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ONOSAKPONOME, OGAGA ROBERT
PG/M.ENG/2008/48538
PG/M. Sc/09/51723
COMPARATIVE STUDY OF DIFFERENT METHODS
OF RUNOFF DISCHARGE ESTIMATION FOR
DRAINAGE DESIGN
CIVIL ENGINEERING
A THESIS SUBMITTED TO THE DEPARTMENT OF CIVIL ENGINEERING , FACULTY
OF ENGINEERING, UNIVERSITY OF NIGERIA, NSUKKA
Webmaster
Digitally Signed by Webmaster’s Name
DN : CN = Webmaster’s name O= University of Nigeria, Nsukka
OU = Innovation Centre
OCTOBER, 2009
COMPARATIVE STUDY OF DIFFERENT METHODS
OF RUNOFF DISCHARGE ESTIMATION FOR
DRAINAGE DESIGN
BY
ONOSAKPONOME, OGAGA ROBERT
PG/M.ENG/2008/48538
DEPARTMENT OF CIVIL ENGINEERING
UNIVERSITY OF NIGERIA, NSUKKA
OCTOBER, 2009.
CERTIFICATION
This is to certify that this research is an authentic work of
Onosakponome, Ogaga Robert and has been approved under the supervision
of Engr. (Prof.) J.C. Agunwamba as part of the requirement for the award of
the Master of Engineering in Water Resources and Environmental
Engineering in the Department of Civil Engineering, at the University of
Nigeria, Nsukka.
Engr. (Prof.) J.C. Agunwamba ______________ __________
Supervisor Signature Date
Engr. (Prof.) J.C. Agunwamba ______________ __________
Head of Department Signature Date
____________________ _____________ __________
External Examiner Signature Date
DEDICATION
This work is dedicated to my Lord and saviour, JESUS CHRIST to
whom I will forever remain eternally grateful. The KING OF kings, LORD
of Lords, who also is my life – in HIM I live, move and have my whole
being!
ACKNOWLEDGEMENT
I express my sincere gratitude and thanks to my supervisor and head
of department of civil Engineering, Engr. (Prof.) J.C. Agunwamba for his
concern, advice and contribution to my success. I owe many thanks to my
dearly and wonderful sisters, Mrs. Mercy Lilian Akomah for her care and
financial support.
A special thanks to the engineers and staff members of the department of
physical planning unit, UNN for enabling me obtain a copy of the
topographical map of the UNN campus. I also appreciate the kind gesture of
Mr. Onu and the entire department of crop science, UNN for allowing me
retrieve necessary hydrologic data required for this work. I will not forget to
appreciate the effort of Mr. Eze who contributed immensely to this project.
May the works of your hands be blessed and multiplied in Jesus name
– Amen!
ABSTRACT
This project is a comparative study of the different established empirical and
predictive methods used in the estimation of runoff discharge. A catchment
area was selected within the campus (University of Nigeria, Nsukka) and
data were collected to determine the peak flow (runoff discharge). Observed
peak discharge was compared to discharges computed for each of the
empirical methods discussed. From the results, the unit hydrograph gave the
best estimates, followed by the Khosla`s formula, the rational method was
the last.
