongest winds tend to come from the West, and the coldest winds from the East).

In practice, the decision whether to take account of the joint probability of extremes in design may often be conditioned by the availability or otherwise of good quality long term measurements from which reliable joint probability estimates can be made. In a well-established operating area such as the North Sea it is possible to derive joint probability distributions for many combinations of environmental parameters from which extreme design combinations can be derived. In other, less well documented, parts of the world a conservative approach may be the only safe option.

The UK Health & Safety Executive 4th Edition Guidance Notes (HSE, 1995) and the supporting report to this (OTH 89 299, 1990) provide useful guidance on how to deal with these joint probabilities and how to derive the necessary joint probability distributions from environmental data.

2.1 1.7 Response based methodology

Joint probability is beginning to be taken into account using 'response based methods'. In response based methodology many tens of years of hindcast data, e.g. from the 'Ness' project (Peters et al., 1993) is applied to an empirical or simplified platform model, in order to obtain response statistics and to choose suitable extreme combinations for application to more detailed models (Tromans and Vanderschuren. 1995).

The use of this methodology is at an early stage; requires large quantities of computer time, and improvements are to be expected. The method avoids the need to generate joint statistics; nevertheless it would be advisable to look atjoint statistics, as presented in bivariate scatter diagrams, as a check that the data used for the analysis is reasonable. If techniques can be developed for fitting multidinlensional models to the underlying environmental data then they could be used either to improve the environmental data used in the response based method or to perfom a many dimensional equivalent of the two-dimensional procedure in Figure 2.38.

2-98 Floating structures: a gu~de for design and analysis

2.12 Effects of proximity to land

2.1 2 .1 Introduction

This part of the guide is not an introduction to coastal engineering but is intended to be of assistance in the preliminary assessment of inshore construction sites for floating structures. Concrete platforms, for example, typically spend many months at one or more sites with towages between different stages of construction. As construction proceeds the shape, height and draft of the structure will change so that the forces on the structure due to winds, waves and currents will also change. Given the nature of air and water flow at inshore locations it is likely that vertical profiles of both wind speed with height and current speed with depth will be required to accurately assess the forces on the structure. Although waves are likely to be small in height and period, some low amplitude swell may penetrate to a sheltered site and there may be some oscillation of water level due to seiche. The ebb and flow of the tide and meteorological induced surges may produce strong currents in narrow channels.

Proximity to land may also result in extreme conhtions of temperature which are much less common offshore due the moderating influence of the sea. In particular in winter this can lead to problems with ice and snow.

2.12.2 Effects on winds

The motion of air experienced at ground level is generally the result of stress exerted by winds at higher levels whch in turn are due to large scale weather systems (see Section 2.3.2). Small scale systems (Section 2.3.3) may also be of importance locally.

The atmospheric boundary layer is the lowest layer of the atmosphere where airflow is affected by friction. It is a region of turbulent flow between the free atmosphere and the ground where the character of strong winds is affected by a nurnber of factors. For a given site of known altitude, surrounded directional sectors with known terrain roughnesses and topography, the characteristics of the strong winds at the site can be determined.

A design wind may be thought of as consisting of a regionally consistent reference mean wind speed (such as the once in 50 year extreme hourly mean wind speed) multiplied by a number of factors. Topography and altitude factors will equal 1.0 for sea level sites. The directional factor is also regionally consistent (at least in temperate latitudes) but may otherwise equal 1.0 for each sector. Exposure and fetch factors will vary according to dvectional sector and can be calculated by studying detailed maps. Using extreme value analysis on mean wind speeds for nearby stations where wind speed has been measured and calculating the values of various factors which influence the extreme wind speeds at the site the values of the regionally consistent factors can be determined and then used to generate directional estimates of extreme values of mean wind speed for the site under consideration. Further factors such as height factor, turbulence intensity factors, gust factors and seasonal factors can also be determined so that design wind speeds for the appropriate height, averaging period and season can be estimated.

The motion of the air is retarded by the frictional effect of the land or sea surface and this effect varies considerably. Ths frictional effect is measured using a scale of surface roughness (2,) (see Section 2.5.4; Barltrop and Adams: 1991 and ESDU, 1985).

The value of z, for water varies between 0.0005 with winds of 10 rnls to 0.0 1 with winds in excess of 40 m/s and is approximately given by 5x 10-5V ' / g (Cook, 1985; also Section 2.5.4).

The surface roughness will effect both the mean wind speed and the variability or gustiness of the wind so that, given the same wind speed in the free atmosphere, in a city the mean wind speed will be much less but more variable and gusty than usually experienced at sea. The standard level usually associated with wind speed is 10 metres above the zero plane whch is sealevel at sea but may be 25 metres above the ground in a city. Above the zero plane wind speed rises with height until a maximum is reached at the edge of the boundary layer which varies

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bch~ecn 1000 and 3000 metres dependmg on defmtlon. For a glven 10 m wmd speed, wnd speed increases M lth hc~ght much more rapldly over rough surfaces than it does over smooth surfaces.

Terrain Surface roughness Height of zero plane

City centres, forests 0.7 15 to 25

Small towns, city suburbs, wooded country 0.3 5 to 10

Villages, countryside with hedges, trees and buildings 0.1 0 to 2

Open level country, few hedges, trees or buildings 0.03 0

Fairly level grass covered plains with isolated trees 0.0 1 0

Flat areas, short grass with no obstructions 0.003 0

Flat snow covered farmland or desert 0.001 0

Table 2.9 Typical values of terrain parameters z, and d (after ESDU, 1985)

An exposure factor (S,: Table 2.10) may be defined for each direction at a site as a factor relating mean hourly wind speed experienced at the site with that llkely to be experienced over standard terrain (z,= 0.03) assuming equhbrium boundary layer conditions. Although equilibrium boundary layer conditions rarely occur in practice (because of changes in surface roughness upstream from the site) such an exposure factor indicates the change in wind speed llkely to be experienced over different terrains. A height factor (S,) is also useful for the same reasons and gwen the same qualifications may be defined as the ratio of the mean wind speed at any height to that at the zero plane level. For heights below 300 m a power law with exponent varying with surface roughness gives sufficient accuracy in this context.

Terrain roughness category 00 0 1 2 3 4 5

Aerodynamic roughness (z,) 0.001 0.003 0.01 0.03 0.10 0.30 0.70

Exposure factor (S,) 1.29 1.21 1.11 1.00 0.86 0.71 0.58

Exponent (a) (O<z-d<50 m) 0.11 0.12 0.14 0.16 0.20 0.24 0.32

Exponent (a) (O<z-d<300 m) 0.11 0.12 0.14 0.16 0.18 0.22 0.27

Table 2.1 0 Exposure factors and for height factor exponents

2-100 Floating structures: a guide for design and analysls

The calculation of wind speeds with shorter averaging times requires a gust factor S, which in turn requires a turbulence intensity factor. These parameters may be calculated readily for over water locations assuming equilibrium boundary conditions (see API RP2A, 1993) but for locations close to land with upstream changes in surface roughness and topographical effects, the calculation becomes more sophisticated and space does not allow a full treatment here. Interested readers should consult ESDU (1989); software is also available (Cook et al., 1985).

While in general wind speed is less near the coast than it is over the open sea there are one or two exceptions. Notable among these are katabatic winds which can attain speeds in excess of 40 m/s in fjord type inlets in polar regions and a number of local winds such as listed in Section 2.3.3. These winds occur when cold, dense air, possibly overIying an ice cap, spills down a valley under the force of gravity. In warmer regions thunderstorms with associated gusts and tornadoes are more prevalent over land than at sea. Land and sea breezes occur at most coastal locations but are unlikely to be strong enough to cause design problems.

