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CEL251 Hydrology

Precipitation

Definition:

The term precipitation denotes all forms of water that reach the earth surface from the

atmosphere. The usual forms are rainfall, snowfall, hail, frost and dew. Precipitation is the

natural stating point for the hydrologic cycle and main input to the hydrologic systems.

Precipitation Process

When the right temperature and pressure conditions exist, water vapour in the atmosphere

will condense to water droplets, water droplets accumulate to large enough size, and the

gravity pulls the droplets to the earth surface as precipitation. For precipitation to occur, some

mechanism is required to cool the air sufficiently to bring it to or near saturation. The large

scale cooling needed for significant amounts of precipitation is achieved by lifting the air. If

the moist air is lifted adiabatically its temperature will decrease, at certain level air become

saturated. Saturation however does not necessarily lead to precipitation. Similarly,

atmospheric moisture is a necessary but not sufficient condition for precipitation. Necessarysteps involved in precipitation formation are

1.) Presence of moisture in the atmosphere

2.) Cooling of the air to the dew point temperature by air lifting mechanism

3.) Condensation on nuclei to form cloud droplets

4.) Growth of droplets into raindrops under favourable weather conditions

5.) Importation of water vapour to sustain the process.

Presence of Moisture in the Atmosphere

Precipitation is derived from atmospheric water vapour. Moisture is always present in theatmosphere even on cloudless days. Atmospheric moisture is derived from evaporation and

transpiration. Atmospheric water mostly exits as gas, or vapour, but briefly and locally it

becomes a liquid in rainfall and in water droplets in clouds, or it becomes a solid in snowfall,

in hail, and in ice crystals in clouds. The fraction of water vapour in the atmosphere is very

small compared to quantities of other gases present, but it is exceedingly important to our

way of life. Also the amount of water vapour in the atmosphere is less than 1 part in 100,000

of all the waters of the earth, but it plays a vital role in the hydrologic cycle.

Humidity and vapour pressure are measures of the amount of water present in the

atmosphere. In any mixture of gases, each gas exerts a partial pressure independent of the

other gases. The partial pressure exerted by water vapour is called vapour pressure(e). It is

measured in: (a) inch or cm of mercury (Hg), (b) millibar (mb), or (c) SI units kilopascals

(kPa) = 1000 N/m2= 10 mb = 0.295 inch Hg. Total air pressure (pa) is the sum of dry air

pressure (pd) and water vapor pressure (e). Water vapor pressure is typically 1-2% of total air

pressure. The maximum amount of water vapour that can exist in any space is a function of

temperature and is practically independent of the coexistence of other gases. When the

maximum amount of water vapour for a given temperature is contained in a given space, the

space is said to be saturated. The pressure exerted by the vapour in a saturated space is called

the saturation vapour pressure (es). At the saturation vapour pressure, the rates of

evaporation and condensation are equal. Condensation occurs when the actual vapour


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pressure exceeds the saturation vapour pressure. An approximate equation widely used for

the saturation pressure esis

+=

T

Tes

3.237

27.17exp78.610

where es is in Pa and T is in C. The slope of the saturated vapour pressure curve can befound by differentiating this equation

2)3.237(

4098

T

e

dT

ed ss

+==

Vapour pressure is one measure of how much amount of water present in the atmosphere:

higher vapour pressure, more water vapour (moister) for a given temperature. Two other

measures of air moisture content are relative humidity and dew point temperature. The

relative humidity (Rh) is the ratio of the actual vapour pressure to its saturation vapour

pressure at a given air temperature ie sh eeR = . In other words it is a ratio or percentage of

the amount of moisture in a given space to the amount the space could contain if saturated.