TABLE OF CONTENTS
Certification----------------------------------------------------------------------------i
Dedication-----------------------------------------------------------------------------ii
Acknowledgement-------------------------------------------------------------------iii
Abstract--------------------------------------------------------------------------------iv
Table of Contents---------------------------------------------------------------------v
CHAPTER ONE: INTRODUCTION-------------------------------------------1
1.1 Significance of the Research----------------------------------------------2
1.2 Research Objectives--------------------------------------------------------3
1.3 Scope and Limitation of the Research-----------------------------------4
1.4 Description of Catchment area--------------------------------------------4
CHAPTER TWO: LITERATURE REVIEW---------------------------------5
2.1 Runoff------------------------------------------------------------------------5
2.1.1 Sources and components of Runoff--------------------------------------6
2.1.1.1 Channel Precipitation------------------------------------------------------8
2.1.1.2 Overland Flow--------------------------------------------------------------8
2.1.1.3 Interflow---------------------------------------------------------------------9
2.1.1.4 Groundwater flow---------------------------------------------------------10
2.1.1.5 Snowmelt------------------------------------------------------------------10
2.1.1.6 Quickflow and Baseflow-------------------------------------------------11
2.2 Types of stream-----------------------------------------------------------11
2.3 The Runoff Process------------------------------------------------------12
2.3.1 The Horton Runoff Model---------------------------------------------13
2.3.2 The Hewlett Runoff Model---------------------------------------------15
2.3.3 Variable Source Areas---------------------------------------------------16
2.4 Factors Affecting Runoff-----------------------------------------------17
2.4.1 Factors Affecting the Total Volume of Runoff----------------------17
2.4.2 Factors Affecting the Distribution of Runoff in Time--------------18
2.4.2.1 Meteorological factors--------------------------------------------------18
2.4.2.2 Types of Precipitation--------------------------------------------------19
2.4.2.3 Rainfall Intensity and Duration----------------------------------------19
2.4.2.4 Rainfall Distribution ---------------------------------------------------21
2.4.3 Catchment Factors-------------------------------------------------------21
2.4.3.1 Topography--------------------------------------------------------------22
2.4.3.2 Geology ------------------------------------------------------------------24
2.4.3.3 Soil------------------------------------------------------------------------25
2.4.3.4 Vegetation----------------------------------------------------------------26
2.4.3.5 Drainage network--------------------------------------------------------27
2.4.4. Human Factors-----------------------------------------------------------28
2.4.4.1 Hydraulic Structures----------------------------------------------------28
2.4.4.2 Agricultural Techniques------------------------------------------------29
2.4.4.3 Urbanization-------------------------------------------------------------30
2.4.4.4 Severity of Flooding----------------------------------------------------30
2.5 Variations of Runoff----------------------------------------------------31
2.5.1 Areal Variations---------------------------------------------------------32
2.5.2 Seasonal Variations-----------------------------------------------------32
2.5.2.1 Simple Regimes---------------------------------------------------------32
2.5.2.2 Complex I Regimes-----------------------------------------------------34
2.5.2.3 Complex II Regimes----------------------------------------------------34
2.6 Hydrograph---------------------------------------------------------------35
2.6.1 Unit Hydrograph Method-----------------------------------------------37
2.6.2 Construction of Unit Hydrograph -------------------------------------39
2.6.3 Assumptions--------------------------------------------------------------41
2.6.4 Limitations of Unit Hydrograph Method-----------------------------42
2.7 The Estimation, Prediction, and Fore-casting of Runoff------------43
2.7.1 Annual and Seasonal Runoff--------------------------------------------45
2.7.2 Peak Flows-----------------------------------------------------------------46
2.8 Empirical formulae-------------------------------------------------------47
2.8.1 Rational Method----------------------------------------------------------48
2.8.1.1 Assumptions of the Rational Method----------------------------------49
2.8.1.2 Rainfall Intensity (I)------------------------------------------------------50
2.8.1.3 Runoff Coefficient (C)---------------------------------------------------55
2.8.1.4 Catchment Area (A)------------------------------------------------------57
2.8.1.5 Design Computations-----------------------------------------------------57
2.8.1.6 Time of Concentration---------------------------------------------------58
2.8.2 Khosla’s Formula--------------------------------------------------------62
2.8.3 Inglis Formulae for Hilly and Plain Areas-----------------------------62
2.8.4 Lacey’s Formula----------------------------------------------------------62
2.8.5 Statistical Method---------------------------------------------------------63
2.9 Direct Measurement of Runoff -----------------------------------------69
2.9.1 Velocity-Area Method---------------------------------------------------70
2.9.2 Weirs and Flumes---------------------------------------------------------71
CHAPTER THREE: METHODOLOGY-------------------------------------73
3.1 Gauge Stations--------------------------------------------------------------73
3.2 Empirical Formulae--------------------------------------------------------74
3.3 Velocity-Area Method------------------------------------------------------74
3.4 Unit Hydrograph Method---------------------------------------------------75
CHAPTER FOUR: RESULTS AND ANALYSIS---------------------------76
4.1 Unit Hydrographs-----------------------------------------------------------80
4.2 Rational Formulae----------------------------------------------------------82
4.3 Relationship between Estimated and Measured Runoff Discharge- 85
CHAPTER FIVE: CONCLUSION AND RECOMMENDATION -----86
5.1 Conclusion--------------------------------------------------------------------86
5.2 Recommendation------------------------------------------------------------87
References--------------------------------------------------------------------88
Appendices-------------------------------------------------------------------94
CHAPTER ONE
INTRODUCTION
The design of a drainage structure requires hydrologic analysis of
precipitation amount and duration, peak rate of runoff and the time
distribution of runoff from a given basin or catchment. Many hydrologic
methods are available for estimating peak flows (runoff) from a catchment
area, and no single method is applicable to all catchments. There is usually
disparity between measured values and those determined from other
methods, viz; the unit hydrograph method, simulation or the rational method.