2.1 2.3 Effects on waves

Most inshore construction sites are likely to have been chosen to obtain shelter from waves so any waves which do occur are most hkely to be locally generated and rather small and short. Methods described in earlier editions of the Shore Protection Manual (1984) are popular for calculation of such waves but in this edition it is pointed out that the effective fetch method used for many years should be replaced with a straight line fetch. In addition wind speed is replaced with a parameter called the 'wind stress factor' which is defined as V, = 0.7 1 V ' 23.

A procedure for calculating design wave heights for short fetches is to use the design wind speed by direction in a deep water wave forecasting formula which involves fetch. The waves which are generated are likely to be fetch limited although if the area of water is large the calculated sea state may be duration limited if the length of time that the wind blows is short. It is not realistic to assume that the extreme hourly mean wind speed will blow for several hours and a lower value appropriate to a longer period is required. Examples of wave forecasting formulae from the Shore Protection Manual are:

where H, is the sipficant wave height in metres, V, is the wind stress factor in metres per second, F is the fetch in kilometres, T, is the spectral peak period in seconds and t is the time (in hours) required for the fetch limited sea to be generated. These formulae derive from the JONSWAP results and Carter (1 982) gives very similar formulae but based on wind speed rather than wind stress factor. Use of wind speed results in lower wave heights and periods than the use of wind stress factor.

Small changes in wind speed over a period can be accommodated. For example if a higher wind and a lower wind is being considered subtract one quarter of the difference between the two winds from the higher wind speed and apply thls for the whole period. However computer modelling is generally taking over from manual methods and a useful review of typical computer models is given by Hawkes and Jelliman (1 993).

Consideration of swell waves entering a sheltered location from the open sea will probably require estimation of refraction and dffraction effects. Although manual methods are gwen in the Shore Protection Manual (1984) once again computer modelling has become popular and models are easy to acquire The modelling of shallow water effects (such as refraction) requires a digital file of water depths as input to the model.

The env~ronrnent 2-101

2.12.4 Effects on currents

Variation in water level, due to astronomical tides or meteorological surges, will result in currents which can be \cry strong in narrow channels where the flow of water is constricted. It is possible to make a reasonable estimate of such flows by consideration of the volumes of water involved and the time taken for some change in level to take place. During one half of the tidal cycle of duration (tl2) a volume of water equal to the tidal range (R) multiplied by the area of basin (B) (noting that the surface area may change as the tide falls) must flow through a channel of average cross sectional area (a). Then the average velocity (u) through the channel will be:

At the midpoint of the fall in water level the rate of fall is at approximately 1 S times the average rate over the period. In addition the current rate in the middle of the channel is llkely to be approximately 1.5 times the average flow so that maximum current rates in the channel are likely to be in excess of twice the value of u calculated above.

The structure of the water column in deep inland waters such as fjords can be complex with two or more stratified layers. Such layers may arise due to river outflow overlying denser salt water and such layers may move independently particularly where a sill at the seaward exit of a fjord restricts the flow of deep water. This can result in stronger currents than might be calculated assuming that the whole water column moves simultaneously. Estimation of wind driven currents in semi-enclosed basins is extremely difficult because any motion in one part of the basin is likely to result in a compensating flow in another part. It seems reasonable to assume that wind driven currents under these circumstances will, apart from short lived jets or eddies, be less than those generated offshore and will have limited vertical extent. Application of standard offshore formulae such as 3 per cent of the wind speed are likely to be conservative.

2.13 Directionality and seasonality

2.1 3.1 Introduction

Mention has been made at several points in this chapter about directional considerations, (for example at 2.10.3 in dmussing fatigue) and h s section is intended to summarise some aspects of directionality together with some comments about seasonality as consideration of both often results in changes to design criteria or operability. Consideration of directionality, particularly with regard to the design of fixed structures, usually leads to less conservatism (see for example Nielsen et al., 1986) because maximum wave loads and current loads often operate in different directions but in the case of floating structures such an assumption may be invalid because weathervaning of a floating structure may allow waves to approach the beam resulting in unacceptable motions. Cnven the structure of temperate weather systems with rapid changes of wind direction occurring as a trough of low pressure or a front passes a location (see Section 2.3.2) it is not surprising that extremes of wind speed and wave height may not act collinearly. In addition both astronomical and meteorological forcing of currents leads in the former case (see Section 2.6.4) to a direction of action completely independent of both winds and waves whle in the latter case (see Section 2.6.6) to a direction which theoretically at least, is significantly different to that of the wind. As more coincidentally measured wind, wave and current data becomes available it is becoming Increasingly clear that duectional dwergence between wind, wave and current is the rule rather than the exception for design scenarios. Response based methods, as described in Section 2.1 1.7, can handle directional problems.

It is worth briefly considering the statistical aspects of directionality and seasonality and how the division of data into directional andlor seasonal classes affects the statistics which are commonly calculated (see also Section 2.1 1.1). IfX is the random variable wind speed measured at a location and Y is the random variable wind direction measured coincidentally at the same locatlon then the random variables will have a joint distribution which can be represented as a frequency table of measurements over a period of time. Such frequency tables (or a graphical representation of the mformation called a Wind Rose) are in common use in the engineering industry. The relative

2-102 Floatrig structures: a gu~de for des~gn and analys~s

frequency of various combinations of wind speed and wind direction can be represented mathematically by a bivariate probability density functionf,Ax,y) and the probability that values ofX lie within the range (a,, 6,) at the same time as values of Y lie withn the range (a,, 6,) is given by:

Ifvalues of the wind speed X, vary across the columns of the relative frequency table then the row total represents the marginal distribution ofX Similarly if wind direction Y varies across the rows of the relative frequency table then the column total represents the marginal distribution of Y. This is represented mathematically:

For each class value of wind speed, the row of the frequency table represents a conditional distribution of wind drection Y given the value of X and similarly for each class value of wind direction the column of the frequency table represents a conditional hstribution of wind speed X given the direction Y. This is represented mathematically:

The events having an average conditional recurrence interval of some period N, will always be (theoretically) smaller than the equivalent margmal value. This normally leads to a re-calibration of conditional design criteria so that conservatism is not lost artificially simply by subdividing marginal distributions into a number of conditional distributions (see Section 2.1 3.3).

2.1 3.2 Seasonality

At most locations in the world there is a change of weather with season. In high and temperate latitudes this is usually a function of temperature gven the variation in solar radiation and length of daylight. In sub-tropical and tropical latitudes the temperature may change little but nevertheless the weather can change dramatically from dry to wet season or from northeast monsoon to southwest monsoon. Designers of floating structures may be less concerned about temperature and precipitation (unless ice and snow are important) than about wind speed and drection, wave heights and current and it is recommended that due consideration is given to seasonal variations in these parameters both in respect of design and operations.

As described in Section 2.8 the classical approach to extreme value analysis requires independent and identically dstributed samples from the parent distribution. In many cases each sample represents a year's data and only the single maximum value is used for prdcting extreme values. This is clearly extremely costly in terms of data and methods have been developed which may make better use of the data. One example using monthly maxima is described by Carter and Challenor (1979). However, given the common situation where lack of suitable data prevents the use of either annual or monthly extremes, the approach taken is to fit a statistical distribution function to cumulative frequency hstributions, of e.g. wind speed, using the method of moments or least squares (see Section 2.8.3). The 2 or 3 parameter Weibull distribution is often used for this purpose (equation 2.75 of Section 2.8.3). Also gven are expressions for calculating annual extremes using all the data (the marginal hstribution). The method should be adjusted if it is based on monthly, seasonal or directional data (the conditional distributions).