Thespecific humidityqvis the mass of water vapour per unit mass of moist air and is equals

the ratio of the densities of water vapour v and moist air a ie avvq = .Since

TReTRe dvv 622.0== ; TRep dd )( = and TRep ddva )378.0( =+= so it

can also be given by peepeqv 622.0)378.0(622.0 = , wherep= total pressure exerted

by moist air and 0.622 = ratio of the molecular weight of water vapour to the average

molecular weight of dry air. The dewpoint temperatureTdis the temperature at which space

becomes saturated when air is cooled under constant pressure and with constant water vapour

content. It is the temperature giving an esequal to the existing e. That is why although it is

called dewpoint temperature, it is actually a measure of moisture content. With the known

temperature versus esrelationship, given dewpoint, the actual ecan be determined as

+

=d

d

T

Te

3.237

27.17exp78.610

Psychrometer is used to measurement of vapor pressure. It consists of two identical glass

thermometers in which one has a wet fabric applied to the liquid bulb and a fan blows air

over the thermometers. Dry-bulb thermometer measures air temperature, while the wet-bulbthermometer measures dew point temperature as the wet bulb temperature is reduced due to

evaporation.

( )was ttee =

where ta = dry-bulb temperature C, tw = wet-bulb temperature C, es = saturation vaporpressure corresponding to the wet-bulb temperature, = 66 Pa /C psychrometer constant.

Vaporization removes heat from the liquid being vaporized, while condensation adds heat.

The latent heatof vaporization is the amount of heat absorbed by a unit mass of a substance,

without change in temperature, while passing from liquid to the vapour state. The change

from vapour to the liquid state requires an equivalent amount of heat. The latent heat of

vaporization varies with temperature which is in calories per gram and in joules per kilogram

are

TLhv 564.03.597 = and TLhv 237010501.26 =

respectively wherein Tis in C.


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Cooling of Air by Air Lifting Mechanism

The ideal gas law: RTp = wherep= pressure, = density of gas, T= absolute temperature

K, andR= gas constant (depends on the molecular weight of the gas = 287 J/kg.K for air).

This indicates that there is decrease in pressure with decrease in temperature and density (and

vice versa). Water vapor can be considered an ideal gas. Adiabatic process is one in which

there is no heat exchange with the environment. Adiabatic processes in the atmosphere -when a parcel of air is lifted up, the surrounding pressure decreases and the parcel expand.

According to the ideal gas law, temperature will decrease. Rate of change in temperature with

altitude is known as Lapse rate. An unsaturated parcel of air cools at the dry adiabatic lapse

rate of 10C/1000m. When condensation begins, latent heat is released, partly offsetting the

cooling. The wet adiabatic lapse rate depends on the humidity of the air, but is in the range of

5-9 C/1000m. The actual lapse rate for a given location/time is called Environmental lapse

rate. The average rate of temperature change in the troposphere is 6.5 C/1000m

Air mass may be lifted in the atmosphere by (1) Orographic lifting, (2) Frontal lifting, (3)

Convergence, and (4) Convective lifting mechanisms as shown in Figure.


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In convective lifting there is uneven heating of the

ground and the air just above it. So the warm air

pockets become buoyant and rise and expand due

to decreased pressure and resulting adiabatic

cooling. The moisture is provided by intense

evapotranspiration. For example Surface heated

from T0 to T1 Surface air is warmer than

surrounding air and will rise The rising air will

initially cool at the dry adiabatic lapse rate IF

the condensation level is not reached before point

S, the vertical rise will cease as S and there will be

no precipitation IF

condensation occurs

before point S, air will

cool at the wet adiabatic

lapse rate and continue

to rise and Precipitation

will occur.

Temperature

Altitude

Dry adiabaticlapse rate

Wet adiabaticlapse rate

T0

Condensationbegins

T1

S

Environmentallapse rate


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Condensation on nuclei

Condensation requires a seed called a condensation nucleus around which the water

molecules attach or nucleate themselves. These nuclei are small particles of various

substances usually ranging 10-3

to 10 m (aerosols), products of combustion, oxides of

nitrogen, salt particles, clay/dust minerals. Salt particles are most effective as a condensation

nuclei (Rh = 75%) and clay minerals (kaolin) as freezing nuclei. Pure water droplets may

remain in the liquid state to temperatures as low as -40C.

Growth of droplets into raindrops

Upon nucleation the droplets or ice

crystals grows to visible size in a

fraction of a second through

diffusion of water vapour to it but

growth thereafter is slow.