Often, extensive hydraulic analysis and design are needed to reduce
the impact of highway and bridge crossings on floodways and drainage,
there is potential for stormwater runoff to create or increase flood and water
quality problems. Many government agencies are trying to mitigate the
increased runoff and diminished water quality associated with transportation
infrastructure through better design of drainage structures. Detention
structures and channel improvements have often helped to manage runoff
volume and maintain water quality. Various types of drainage structures are
necessary to protect human life, highways and highway structures, adjacent
structures, and the flood-plain environment from surface and subsurface
water. Drainage structures are designed to convey water in a manner that is
efficient, safe and least destructive to the highway and adjacent areas.
(Washington State Department of Transportation; 1997).
The VDOT design manual (Virginia Department of Transportation,
2002) recommends that transportation engineers follows several well-
documented, standard engineering methods to estimate runoff volumes and
peak flows from small drainage basins. The appropriate method of
determination of runoff depends on its applicability to the area concerned,
the quantity and type of data available, the detail and accuracy required, and
the importance of the structure. Usually, the unit hydrograph method,
simulation or the rational method is applied (Agunwamba, 2001).
Although, (Agunwamba, 2001), (VDOT, 2002), recommend the use
of the rational method for estimating the design-storm peak runoff from
small basins with areas up to 200 acres and for up to 300 acres in low-lying
tide water areas, this study was conducted to determine the reliability of
methods recommended as to ascertain the most appropriate as the case may
be. Data collected at the catchment were analyzed and compared to the ones
obtained by empirical methods. The results of this study should be similar to
results obtained by comparable studies in other areas of the metropolis.
1.1 SIGNIFICANCE OF THE RESEARCH
The purpose of this research is to present a comparison of design
estimates of runoff discharge to observed peak flow, obtained through data
collected within the catchment area of the Nsukka campus. This report
describes the results of a small basin runoff study conducted in 2009 and
presents a summary of peak-flow data within the metropolis. This report also
presents background information on the processes that control runoff from
drainages with various soil, geologic, topographic and land-use
characteristics; comparison of runoff characteristics (time flow) observed
and estimated by various methods from storm data to runoff characteristics.
A more effective method for the estimation of the runoff discharge is
expected to emerge at the end of the research, which will serve as a major
contribution to the body of knowledge.
1.2 RESEARCH OBJECTIVES
The objectives of this study are:
1. To review the various methods available for estimation of run-off
discharge required for drainage design.
2. To use available data obtained from the catchment area to compute
for the runoff discharge using the empirical methods reviewed.
3. To compare the results obtained through these empirical methods
with the observed runoff discharge at the catchment, in order to
determine which method gives a more accurate value of the runoff
discharge.
1.3 SCOPE AND LIMITATION OF THE RESEARCH
The scope of the project will be limited to investigations and data
collection with regards to the catchment (i.e., the University of Nigeria,
Nsukka campus).