The env~ronment 2-1 03

G~\,cn the lariation in weather with season, wluch as discussed above. occurs almost everywhere in the world and also the unportance of getting the best fit to the data. statistical distribution functions are often fitted to monthly or seasonal data. The equivalent expression for probabilit~r to equation 2.75 for monthly data is

where D, is the number of days in month i . It should be noted that even if the monthly distribution and the annual distribution have the same parameters the extreme values for the same return period will be different because of the difference in the calculation of probability shown in Equation 2.120 compared with-Equation 2.77. In reality monthly distributions usually have different parameters to those of annual distributions and in addition there is the danger that a poor fit to some conditional distribution will result in an estimate of extreme value which is inconsistent with the marginal distribution. It is therefore usually necessary to calibrate extreme values for conditional distributions so that the worst conditional case is equal to the marginal case; in other words the extreme value calculated for the worst month is made equal to that for all year.

Data sufficient to define seasonal variation is widely available and is required for the approval of temporary operations such as exploration drilling, ocean tows, maintenance etc. For the U.K. continental shelf a comprehensive atlas of expected wave height by season does exist based on measured data (Draper, 199 1). There is also a wind atlas for the North Sea and Norwegian Sea (Borresen, 1987). For the coasts of the U.S.A summaries of data measured from data buoys are available (NDBC/NCDC, 1990) while for broad scale information see Global Wave Statistics (Hogben et al., 1986) and the U.S. Navy Atlases (1981).

The types of weather which occur in the different seasons in the various ocean basins of the world are shown in Table 2.2. The tropical cyclone seasons in each regon should always be borne in mind given that tropical cyclone effects may be completely absent from data sets of limited duration. If operations are to take place in an area where tropical cyclones have been experienced in the past a separate analysis should always be made of the frequency and severity of such storms.

2.13.3 Directionality

Directionality and seasonality are often linked, particularly in areas subject to a monsoon climate such as the Indlan Ocean and China Seas. However there is a fundamental difference between the results of directional and seasonal analyses which is that seasonal results are statistically independent between adjacent months since a storm whlch occurs in one month cannot also occur in another, whilst a wind in a storm may change direction as it passes. The importance of this difference is discussed by Cook (1983) but it is not always possible to make allowance for it. The analysis of measured or estimated directional wave data is often very difficult, due mostly to a lack of suitable data, and recourse is often made to estimating wave direction from consideration of one or more of wind speed and direction, duration of storm, fetch and water depth. However results from the computer modelling of storms are becoming available and the latest editions of API RP2A(1993) do include directional factors for hurricane generated waves in the Gulf of Mexico. Directional wave spectra, representing directional spread within a sea as distinct from mean wave direction, are considered in Section 2.13.4.

The direction associated with currents is fundamental and examples are published in many publications (see Section 2.6). The directionality associated with the tidal component of a current is predictable, being associated with astronomical forces. Tidal currents may be further subdivided into harmonic constituents and visualised as the resultant of two vectors of equal magnitude rotating in opposite directions. During each cycle the resultant vector nil1 have two maxima and two minima and its tip will describe an ellipse. Such ellipses are often used to graphcally represent tidal currents. Further information is given by Pugh (1 987). Current analysis will normally require that the tidal and residual components are separated. The direction associated with both tidal and non-tidal components of a current can be very site specific being dependent, particularly in shallow water, on the local topography.

2-104 Floating structures: a guide for design and analysis

Extrapolation of dstributions conditional on duection and estimates of extreme values requires a revised estimate of probability as was the case with seasonality. In this case the equivalent expression for probability to equation 2 75 is:

where p, is the percentage of the time during the year when the parameter being analysed is associated with direction 8. As mentioned above the analysis of directional data is often difficult and it is as well to have procedure which although tending to err on the conservative side will produce more consistent results. Firstly analyse the marginal (i.e. all direction data) to calculate a basic reference criterion such as the 50 or 100 year return period extreme. Define ratios to derive values for other return periods such as 1/12, 1, 2, 5, 10 years assumiTlg that these will be the same for each direction. For each conditional (directional) distribution calculate the extreme with the same return period as the reference, all direction value and then scale up this extreme value for the worst direction so that it becomes equal to the all direction value and apply the same scaling factor to all the other directional extreme values.

2.1 3.4 Directional wave spectra

The precise way in whlch wind energy is converted into wave energy is a subject of continuing research (see also Section 2.7.1). Given that the flow of air over the sea surface generating waves is turbulent then the result is complex and is often expressed as a one or two dimensional wave energy spectrum. Generally the first dimension corresponds to frequency and the second to direction. Note that waves also have a general direction in addition to that within the spectrum.

The generalised Pierson-Moskowitz spectrum is an example of a wave energy spectrum and has the form:

The duectional wave spectrum SK8) describes the distribution of surface variance with frequencyf; and direction 8 where 8 is the hection from which the wave component is travelling. The non-directional spectrum may be obtained from the directional spectrum by integrating over the range (-n, n) for 8. It is usual to express S ( j 3 ) in terms of S ( f ) and a spreading function G(J8) such that:

S(l; 8) = S(f)G(A 8) where j ' ' ~ ( f ; 8)d8 = 1 - X

Two common expressions are used for G@ 8) and it is important to distinguish between them. One version is:

where 8 - 8, < n, 8, is the dominant direction and s is the spreading parameter. Both 8, and s are functions of J: N is a normalising constant which ensures that G g 8 ) integrates to 1 and is given by:

The envtronment 2-105

For slmple analysis where a constant value of s, independent of frequency is used, the value s = 10 is

rccornrnended in which case N = 0.903 (UK HSE, 1995). An alternative version of the equation 2.13 1 is:

where 8 - 0, < x/2,0, is the dominant direction, n is the spreading parameter and the normalising constant. M is given by:

Clearly formulae 2.124 and 2.126 are related and Haver(1990) reports Mitsuyasu et al. (1975) as showing that n =0.465s. Thls is, however, an approximation and more accurate relations may be found in ISSC (1970) which cites an exact equation:

and an associated approximate formula:

The exact equation is based on an amplitude matching criterion explained in ISSC (1 970). The approximation equation 2.129 agrees more closely with the exact equation than the Mitsuyasu formula.

In API RP2A (1 993) the commentary on fatigue analysis suggests values of n of 2 for wind dnven seas or 4 for limited fetch situations (which corresponds to values of s of 4 and 8 approximately).

Considerable variation in the value of spreading parameter with frequency has been observed. Spreading is less near the peak frequency and Mitsuyasu suggests the following:

with s,, = 10 for wind waves, 25 for swell generated nearby and 75 for swell generated far away. However more recent measurements may lead to reductions in the recommended values of spreading parameter.

2-1 06 Floating structures: a guide for design and analysis

Notation

wave amplitude wave crest speed drag coefficient depth, height of zero plane duration, vessel draught frequency Coriolis effect fetch cumulative distribution function acceleration due to gravity (= 9.8 lrnls) gust factor gradient height wave height maximum individual wave height in a sea-state root mean squared wave height sigmficant wave height 50 year extreme significant wave height response amplitude operator turbulence intensity length, lifetime event duration return period n~ moment of spectrum pascal probability density function probability of non-exceedance of X = 1 - Q(X) probability of exceedance of X = 1 - P(X) risk wave steepness significant steepness energy spectrum directional energy spectrum response spectrum time period air temperature peak energy period significant period sea temperature zero crossing period mean period current speed friction velocity in water tidal current at height z wind speed gradient wind speed mean wind speed at height z friction velocity in air horizontal distance response height above zero plane aerodynamic surface roughness, mean level

The envlronrnent 2-1 07

Glossary

Phllllp's constant (= 0.008 1 ) JONSWAP peak enhancement factor phase lag temperature difference phase difference relative vorticity angle water level, damping ratio wave length 1 0-6 metres angular velocity latitude density of seawater (= 1027 kg/m3) density of air (= 1.25 kg/m3) standard deviation surface stress, duration frequency

Albedo: the ratio expressed as a percentage of the radiation reflected by a surface divided by the radiation incident upon it.