Diffusion by itself leads only to

fog or cloud elements tend

generally smaller than 10 m in

diameter. While cloud elements

tend to settle, the average element

weighs so little that only a slight

upward motion of air is needed to

support it (0.5 m/s). Ice crystals

can be supported by even lower

velocities. The tiny droplets grow

by condensation and impact with

their neighbours as they are carried

by turbulent air motion until they

become large enough so that the force of gravity overcomes that of friction and then begin to

fall, further increasing in size as they hit other droplets in the fall path. However, as the drop

falls, water evaporates from its surface and the drop size diminishes, so the drop may bereduced to the size of aerosol again and be carried upwards in the cloud through turbulent

action. The cycle of condensation, falling, evaporation and rising occurs on average about

ten times before the drop reaches a critical size of about 0.1 mm, which is large enough to fall

through the bottom of the cloud. Upto 1 mm in diameter the droplets remain spherical in

shape, but beyond this size they begin to flatten out on the bottom until they are no longer

stable falling through air and break up into small raindrops and droplets. Normal raindrops

falling through the cloud base are 0.1 mm to 3 mm in diameter (Vc= 2 8 m/s).

Forms of precipitation

1.) Rain 0.5 mm < d < 6.0 mm; light if intensity < 2.5 mm/h & heavy > 7.5 mm/h

2.) Snow ice crystals into snowflakes3.) Drizzle 0.1mm < d < 0.5mm; intensity < 1mm/h; appear to float in air

4.) Hail balls of ice 5mm


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Measurement of precipitation

Precipitation is expressed in terms of the depth to which rainfall water would remain stand on

an area if all the rain were collected on it. In case of snowfall an equivalent depth of water is

used as the depth of precipitation. The precipitation is collected and measured in a raingauge,

also called hyetometer, pluviometer,

or ombrometer.

A raingauge essentially consists of a cylindrical vessel assembly kept in the open to collect

rain. Raingauges can be broadly classified into two categories as (a) nonrecording raingauges

(Symons) and (b) recording gauges (weighing bucket, tipping bucket, natural syphon type).

Raingauge Network

To get a representative/real distribution of a rainfall event over space and time in a catchment

the number of raingauges should be as large as possible. On the other hand economic

considerations, topography, accessibility, maintenance etc restrict the number of gauges to be

installed. An optimum density of gauges is desired from which reasonably accurate

information about the storm can be obtained. Ten percent of raingauge stations should be

equipped with self recording gauges to know the intensities of rainfall. From practical

considerations of Indian conditions the Indian Standard (IS: 4987-1968) recommends (a)

plains - 1 in 520 km2(b) elevation upto 1000m - 1 in 260 km

2(c) hills - 1 in 130 km

2.

Adequacy of Raingauge Stations

If there are already some raingauge stations in a catchment, the optimal number of stations

that should exist to have an assigned percentage of error in the estimation of mean rainfall is

obtained by

( )2

vCN=

where = % error; Cv= coefficient of variation = Pm 1100 ; P= mean rainfall; m-1=

standard deviation. It is usual to take = 10%. If is smallNwill be large.

Preparation of Data

Before using the rainfall records of a station, it is necessary to first check the data for

continuity and consistency. The continuity of a record may be broken with missing data due


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to many reasons such as damage or fault in a raingauge during a period. The missing data can

be estimated by using the data of the neighbouring stations. In these calculations the normal

rainfall is used as a standard of comparison. The normal rainfall is the average value of

rainfall at a particular date, month or year over a specified 30 year period.