1.4 DESCRIPTION OF CATCHMENT AREA
Two broad categories of factors affect runoff: precipitation
characteristics and basin or watershed characteristics. Basin characteristics
are; size, shape, topography, soils, geology, and land use (Schwab and
others, 1997). Other factors such as site accessibility, proximity to site, and
capability to be instrumented with monitoring equipment also were
considered in selecting the area within the University of Nigeria, Nsukka
campus as the study basin. Land use for the study watershed consists of
combined road and ditch, pasture, residential and recreational areas.
CHAPTER TWO
LITERATURE REVIEW
2.1 RUNOFF
Runoff or streamflow comprises the gravity movement of water in
channels which may vary in size from the one containing the smallest ill-
defined trickle to the ones containing large rivers. Precipitation is the
primary natural supplier of water to a basin. Runoff is that part of the
precipitation that exits the basin as streamflow at a concentrated point. A
hydrograph is a geographical representation of streamflow (runoff) plotted
with respect to time (Langbein and Iseri, 1960) and can be used to analyze
runoff characteristics associated with a basin and storm. The hydrograph
shows the integrated effects of the physical basin characteristics and storm
characteristics within the basin boundaries (Chow, 1964; Freeze, 1974), and
the separation of a hydrograph in terms of time can be useful for hydrologic
analysis of drainage structures.
The single most important property of the hydrograph that is essential
to drainage structure design is the peak rate of runoff (Wigham, 1970). The
design of a drainage structure requires the hydrologic analysis of the peak
rate of runoff, the volume of runoff and the time distribution of flow from
the contributing drainage area (Virginia Department of Transportation, 2002;
Washington State Department of Transportation, 1997). However, the
relation between the amount of rainfall over a drainage basin and the amount
of runoff from the basin is complex and not well understood. The hydrologic
analysis allows for estimates of runoff characteristics such as peak rate of
runoff or runoff volume, but exact solutions to drainage design problems
should not be expected (Virginia Department of Transportation, 2002).
Errors in runoff estimates can result in either an undersized drainage
structure that causes potential hazards, inconvenience, and drainage
problems; or an oversized, inefficient drainage structure.
Runoff, which may be variously referred to as streamflow, stream or
river discharges or catchment yield, norm ally expressed as a volume per
unit of time. The cumec, i.e, one cubic metre per second is a commonly used
unit. Runoff may also be expressed as a depth equivalent over a catchment,
i.e., millimeters per day or month or year.
2.1.1 SOURCES AND COMPONENTS OF RUNOFF
The persistent misuse of runoff terminology has resulted in much
confusion and ambiguity about the sources and components of runoff.
(Freeze, 1972) provided a consistent aid unambiguous terminology which
has been adopted with only slight modification. The total runoff from a
typically heterogeneous catchment area may be conveniently divided into
four component parts: channel precipitation, over land flow, interflow, and
groundwater flow.
The runoff process is represented diagrammatically as shown in figure 2.1
below
BASIN PRECIPITATION
(excluding storage, interception and other losses)
CHANNEL
PRECIPITATION
OVERLAND
FLOW
INTERFLOW
(SUBSURFACE
STEM FLOW)
GROUND
WATER
FLOW
SURFACE
RUNOFF SUBSURFACE
RUNOFF
DELAYED
INTERFLOW RAPID
INTERFLOW
Channel
flow Channel
flow Channel
flow
Channel
flow
INFILTRATION
Fig. 2.1 Diagrammatic representation of the runoff process.
2.1.1.1 CHANNEL PRECIPITATION
Direct precipitation onto the water surfaces of streams, lakes, and
reservoirs makes an immediate contribution to streamflow. In relation to the
other components, however, this amount is normally small in view of the
small percentage of catchment area normally covered by water surfaces. The
water surface for most catchments does not exceed 5 per cent of the total
area even at high water levels (Linsley et al, 1938). However, (Rawitz and
others, 1966), in an analysis of ten storms over a small Pennsylvania
watershed, estimated that channel precipitation accounted for between 3 and
61 percent of total runoff. In catchments containing a large area of lakes or
swamps, channel precipitation may make a substantial contribution to
streamflow.