Amphidrome: a point in the sea where there is zero tidal amplitude due to the cancelling of tidal waves. Cotidal lines radiate from an amphidromic point and corange lines encircle it.

Anticyclone: a circulation; c l o c h s e (anti-clockwise) in the northern (southern) hemisphere; around a region of high atmospheric pressure.

Astronomical tide: the regular variation in sea level whlch is due to the gravitational forces exerted by the sun and the moon.

Beaufort Scale: a numerical scale first adopted by A h r a l Beaufort in 1808 relating wind speed to the state of the sea (see Table 2.11, also see Tables 2.12 and 2.13 for descriptions of the sea).

Baroclinic: a baroclinic atmosphere is one which is not barotropic. Horizontal temperature variations are the rule rather than the exception with large, generally uniform air masses separated by baroclinic zones (fronts). Strong baroclinicity indicates large changes in temperature and strong winds.

Barotropic: a barotropic atmosphere is one in which surfaces of constant atmospheric pressure and constant temperature do not intersect. Thus in a single column of air both temperature and pressure decrease uniformly with height.

Chart datum: the datum to which to which levels on a nautical chart and tidal predictions are referred. In recent years, where tides are semidiurnal, chart datum has been defined as lowest astronomical tide.

Coriolis effect: an apparent force due to measuring fluid motion with respect to the rotating earth rather than with respect to a constant velocity axis system.

Current blockage factor: a factor incorporated into current force calculations which varies according to heading and takes account of the affect on currentspeed of the structure itself.

Current profile: the variation in current speed and direction between the sea bed and the surface.

2-108 Floatmg structures: a g u ~ d e for destgn and analysts

Beaufort Number Descriptive Term Mean wind speed Mean wind speed Probable mean (knots) (m/s) wave height (m)

0 C alrn less than 1 less than 0.5 0.0

1 Light air 1-3 0.5-1.7 0.1

2 Light breeze 4-6 1.8-3.3 0.2

3 Gentle breeze 7-10 3.4-5.4 0.6

4 Moderate breeze 11-16 5.5-8.4 1 .O

5 Fresh breeze 17-21 8.5-1 1.0 2.0

6 Strong breeze 22-27 11.1-14.1 3.0

7 Near gale 28-33 14.2-17.2 4.0

8 Gale 34-40 17.3-20.8 5.5

9 Strong gale 4 1-47 20.9-24.4 7.0

10 Storm 48-55 24.5-28.5 9.0

11 Violent storm 56-63 28.6-32.6 11.5

12 Hurricane 64 and over 3 2.7 and over 14.0

Table 2.1 1 Beaufort Wind Scale

Cyclone: a circulation; anti-clochse (clockwise) in the northern (southern) hemisphere; around a region of low atmospheric pressure. See also depression and tropical cyclone.

Depression: the more common name for a cyclone in temperate latitudes.

Ebb tide: that part of the tidal cycle when water level is falling and water moves away from shore or down a river. Tidal currents will normally set parallel to the coastline.

Eulerian current: fluid flow past a fixed point as measured, for example, by a moored current meter.

Flood tide: that part of the tidal cycle when water level is rising and water moves towards the shore or up a river. Tidal currents will normally set parallel to the coastline.

Front: the leadmg edge of an advancing cold (warm) air or water mass displacing a warmer (cooler) air or water mass.

Geostrophic wind: the motion of air above the friction layer in the atmosphere such that the pressure gradient force and the Coriolis effect are in equilibrium.

Harmonic analysis: the representation of tidal variations as the sum of several harmonics, each with different period, amplitude and phase.

High water: the maximum water level reached during a tidal cycle.

The environment 2-109

Highest astronomical tide: the maximum possible high water.

Isobar: a line joining points having the same atmospheric pressure.

Knot: one nautical mile per hour (0.5 15 dsec) .

Lagrangian current: the movement through space of a particle of fluid (as measured by monitoring the movement of a float).

Latent heat: the quantity of heat absorbed or emitted, without change of temperature, during a change of state of unit mass of a material e.g. from liquid to vapour.

Low water: the minimum water level reached during the tidal cycle.

Lowest astronomical tide: the lowest possible low water.

Mean high water springs: average spring tide high water level averaged over a long period.

Mean higher high water: average of the hlgher of two high waters which occur during a (two peaked) tidal cycle averaged over a long period.

Mean low water springs: average spring tide low water level averaged over a long period.

Mean lower low water: average of the lower of two low waters which occur during a tidal cycle averaged over a long period.

Mean sea level: the arithmetic mean of water levels measured at hourly intervals over a long period.

Nautical mile: one minute of arc of latitude which is a variable distance due to the non-uniform shape of the Earth. The international nautical mile is 1852 metres (6076.12 feet or 1.15 1 miles). Minor variations are the British Adrmralty nautical mile which is 6080 feet while the U.S.A. nautical mile is 6080.2 1 feet.

Neap tides: name given to the tides of smallest range which occur twice a month.

Return period: the predicted average interval between successive extreme events.

Spring tides: name gven to the tides of largest range which occur twice a month when the moon is either new or full.

Squall: a sudden increase in wind speed by at least 8 m/s (1 6 kt), the speed rising to 1 1 m/s (22 kt) or more and lasting for at least one minute.

Squall line: a narrow band of convectional storms such as showers or thunderstorms. - Storm surge: a large scale change in water level with associated currents due to the effects of wind stress and atmospheric pressure.

Storm tide: the combination of storm surge with astronomical tide.

Tidal cycle: the variation in water level and current caused by astronomical forcing. Meteorological forcing in the form of storm surges can further affect both water levels and current speed and direction.

Tidal wave: tides may be considered to propagate as long waves where wavelength is long compared to water depth. However waves associated with seismic effects are called Tsunamis.

2-1 10 Floating structures: a guide for design and analysis

Tropical cyclone: an intense cyclone of the tropics with regional names: hurricane in North Atlantlc and Northeast Pacific, typhoon in Northwest Pacific and cyclone in the Indian Ocean.

Tsunami: long waves generated by submarine landslides for example which are triggered by seismic effects. 3 .k

Turbulence intensity: the standard deviation of wind speed normalised by the mean wind speed over one hour i Wave kinematics factor: a factor incorporated into wave force calculations which varies inversely with directional wave spreading.

--

Description of the height of sea waves Height in metres

Calm - glassy 0

Calm - rippled 0 - 0.1

Smooth wavelets 0.1 - 0.5

Slight 0.5 - 1.25

Moderate 1.25 - 2.5

Rough 2.5 - 4.0

Very rough 4.0 - 6.0

High 6.0 - 9.0

Very high 9.0 - 14.0

Phenomenal over 14.0

Table 2.12 Terminology used to describe the height of sea waves( WMO Sea State Scale: see UK Meteorological Office ,1977)

- -

Length of swell waves Length in metres Height of swell waves Height in metres

short 0 - 100 low 0 - 2

average 100 - 200 moderate 2 - 4

long over 200 heavy over 4

Table 2.1 3 Terminology used to descr~be the length and height of swell waves

The env~ronment 2-1 11

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2-1 14 Floating structures: a gu~de for design and analysis

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2-1 24 Float~ng structures: a guide for design and analysis

Annex 2A Data sources

Introduction

Each of the following sections refers to a particular type of environmental data or product and gives a list of codes which refer to a supplier in the list below. Additionally after the address of each supplier the numbers in [ ] refer to the data types which can be obtained from the same supplier using the following codes:

winds waves currents water levels ice and snow soils temperature marine fouling information on reliability assessment

N.B. The list of suppliers has been compiled following ana[vsis of a questionnaire circulated to the participants of this book. The list of suppliers is b-v no means exhaustive and is not intended to imply any recommendation or approval of the services supplied by the organisations mentioned nor is the fact that a particular supplier is not mentioned intended to imply any criticism of the products or services which ma-y be ooffered b-y such a supplier.