Estimation of missing data

Given the annual precipitationP1,P2,P3, ,Pmat neighbouringMstations andPxat station

xis missing. Further the normal annual precipitation N1,N2,N3, ,NmandNxat eachM+1

stations are known. If the normal annual precipitations are within 10% of the normal annual

precipitationNxat stationX, then a simple arithmetic average can be used

( )mx PPPPM

P ++++= ...1

321

If it vary considerably then normal ratio method be used

+++=

m

mxx

N

P

N

P

N

P

N

P

M

NP

3

3

2

2

1

1

Test for consistency of record

If the conditions relevant to the recording of a raingauge station have undergone a significant

change during the period of record, inconsistency would arise in the rainfall data of that

station. Some of the common causes for inconsistency of record are (a) shifting of a

raingauge station to a new location (b) the neighbourhood of the station undergoing a marked

change (c) change in the ecosystem

due to calamities such as forest

fires, land slides and (d) occurrenceof observational error from a certain

date. The checking for

inconsistency of a record is done bythe double mass curve technique.

This technique is based on the

principle that when each recorded

data comes from the same parent

population, they are consistent. A

group of 5 to 10 base stations in the

neighbourhood of the problem

station X is selected. The rainfall

data of X and the average rainfall

data of neighbouring 10 stations are

arranged in reverse chronological

order and plotted as double mass curve. The decided break in plot of Px versus Pindicates a change in precipitation regime of station X. The data beyond break point is

corrected by slope ratioa

cPP xxc = In this way older records are brought upto new regime of

the station. However the base stations (5 to 10) records must be homogeneous.


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Presentation of rainfall data

Mass curve of rainfall

The mass curve of rainfall is a plot of the accumulated precipitation against time plotted in

chronological order. Mass curve of rainfall is very useful in extracting the information on the

duration and magnitude of a storm. Also, intensities at various time intervals in a storm canbe obtained by the slope of the curve.

Hyetograph

A hyetograph is a plot of the intensities of rainfall against the time interval. The hyetograph

is derived from the mass curve and is usually represented as a bar chart. It is a very

convenient way of representing the

characteristics of a storm and is

particularly important in the development

of design storm to predict extreme floods. The area under a hyetograph represents the total

precipitation received in the period. The time interval used depends on the purpose in urban

drainage problems small durations are used while in flood flow computations in larger

catchments the intervals are of about 6 hour.

Mean precipitation over an area

Raingauges represent only point sampling of the areal distribution of a storm. In practice

hydrological analysis requires a knowledge of the rainfall over an area. To convert the point

rainfall values at various stations into an average value over a catchment the following three

methods are used (a) Arithmetic mean (b) Thiessen polygon and (c) Isohyetal method.

Arithmetic mean

When the rainfall measured at various stations in a catchment show little variation, the

variation rainfall over the catchment area is taken as the arithmetic mean of the station values

==+++

=

n

ii

n

PNN

PPP

P1

21 1....

Theissen polygon Method

In this method the rainfall recorded at each station is given a weightage on the basis of an

area closest to the station

A

AP

AAA

APAPAPP i

n

i

i

n

nn =

=+++

+++=

121

2211

....

....


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where Ai = area bounded by the bisectors

around the raingauge station Pi; Ai/A =

wieghtage factors. It is superior to the

arithmetic average method as some

weightage is given to the various stations

on a rational basis. Further the raingauge

stations outside the catchment are also usedeffectively. Once the WF are determined

for a catchment calculation of the average precipitation is relatively easy for a fixed network.

Isohyetal Method

An isohyetal is a line joining points of equal rainfall magnitude. The average value of the

rainfall indicated by two isohyets is assumed to be acting over the inter isohyet area.

( ) ( ) ( )Aa

A

PPaPPaPPaP

n

i

innn =

++++++=

=

1

1

11322211 2....22

where ai = inter isohyet area; and Pi =

isohyet. This is superior to the other twomethods when stations are large in number.

Weather modification:

Weather modification means to alter artificially the natural meteorological phenomena of theatmosphere. Attempts to increase or decrease precipitation, suppress hail and lightning,

mitigate hurricane, dissipate fog, prevent frost, alter radiation balance etc are included in

weather modification. Cloud seeding is used for either dissipation of the cloud or stimulation

of precipitation. Silver iodide and dry ice are commonly used nucleating agents.

30 mm

25 mm

20 mm

22 mm

10 mm

30 mm

25 mm20 mm15 mm10 mm

A1

A2

A3

A4

A5

P1

P2

P3

P4

P5

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