2.1.1.2 OVERLAND FLOW
Overland flow comprises the water which, failing to infiltrate the
surface, travels over the ground surface towards a stream channel either as
quasi-laminar sheet flow or, more usually as flow anatomizing in small
trickles and minor rivulets. The main cause of over-land flow is the inability
of water to infiltrate the surface and in view of the high value of infiltration
characteristic of most vegetation-covered surfaces, it is not surprising that
overland flow is a rarely observed phenomenon. Conditions in which it
assumes considerable importance include the saturation of the ground
surface, the hydrophobic nature of some very dry soils, the deleterious
effects of many agricultural practices on infiltration capacity and freezing of
the ground surface. Surface runoff may then be defined as that part of the
total runoff which travels over the ground surface to reach a stream channel
and thence through the channel to reach the drainage basin outlet.
2.1.1.3 INTERFLOW
Water which infiltrates the soil surface and then moves laterally
through the upper soil horizons towards the stream channels, either as
unsaturated flow or, more usually , as shallow perched saturated flow above
the main ground water level is known as interflow. Alternative terms used
include; subsurface storm flow, storm-seepage, and secondary base flow.
The general condition favouring the generation of interflow is one in which
lateral hydraulic conductivity in the surface horizons of the soil is
substantially greater than the overall vertical hydraulic conductivity through
the soil profile. Then during prolonged or heavy rainfall, water will enter the
upper part of the profile more rapidly than it can pass vertically through the
lower part, thus forming a perched saturated layer from which water will
‘escape’ laterally, i.e., in the direction of greater hydraulic conductivity.
In addition, some hydrologists argue that water may travel down slope
through old root holes and animal burrows and other subsurface pipes. In
view of the variety of possible interflow routes, it is to be expected that some
will result in a more rapid movement of water to the stream channels than
will others, so that it is sometimes helpful to distinguish between rapid and
delayed interflow (see fig. 2.1). Experimental evidence has long indicated
that interflow may account for up to 85 percent of total runoff (Hertzler,
1939).
2.1.1.4 GROUNDWATER FLOW
Most of the rainfall which percolates through the soil layer to the
underlying groundwater will eventually reach the main stream channels as
groundwater flow through the zone of saturation. Since water can move only
very slowly through the ground, the outflow of groundwater into the stream
channels may lag behind the occurrence of precipitation by several days,
weeks, or often years. In general, groundwater flow represents the main
long-term component of total runoff and is particularly important during dry
spells when surface runoff is absent.
2.1.1.5 SNOWMELT
In some areas, particularly at high altitude or in high latitudes, a large
proportion of streamflow may be derived from the melting of snows and
glaciers. Where this melting occurs gradually, over a long period of time, the
resulting contribution to stream flow will resemble that of groundwater flow.
Where, however, it occurs suddenly, a large volume of water will enter the
streams during a short period of time, giving a runoff peak which closely
resembles that derived from storm rainfall.
2.1.1.6 QUICKFLOW AND BASEFLOW
Quickflow or direct runoff, is the sum of channel precipitation,
surface runoff and rapid interflow and will clearly represent the major runoff
contribution during storm periods and is also the major contributor to most
floods. Baseflow or base runoff may be defined as the sustained or fair-
weather runoff (Chow, 1964) and is the sum of groundwater runoff and
delayed interflow, although some hydrologists prefer to include the total
interflow as illustrated by the broken line in fig. 2.1.
2.2 TYPES OF STREAM
The long-term relationship between baseflow and quickflow
determines the main characteristics of a stream or river; whether, for
example, it will flow steadily or flashily through the year, whether, indeed, it
will flow throughout the year or only for part of the time; and this provides a
basis for classifying streams into three main types, i.e., ephemeral,
intermittent, or perennial (Wisler and Brater, 1959).