Winds

Waves

Currents

Water levels

Ice and snow

Soils (geology)

Temperature

The env~ronrnent 2-1 25

Marine fouling

Information on reliability assessment

Sources of environmental data

(Al) Aberdeen University Marine Studies Ltd., AURIS Business Centre, 23 Machar Drive, Aberdeen AB2 1RY.[8]

(A2) AEA Technology, Petroleum Services, Harwell, Didcot, Oxfordshire, OX1 1 ORA.[9]

(A3) ASA Consulting Ltd. PO Box 2025, Dartmouth, Nova Scotia, B2W 3x8, Canada. [3]

(A4) ASL Environmental Sciences Ltd., 1986 Mills Road, R.R.2, Sidney, British Columbia, V8L 3 s 1, Canada. [3 I

(B 1) Bedford Institute of Oceanography, Fisheries and Oceans Canada, PO Box 1006, Dartmouth, Nova Scotia, B2Y 4A2, Canada. [I235781

(B2) BMT Fluid Mechanics Limited, Orlando House, 1, Waldegrave Road, Teddington, Middlesex, TWl1 8LT. [I234571

(B3) British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 OET. [57]

(B4) British Geological Survey, Murchison House, West Mains Road, Edinburgh EH9 3LA. [6]

(B5) British Oceanographic Data Centre, Proudrnan Oceanographic Laboratory, Bidston Observatory, Birkenhead, Merseyside L43 7RA. 12341

(Cl) Canadian Hydrographic Service, 615 Booth Street West, Ottawa, Ontario, KIA OE5, Canada. [4]

(C2) CANATEC Consultants Ltd., #1730, 700 - 6th Avenue SW, Calgary, Alberta, T2P OT8 Canada. [57]

(Dl) Dames & Moore, Booth House, 15-17 Church Street, Twickenharn, Middlesex, TWI NJ. [68]

(D2) Danish Geotechnical Institute, 1 Maglebjergvej, PO Box 1 19, DK-2800 Lyngby, Denmark. [6]

(D3) Danish Hydraulic Institute, Agern Alle 5, DK-2970 Horsholm, Denmark. [I2341

(D4) Delft Hydraulics, PO Box 152, 8300 AD Ernrneloord, The Netherlands. [I2341

(D5) DNV - Technica Ltd., Lynton House, 7- 12 Tavistock Square, London WC 1H 9LT. [9]

(D6) Dovre - SikteC, PO Box 4163, Granasveien 3,7048 Trondheim, Norway. [9]

(El) Environment Canada, Atmospheric Environment Service, 4905 Dufferin Street, Downsview, Ontario, M3H 5T4 Canada. [17]

2-126 Floating structures: a gu~de for des~gn and analysis

(E2) Environment Canada (Ice Centre), Atmospheric Environment Service, 373 Sussex Drive, Block E, Ottawa, Ontario, KIA OH3, Canada. [5]

(F 1) Fugro Mclelland, 18 Frogmore Road, Hemel Hempstead. [68]

(Gl) Geological Survey of Canada, Atlantic Geoscience Centre, PO Box 1006, Dartmouth, Nova Scotia, B2Y 4A2, Canada. [6]

(G2) GEOS, Hargreaves Road, Groundwell Industrial Estate, Swindon, Wiltshire, SN2 5AZ. [I23456781

(G3) A.H. Glenn and Assoc., Lake Front Airport, P.O. Box 26337, New Orleans, Louisiana 70126, U.S.A. [I234571

(HI) HR Wallingford Ltd., Howbery Park, Wallingford, Oxfordshire, OX10 8BA. [234]

(I 1) Institute for Engineering in the Canadian Environment, National Research Council Canada, Cold Regions and Thermal Engineering Program, Montreal Road Campus, Ottawa, Ontario, K1A 0R6, Canada. [5]

(12) Institute for Marine Dynamics, National Research Council Canada, Memorial University Campus, PO Box 12093, Station A, St. John's, Newfoundland, A 1 B 3T5, Canada. [5]

(13) Institute of Ocean Sciences, Fisheries and Oceans Canada, PO Box 6000, 9860 West Saanich Road, Sidney, British Columbia, V8L 4B2, Canada. [I2351

(Kl) KNMI, Bureau Marine Affairs, PO Box 201, 3730 AE De Bilt, The Netherlands. [1237]

(Ml) MacLaren Plansearch (1991) Limit4 Suite 200, Park Lane Terraces, 5657 Spring Garden Road, Halifax, Nova Scotia, B3J 3R4, Canada. [I234571

(M2) Marine Environmental Data Service, Fisheries and Oceans Canada, 1202-1220 Kent Street, Ottawa, Ontario, KIA 0E6, Canada. [2]

(M3) Met. Office, Marine Advisory & Consuitancy Service, Johnson House, London Road, Bracknell, Berkshre, RGl2 2SY [I23571

(M4) Metocean plc, Hamilton House, Kings Road, Haslemere, Surrey, GU27 2QA. [I2341

(Nl) National Hydrology Research Centre, 11 Innovation Boulevard, Saskatoon, Saskatchewan, S7N 3H5, Canada. [4]

(N2) National Oceanographc Data Center, User services Branch, NOAALNESDIS, E/OC2 1, SSMC3,4th Floor, 13 15 East-West Highway, Silver Spring; Maryland 209 10-3282, U.S.A. [12347].

(N3) Noble Denton Consultancy Services Limited, Noble House, 13 1, Aldersgate Street, London EC 1A 4EB. [I23456791

(N4) Norwe~an Hydrotechnical Laboratory (NHL), PO Box 4 1 18 - Valentinlyst, 700 1 Trondheim, Norway. [I2341

(Nj) Det Norske Meteorologiske Institutt (Environmental Data Centre), PO Box 43,Blindern 0313 Oslo 3, Norway. [I234571

(N6) Norwegan Petroleum ~irectorat; (NPD), PO Box 600,4001 Stavanaer, Norway [I23481

( N 7 ) Det Norske Veritas, PO Box 300: N-1322 Hovik: Norway. [I2341

The env~ronment 2-1 27

x ttorgcs Geotekn~ske lnstitutt (Norweg~an Geotechmcal Inst~tute). PO Box 3930, Ullevaal Hageby,0806 Oslo. Norway [ 61

(0 I ) Oceanweather Inc., Suite One, 5, Rwer Road, Cos Cob, Connecticut, 06807 USA. [ 12341

( 0 2 ) Oseanografisk Datasenter (Oceanographic Data Centre, Ocean Research Centre), Havforskningssenteret, Nordnesparken 2,5005 Bergen, Norway. [3]

(04) Oceanor, PO Box 25 14,7002 Trondheim, Norway. [I2341

(05) Oceanroutes (UK) Ltd., Swire House, Souterhead Road, Altens, Aberdeen, AB1 4LF. El234571

(P I ) Paras, 120a, High Street, Newport, Isle of Wight, PO30 ITP. [I234571

(P2) Polarinstituttet (Norwegian Polar Institute), Rolfstangveien 12, 1330 Oslo Lufthavn, Norway. [57]

(S 1) Scandpower, Gaseviveien ,2007 Skedsmo, Norway. [9]

For the United fingdom Meterological Office - see Met. Office (M4).