Ephemeral streams are those which comprise quickflow only and
which, therefore, flow only during and immediately after rainfall or
snowmelt.
In the case of intermittent streams, which flow during the wet season,
but which dry up during the seasons of drought, streamflow consists mainly
of quickflow, but baseflow makes some contribution during the wet season,
when the water table rises above the bed of the stream.
Finally, as the term suggests, perennial streams flow throughout the
year, because even during the most prolonged dry spell, the water table is
always above the bed of the stream, so that groundwater flow can make a
continuous and significant contribution to total runoff at all times.
2.3 THE RUNOFF PROCESS
The broad relationship between precipitation and streamflow is
obvious and has been evident since the work of Mariotte in the Seine basin
during the seventeenth century. On a seasonal basis streamflow tends to
reach a maximum during the wet season and declines slowly during the drier
part of the year. It usually peaks sharply during a storm and declines
relatively slowly after the end of rainfall. In other words, quite clearly,
streamflow results from precipitation and some water arrives in the channel
quickly while some arrives much more slowly and continues to arrive even
during prolonged dry periods. A successful model of the runoff process must
incorporate and explain these two facts.
For many years, most explanations and analyses of runoff behaviour
have been made in terms of the infiltration theory of runoff developed by
Horton (Horton,1933). Recently, however, this classical model has been
seriously questioned and is now seen to be applicable only in specific
circumstances. A more realistic dynamic model of the runoff process
developed by Hewlett, Hursh and others in the United States in the fifties is
now believed to provide a more accurate representation of the runoff process
over a wide orange of conditions.
2.3.1 THE HORTON RUNOFF MODEL
The Horton infiltration theory of runoff (Horton, 1933) considers
average conditions over an entire catchment area. It is assumed that at the
end of a dry period most streamflow will be derived from groundwater flow,
although Horton also recognized that baseflow could be supplied from other
storage such as that in lakes, marshes, snow, and ice. As groundwater flow
takes place, the groundwater reserves will be depleted and this, in turn, will
lead to a gradual reduction in groundwater flow to the stream channels. This
condition is represented by section AX of the hydrograph in fig. 2.2 below.
10-
8-
6-
Y
Z
B
Run
off
(cu
mec
s)
4-
2-
A X
0
1 2 3 4 5 6
Time (days)
Fig 2.2 Short-period storm hydrograph for a hypothetical catchment.
The Horton model assumes that during a prolonged storm of constant
intensity there will be a continuous exponential decrease of infiltration
capacity which Horton assumed was largely the result of factors operating at
the soil surface such as compaction, structural change, and the inwashing of
fine particles. Eventually a constant low value of infiltration capacity is
reached over the entire catchment area. If this value falls below that of
rainfall intensity, so that rain is falling at a faster rate than the soil can
absorb it, overland flow and subsequently surface runoff will occur.
Overland flow, having built up to a sufficient depth, will reach the stream
channels quite quickly giving rise to the marked increase in streamflow
represented by the line XY in fig. 2.2 above.
Soon after the end of rainfall, the surface runoff will begin to
diminish, rapidly in the initial stages, and later more slowly, as first the
minor channels, and then the larger ones begin to drain dry (see section YZ,
fig. 2.2). Any water which is left on the surface as depression storage will
soak into the soil and may perhaps percolate to the groundwater. Finally,
once all the surface runoff has been disposed of, the flow in the steams will
again consist almost entirely of groundwater flow (see section ZB), which
gradually decreases as the reserves are used up.
2.3.2 The Hewlett runoff model
The Hewlett runoff model embodying the variable source area
concept makes the basic assumption that infiltration is seldom a limiting
factor, i.e., that only in special conditions rainfall intensity exceed
infiltration capacity. Hewlett derived this basic premise from a number of
fundamental field evidence that most precipitation infiltrated the ground
surface, particularly in well-vegetated areas. Even during a 100-year storm
which delivered more than 500mm of rain in five days on one Coweeta
watershed, no overland flow was detected (Hewlett and Nutter, 1970).