(U I ) United States Naval Oceanographic Office 1 Defence Mapping Agency Hydrographic/Topographic Center, Washington, D.C. 203 15, U.S.A. [234]

Guidelines, codes and other publications

Bales S.L., Lee W.T. and Voelker J.M., 1981, Standardised wind and wave environments for NATO operational areas, DTNSRDC Report SPD-09 19-0 1.

Barltrop N.D.P. and Adam A.J., 1991, Dynamics of Fixed Marine Structures, 3rd edition, MTD Ltd and Butterworth Heinemann.

CANICSA-S471-92, General Requirements, Design Criteria, the Environment and Loads; Forms part 1 of the CSA Code for the Design, Construction and Installation of Fixed Offshore Structures.

Carter, D.J.T., Challenor P.G., Ewing J.A., Pitt E.G., Srokosz M.A. and Tucker M.J., 1986, Estimating wave climateparametersfor engineering applications. Dept. of Energy Offshore Technology Report OTH 86 228. London HMSO.

U.S. Department of Commerce, National Data Buoy Center, 1990, Climatic Summariesfor NDBC Buoys and Stations (update I ) , U.S.A.

Det Norske Veritas, 1991, Environmental Conditions and Environmental Loads, Classification Notes no. 30.5.

Hogben N,, Dacunha N.M.C. and Olliver G.F., 1985, Global Wave Statistics, British Maritime Technology Limited, Unwin Brothers Ltd. (Also available as a PC database from BMT Fluid Mechanics Limited.)

Lee, W.T., Bales, S.L. and Sowby, S.E. 1985, Standardised wind and wave environments for North PaciJic Ocean areas, .DTNSRDC Report SPD-09 19-02.

Hydrographer of the Navy, 1987, Ocean Passagesfor thc World, NP 136, Taunton.

MTD Ltd, 1992, Appraisal ofMarine Growths on Offshore Installations.

2-1 28 Floating structures: a guide for design and analys~s

Norwegian Petroleum Directorate, Acfs, Regulations and Provlszons for the Petroleum Activities

Norwegian Petroleum Directorate, Guidelines concerning loads and load effects to regulations concerning loadbearing structures in the Petroleum Activities.

HSE Books, 1995, Offshore Installations: guidance on design, construction and certijcation, consolidated edition.

API, 1993, Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms - Load and Resistance Factor Design. API RP 2A-LFRD. American Petroleum Institute, 1st edition.

API, 1993, Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms - Worhng Stress Design. API RP 2A-WSD. American Petroleum Institute, 20th edition.

Lloyds Register of Shipping, 1989, Rules and Regulations for the Classijcation ofFixed Offshore Installations, Part 3: Environmental and Design Considerations.

Veritas Marine Operations, 1985, Standard for Insurance Warranty Surveys in Marine Operations.

Naval Oceanography Command Detachment, U S . Nmy Marine Climatic Atlas of the World (10 volumes published over several years), Asheville, N.C., U.S.A.

Annex 2B Summary of rules, guidance and recommended practice

This section describes and compares various rules. It must not be used for design purposes - the original documents should be referenced.

2B.1 Health & Safety Executive

Offshore Installations: Guidance on design, construction and certification. Originally published under the drection of the UK Department of Energy, responsibility for the document passed to the Health & Safew Executive and it was then superseded by Safety Case legislation (see Annex 1C). Section 1 1 'provides guidance on the metocean parameters to be considered when designing an offshore installation'. Inhcative values of parameters are presented in the form of contour maps which cover the whole North Sea, Irish Sea and parts of the Atlantic Ocean which include the United Kingdom continental shelf (UKCS). Additional mformation is given in two background documents (OTH 89 299 and OTH 89 300). The metocean parameters described are not necessarily appropriate for marine transportation or towage to location.

Winds - the reference parameter is the 50-year return ornni-directional hourly-mean wind speed at 10 m above still water level and a contour map shows values for the UKCS and adjacent areas. A formula is given to convert 50-year return wind speed to values with other return periods. Tables are presented which allow estimation of gust wind speeds and 50-year return wind speeds of durations longer than one hour. Further tables allow the calculation of hourly, 1 -minute, 15-second and 3-second winds at 20 metre height intervals to 140 m.

The mean profile with height, of hourly mean wind speed, can be calculated from the information given as a power law with an exponent approximately equal to 0.12. Also approximate factors can be calculated to convert hourly mean wind speed at 10 m above sea level to wind speeds averaged over shorter time intervals.

In addition directional and seasonal coefficients are given for a number of representative areas around the UK whch may be applied to the reference parameter. These coefficients were derived by analysis of observations of wind speed and duection made &om shps of passage and the techniques employed are described in the supporting document OTH 89 299 (1990).

The envtronment 2-129

Waves - The reference parameter is the 50-year return significant wave height H,,, and a contour map shows values for the UKCS and adjacent areas. It is recognised that the maximum response of a compliant structure may be developed in response to waves other than the extreme amplitude design wave. Also pointed out is that fatigue life will be dependent on waves of more moderate amplitude which have a much higher frequency than extreme waves.

Wave energy spectra, which may be used both for design and fatigue calculations, are considered and expressions are given for the generalised Pierson-Moskowitz spectrum in terms of H, and T, for locations in open ocean and for the JONSWAP spectrum in terms of H, and T, for fetch limited growing seas in the absence of swell.

Water levels - the reference tidal parameter is the spring tidal amplitude which has been calculated as the sum of the amplitudes of the principal lunar and principal solar harmonic tidal constituents. Values of spring tidal amplitude are presented in contour form on a map of the U.K. continental shelf. Using data derived at coastal tide measuring stations, coefficients have been calculated which allow various required tidal levels to be calculated for offshore locations in the general area of the coastal site.

The reference storm surge parameter is the 50-year return positive storm surge elevation. Values of this parameter are presented as a contour map of the UKCS.

30-year extreme still water level (the combined rise in water level due to both tide and storm surge) may be calculated using further coefficients calculated from data derived from coastal tide measuring stations.

A safety margin of 1.5 metres is to be included in the calculation of air gap with respect to the design extreme crest elevation superimposed on the extreme still water level.

Currents - the current at any location and time is the vector sum of the harmonic constituents of the tide and any other current which cannot be resolved into periodic harmonic constituents. This latter category is termed the residual current and consists of varying contributions from storm surge, wind stress, internal waves, inertial currents, fiontal currents and general circulation. Contour maps and formulae are presented which allow location specific estimates of current profile with depth to be estimated whch includes tidal, surge and wind driven effects. The vertical structure is taken to be a block profile with a 1/7 power law decay below mid-depth to represent the effect of seabed hction. At the surface the imrndate effect of wind stress is assumed to generate a highly sheared current in the upper few metres of the sea with a maximum depth of 10 metres. The wind driven current at the surface is assumed to be equal to 3 per cent of the hourly mean wind speed or the surge current, whichever is the greater. Some directional mformation is available for currents but this is insufficient for estimating the complete directional distribution of current speed for a location.

Temperatures - Contour maps show the probable extreme maximum and minimum air and sea temperatures over the UKCS.

Snow and ice - A table shows the extreme snow and ice accumulations on offshore installations in UK designated waters. Values are gven for thickness and density for wet snow, ice from freezing sea spray and ice from frozen snow for different parts of a typical platform at different latitudes.

Marine growths - A table shows the growth characteristics of common marine fouling species.