Secondly, only about 10 per cent of the annual precipitation in humid areas
such as the eastern United States appears as quickflow in headwater streams
(Woodruff and Hewlett 1970). Thirdly, most of this quickflow leaves the
drainage basins hours after the cessation of rainfall. Fourthly, Hewlett
described as the most intriguing of all the findings at Coweeta, the evidence
that unsaturated soil moisture movement may account entirely for baseflow
from some mountain watersheds.
Essentially the core of the Hewlett runoff model is the response of the
channel system to precipitation. A further proposition of the Hewlett runoff
model is that the shallow subsurface movement of water, resulting from the
very large percentage of total precipitation infiltrating the surface, makes a
vital contribution to the recession limb of the hydrograph as well as to the
rising limb and peak. In some circumstances the contribution of interflow
may entirely account for recession flows which have been explained as the
result of groundwater flow.
2.3.3 Variable Source Areas
It is now widely accepted that widespread Hortonian overland flow
resulting from saturation when rainfall intensity exceeds the infiltration
capacity of the ground surface is more. A number of authors have discussed
the relationships between rainfall intensity and infiltration capacity and have
demonstrated that over a wide range of conditions, typical rainfall intensities
are less than the infiltration capacities of many soils and that in any case
normal storm duration tends to be shorter than the time required for most
soils to become saturated at the surface (Freeze,1972). The concept of
variable (or partial) source areas is an attempt to reconcile the absence of
widespread overland flow with the rapid response of most streams to
precipitation by postulating that over-the-surface movement of water is
restricted to limited areas of a drainage basin.
2.4 Factors Affecting Runoff
It will be convenient at the outset of this discussion of the factors
affecting runoff to differentiate between those factors which combined to
influence the total volume of runoff over, say, a period of several years, and
those other factors which combined to influence the distribution of runoff in
time say, over a period of one year or less.
2.4.1 Factors Affecting the Total Volume of Runoff
The most obvious and probably the most effective influence on the total
volume of runoff is the long-term balance between the amount of water
gained by catchment area in the form of precipitation, and the amount of
water lost from that catchment area in the form of evapotranspiration. In
this sense, the climate of the catchment area sets the broad upper limits to
the total volume of streamflow leaving the area, but this relationship
between annual totals and means of rainfall and evapotranspiration may be
modified by short-term factors, such as the manner in which precipitation
occurs, and sudden changes in the vegetation cover.
In addition to the water balance of the catchment area, a second group
of factors influencing the total amount of runoff comprises aspects of the
physique of the catchment area. Chief amongst these, naturally, is the area of
the catchment since, other factors being equal, this determines the total
amount of precipitation caught. It should be noted, however, that the effect
of area may depend upon the prevailing climatic regime.
Slope, soil, and rock type may indirectly influence the total runoff
from a catchment through their effects in delaying water movement after
precipitation thereby possibly affecting the amount of evapotranspiration. In
general, the highest annual runoff would be expected from steeply sloping
areas having thin soils and impermeable rocks. Finally, the average height of
the catchment may affect total runoff, again indirectly, through its direct
orographic influence on precipitation amounts.
2.4.2 Factors Affecting the Distribution of Runoff in Time
From the hydrologist’s point of view, climate, which it has been
suggested sets the broad upper limits to total runoff, is a comparatively
stable environmental factor; even more so are the catchment factors which
have been discussed. It is, then, the second group of factors which influence
the distribution of runoff in time, and which, themselves, tend sometimes to
be more variable and unpredictable, which have attracted the most attention.
2.4.2.1 Meteorological Factors
In the sense that precipitation forms the raw material of streamflow,
meteorological factors are obviously of great importance and their variation
with time tends to be closely related to similar variations of runoff.
2.4.2.2 Types of Precipitation
For the purpose of this discussion, it may be considered that
precipitation occurs either as rainfall or as snowfall, other forms, such as hail
and sleet may be conveniently grouped with rainfall; hail, for example, often
occurs in conditions which favour rapid melting at the ground surface, and
the snow content of sleet will normally tend to liquefy soon after contact
with the ground.