Combination ofextreme parameters - some advice is gwen on extreme surface elevation, extreme fluid velocity, extreme temperatures combined with extreme wind speed and wave height and extreme snow and ice combined with extreme wind speed. Further dscussions on these points is gwen in the supporting documents (OTH 89 299).

2-1 30 Floatmg structures: a gu~de for design and analys~s

2B.2 American Petroleum Institute

Recommended practices Recommended practice RP 2A-WSD contains engineering design principles and good practices that have evolved during the development of offshore resources. RP 2A-LRFD provisions have been developed from the WSD provisions using reliability based calibration and with regard to environmental considerations the two are the same although the two books use different section labelling conventions. Recommended practice RP 2FP 1 contains a rational method for analysing, designing or evaluating mooring systems used with floating production systems. Users of the documents are urged to become familiar with the scope and content of each document and it is pointed out that the publications are intended to supplement rather than to replace good enpeering judgement. Although RP 2FP1 deals specifically with moored floating structures the fixed structure documents are also considered because the mformation about environmental parameters is more comprehensive in RP 2A-WSD and RP 2A-LRFD.

Recommendedpradice for planning, designing and constructing fuced offshore platforms - working stress design (MI RP 2A- WSD) Section 1 concerns planning, pointing out that the initial planning should include the determination of all the criteria upon whlch the design of the platform (or other structure) will be based. Operational considerations are also stressed which include location, onentation and water depth.

Section 2 is entitled 'Design criteria and procedures' and con- much information on environmental parameters. It contains a table (labelled 2.3.4-1) which presents guideline values of wind speed, maximum individual wave height, wave steepness and storm tide (defined as the mean higher high water plus storm surge associated with the individual maximum wave height) for 20 areas around the United States of America where offshore engineering takes place. These areas include the Gulf of Mexico, west and east coasts of the United States and several areas around the coasts of Alaska. For the Gulf of Mexico north of 27' N and west of 86' W a more detailed treatment is presented which includes information on the variation with location water depth of design wave height, design storm tide and design deck height. It also includes information on the directionality of waves and currents associated with hurricanes (tropical cyclones in the Gulf of Mexico).

Winds - the reference parameter is the 100-year return omni-directional hourly mean wind speed at 10 m above still water level. A distinction is drawn between the wind speed associated with the occurrence of the 100-year return maximum indvidual wave height and the 100-year return maximum wind speed considered alone. A table of gmdehe wind speeds for all 20 areas of the United States shows considerable differences between the former and the latter. No directional information is provided for winds and this is recognised as being conservative.

Waves - The reference parameter is the 100-year return maximum individual wave height. An approximate relationship is provided for calculating significant wave height. Guideline design wave directions and height factors may be applied to omnidirectional wave heights for the Gulf of Mexico north of 27W, and west of 86' W. Directional information is not available for other areas.

Wave kinematics are determined using a suitable wave theory as chosen from a diagram illustrating the applicability of various theories. The concept of a wave hematics factor is introduced whereby hurricane induced wave forces are treated differently to other wave forces because waves generated in hurricanes are short crested compared to other waves. There is also a 'Commentary on wave forces' section which includes discussion on aspects of wave forces including wave-current interaction and directional wave spreading.

Fatigue analysis is covered in Chapter 5 and also in a separate commentary. Fatigue analysis requires the dehtion of the long-term wave climate whlch may be in terms of representative sea-states characterised by wave energy spectra and physical parameters together with a probability of occurrence. Various formats for data are suggested such as H, versus T, scatter diagrams (2 parameter format) which could include directionalih and wave spreadmg function if available (3 and 4 parameter format respectively). The inclusion of separate wind sea and swell mformation results in an 8 parameter fom~at. Sophisticated: site specific wave climate information such as ths is likely to require considerable time and effort to acquire.

The env~ronrnent 2,-131

Cturer 1evel.s - Gudeline storm tide versus water depth information is given for the Gulf of Mexico north of 27" 2 . and west of 86" W. Stress is laid on the importance of designing sufficient deck clearance to avoid the possibility of waves striking the deck andlor equipment. A safety margin of 5 feet (1.5 m) is suggested for the air gap calculation.

Currents - Guideline design current profile (together with current direction for shallow water sites) is given for the Gulf of Mexico north of 27' N, and west of 86' W with surface current in deep water equal to 2.1 knots. The profile has a block structure in the upper, mixed layer down to 200 feet (6 1 m) depth. Current speed reduces linearly by 1.9 knots at 300 fed (91 m) and is fixed in deeper water. For other areas an 'open shelf value is given for the surface together with a range and the same shape profile as proposed for the Gulf of Mexico may be used to give a 'crude' approximation.

ICE - In areas where ice is expected to be a consideration reference should be made to API Bulletin 2N.

Marine growths - Information is gwen on marine growth in the Gulf of Mexico but no detailed information is given for any other areas and a location specific study is recommended.

Recommendedpradice for design, analysis and maintenance of moorings for floating production systems. (MI RP 2FPI) Section 1 is entitled 'Basic Considerations' and gives a review of the various types of floating structure whlch exist. It also draws attention to the difference in approach when desigrung for a floating production system (FPS) compared to a mobile dn lhg unit (MODU). In particular the design environment for the latter is specified as the 99.9 percentile environment whereas for the former it is the 100-year extreme. The 99.9 percentile environment is expected to occur for 0.1 percent of the time each year (8.8 hours) on average.

Section 3 is entitled 'Environmental Criteria' and gwes a description of the aspects to be considered. In particular it is recommended that for FPS two sets of environmental criteria are considered wluch are (i) the 100-year waves with associated winds and currents and (ii) the 100-year wind with associated waves and currents. In addition it is suggested that the most severe directional combination of wind, wave and current forces should be specified consistent with the environmental conditions to be experienced at the site. It is quite possible that extremes of wind and wave may approach a site from different directions so that weathemming of a FPS may expose it to higher loads than would be the case if winds and waves act in the same direction simultaneously.

Winds - The effects of winds may be assessed in two ways which are (i) as a constant in which case the wind speed should be taken as the extreme 1-minute mean wind speed or (ii) as a fluctuating force based on the extreme 1-hour average velocity together with a time-varying component calculated from a suitable empirical wind gust spectrum. It is pointed out however that wind.gust spectra are rarely known accurately and that spectra typical of offshore locations may contain rather more low frequency energy (frequencies typical of the natural periods of floating structures) than is the case on land where most empirical spectra have been defined. Formulae are given for calculating wind force averaged over a vertical area and wind force height coefficients are shown which vary with the height of the centroid of the area (see Annex 2C).

Waves - It is emphasised that the wave data used to determine the design should include measured and accurate hindcast data if available. The wave height and period relationship is of utmost importance since period can simficantly affect surge and sway amplitudes and mean drift forces. A diagram indicates that for the same wave height, swell wave periods are approximately 40% higher than wind driven wave periods.

Mention is made of first and second order forces and steady components of second order forces which are associated with waves and arise because of the interaction between floating structures and waves. This only serves to emphasise the importance of obtaining accurate wave period information.

When it is required to calculate the number of waves in the design storm the duration is usually taken as 3 hours but in areas with long storm durations, such as areas subject to monsoons, a longer duration should be specified.

2-132 Floating structures: a guide for design and analysis

Miscellaneous - Environmental effects can be divided into three categories:

steady state'forces including current force, mean wind and mean wave drift forces, low frequency vessel motions due to wind and waves, wave frequency vessel motions.

Fatigue analysis is conducted by comparing long term cyclic loading in a mooring component with the resistance of that component to fatigue damage. For mooring systems a T-N approach is normally used. The T-N approach uses a T-N w e , which gives the number of cycles to failure for a specific mooring component as a function of constant tension range based on the results of experiments. The long term environment is described in terms of a number of design conditions comprising sea state plus wind velocity and current velocity by direction. The probability of occurrence of each design condition must be specified.

2B.3 Det Norske Veritas Classification AIS

Rules for Classification of Fixed Offshore Installations Rules are continually updated and amended and contain basic environmental information. Fixed offshore installations are to be designed for the environmental conditions causing the 100 year load effect in the ultimate limit state (ULS) condition unless a more appropriate return period can be justified on the basis of an approved risk analysis. -Extreme values of wind, waves and current are assumed to occur simultaneously and in the same direction in the absence of information to the contrary.

Rules for Classification of Mobile Offshore Units The specdied environmental design data used for calculating design loads for intact structure are to correspond with the most probable largest values for a return period of 100 years. For damaged structure calculations a return period of 1 year is to be used.

Environmental Conditions and Environmental Loads - Classification Notes No. 30.5 - March 1991 This publication contains a comprehensive summary of formulae and data items describing environmental conditions and loads. It particularly deals with wind, wave and current parameters which are always important offshore but also includes information on ice, earthquake, soil conditions, temperature, fouling, visibility and tides. The publication is not regon specific and does not include regulations specific to the waters of one counm.

Knds - In general the reference averaging period of the wind is taken as 10 minutes and the reference height is 10 metres above sea level. The average wind speed and profile with height may be estimated using a formula, for hourly mean wind speeds the mean profile up to 100 metres can be approximated with a power law and an exponent of 0.128. No directional information is available.

Waves - The lunematics of regular waves may be described by analytical or numerical wave theories and the following are recommended according to the ratio of water depth (d) over wave length (L).

d/L F 0.1 Solitary wave theory 0.1 F d/L s 0.3 Stokes 5th order wave theory 0.3 s d/L Linear wave theory (or Stokes 5th order)

It is normally sufficient to consider regular wave periods (73 in the range

,~%<T<TH

where His the crest to trough wave height in metres. It is pointed out that maximum loads may not be associated with extreme sea states particularly in the case of floating structures.

The environment 2-1 33

Short term irregular sea states may be described by a wave spectrum; i t . the power spectral density function of the vertical sea surface displacement. For open ocean the Pierson-Moskowitz spectrum is generally applied while for fetch limited growing seas without swell the JONSWAP spectrum is normally used. Directional wave spectra (short-crested waves) may be used if such effects are found to be appropriate for location and design. It is normally sufficient to consider peak energy period (T,) in the range

,jlnq<~~< J2sy (2.132)

where H, is the significant wave height. In an irregular, short-term stationary sea state in deep water the highest crest elevation is approximately equal to H, and the highest individual crest to trough wave height is approximately equal to 1 .8Hs. Long term wave statistics are calculated separately using one or more of three formulae and include consideration of geographical location (which determines formulae parameters) and storm duration.

Current - When detailed field measurements are not available the current profile may be taken as the sum of tidal current plus wind generated current. Tidal current is subject to 1/7 power exponential decay over the whole water column while wind generated current decays linearly fi-om 1.5 per cent of the hourly mean wind speed at still water level to zero at 50 metres depth. Other types of currents should also be included if appropriate.

Water levels - Design still water level is generally taken as highest astronomic tide level plus storm surge. The still water level to be utilised in wave load calculations for storm conditions could be the lowest astronomic tide level if this is more unfavourable for the structure.

2B.4 American Bureau of Shipping, Bureau Veritas and Lloyd's Register

These three classification societies include some environmental information in their respective rules and regulations. A number of items are common to all three such as the requirements for unrestricted offshore operation.

Wnds - For unrestricted offshore operation the unit must be able to withstand a sustained'wind speeds up to 36 mls during normal operations and transit and up to 5 1.5 m/s in the survival condition. Classification for restricted service is associated with a sustained wind speed of 25.8 m/s. ABS and Lloyd's Register provide a table of coefficients for calculating wind force at various heights (see Annex 2C) while Bureau Veritas suggest a power law with different exponents corresponding to the averagmg period of the wind speed.

Waves - All three classification societies propose that waves may be specified by wave energy spectra or deterministically by means of shape, height and period. All specify that the most unfavourable direction should be identified for wave loading and that combinations of height and period other than that of the maximum wave should be considered where, because of wave period, the effect on the structure may be greater. Bureau Veritas suggest that the maximum significant wave height which need be considered is 17 m (corresponding to a maximum individual wave height of 3 1.5 m).

Bureau Veritas have sections on the spectral formulation of waves with a discussion on the use of JONSWAP and the Pierson-Moskowitz spectra and the long term dstribution of sea states and individual wave heights. Some relationships between parameters of Weibull distributions are given. In the absence of any data a distribution of significant wave height and a conditional distribution of zero-up crossing period given significant wave height is provided.

Current - ABS define the current velocity to include components due to tide, storm surge and wind stress. A theoretical profile is suggested showing a sheared surface layer and in the presence of waves the current velocity at the instantaneous f?ee surface is assumed constant. Bureau Veritas define tidal current profile with a power law and exponent of 117 while wind driven current defined as 0.02(10 minute mean wind speed at 10 m) has a rectangular profile.

2-134 Floating structures: a guide for design and analys~s

Other fadors - Maximum and minimum temperatures of air and water and icing and ice and snow loads where appropriate should be considered.

Annex 2C Formulae derived from rules, guidance and recommended practice

The rules, regulations and recommended practices contain a wealth of information which was reviewed in section 2.2. In that section documents were described individually with the intention of establishing a pattern of requirement for environmental information. However the documents are also a source of environmental information in themselves and in particular a number of relationships are given for manipulating data. Some of these relationships and the numbers associated with them become well known throughout the industry and below some of the more commonly used relationships are reproduced with appropriate references. Tables are given which interpret and compare results from the formulae provided in the original publications.

Winds

Several publications reproduce a table showing the coefficient to be applied to the reference wind speed at standard height which will generate wind speed at some other height (ABS, LR, API RP2P).

Height (metres) Height (feet) Coefficient

Table A.1 Table of coefficients to obtain wind speed at a height other than the reference height

The env~ronrnent 2-135

/ , GI \ cn a reference wmd speed and averaging perlod appropriate to a standard he~ght (z ,) ~t 1s often necessq to estmate wmd speeds wlth certam averagmg perlods or at different heights.

Coefficient to use hourly 10 minute 1 minute 15 second 5 second 3 second with hourly mean mean mean mean gust gust gust

wind speed

HSE 1 .OO 1.04 1.18 1.29 1.36 1.40

Coefficient to use hourly 10 minute 1 minute 15 second 5 second 3 second with 10 minute mean mean mean gust gust gust

mean wind speed

DNV 0.92 1 .OO 1.1 1 1.17 1.23 1 .25

Table A.2 Summary of coefficients to apply to reference wind speed to obtain gust speed

Waves

The relationshlp between s ipf icant wave height (H,) and maximum wave height (H,,,,) is often required. The range of value shown below from API RP2A reflects the fact that the ratio changes according to storm type.

HSE MI DNV BV

Hm, H, 1.86 1.7 ... 1.9 no single value 1.86

Table A.3 Ratio of maximum individual wave height with a return period of T years to maximum significant wave height with a return period of T years

Current The relationshlp between mean wind speed and wind driven current varies quite substantially but it is important to reahse that in many parts of the world there are significant currents due to oceanic circulation, tide, surge etc. whlch should also be considered.

HSE API DNV

Coefficient to be 0.03 single value of 0.015 0.02 applied to mean current speed

wind speed specified

Table A.4 Coefficient to be applied to mean wind speed in mls to obtain surface current speed in mls