The most important feature of a snow blanket is its storage capacity,
and the resulting time interval between the occurrence of runoff. Thus, in a
simple and rather obvious example, precipitation falling as snow during the
winter months between December and February will not contribute to runoff
until melting occurs during the spring.
Precipitation falling as rain may, of course contribute directly to
runoff, but the extent to which it does so will depend upon the interaction of
numerous meteorological and other factors, the most important of which will
be discussed below.
2.4.2.3 Rainfall Intensity and Duration
It has already been shown that, in some circumstance, the intensity
with which rain falls, may be an important factor in determining the
proportions of the rainfall which go to overland flow, interflow, and
groundwater flow and, therefore, the speed with which water may reach the
stream channel. The duration of rainfall is important, particularly in relation
to the hydrologically responsive areas of a catchment and particularly in flat,
low-lying areas. Here, if rainfall is sufficiently prolonged, infiltration may
raise the surface of saturation to the ground surface itself, thereby reducing
the infiltration capacity to zero and causing a sudden increase of surface
runoff.
The duration of rainfall also becomes significant when considered in
relation to the mean travel time of a drop of water from its points of impact
on the catchment area as rainfall, to its exit from the catchment area as
streamflow. If the rainfall duration is equal to or grater than this mean travel
time, then the whole of the catchment area is likely to be contributing to
runoff during the later stages of the storm, so that the potential runoff is at a
maximum. If on the other hand, the duration of rainfall is less than the mean
travel time, then the potential runoff will be lower than the maximum
because only part of the catchment will be contributing to runoff before
rainfall ceases. In this context, it is apparent that the importance of rainfall
duration will tend to vary with the size and nature of the catchment. In a
small catchment with steep slopes, maximum potential runoff is likely to be
caused by a rainfall of much shorter duration than would be required in a
large, gently undulating catchment.
2.4.2.4 Rainfall Distribution
The time relationship between rainfall and runoff may be greatly
affected by the distribution of rainfall over the catchment area. A given
volume of rainfall, which is uniformly distributed over the whole of a
catchment, will have lower intensities and is, therefore, less likely to
produce quickflow than is the same volume of rain falling on a small,
localized part of the catchment. The first type of rainfall distribution will
tend to result in an increase in baseflow, and consequently a long-term
increase in streamflow, while the second sort of distribution will tend to give
larger volumes of quickflow and thus, a more sudden, short-lived increase in
streamflow.
When discussing rainfall distribution, one is rarely concerned with a
stationary pattern. Much of the rainfall in the British isles, for example, is
related to series of depressions moving in from the Atlantic, causing belts of
frontal main to cross the country. In this way, a rainstorm may begin in one
part of a catchment area, and end in another, and the direction of movement
of the storm may be very important.
2.4.3 Catchment Factors
The various meteorological factors which have been discussed can all
be measured with reasonable accuracy thus facilitating their correlation with
runoff characteristics. It is, however, much more difficult to apply such
precise determinations to many catchmnent factors. Furthermore, some of
these factors, such as shape, topography, and soil type, remain fairly
constant over long periods while others , such as those associated with land
use, may change very rapidly. The main problems, however, arise partly
from the fact that the various components of runoff may be differently
affected by each of the catchment factors, so that the net effect of any one
catchment factor on variations of total runoff with time are difficult to
establish, and partly from the fact that only limited, hydrologically
responsive areas of a catchment make a substantial contribution to
quickflow, so that is the influence of catchment factors in these limited
areas; and not over the whole of the catchment, which must be determined.
The fact that the variable source areas within a catchment are difficult to
define, means that the present discussion must be largely qualitative in
nature.
2.4.3.1 Topograhy
One of the several factors which may be included under this rather
general heading is the shape of the catchment area, which is known to
influence runoff through its effects on flood intensities, and on the mean
travel time of a drop of water from its point of impact on the surface of the
catchment to its point of exit in the main stream. In a generally square or
circular catchment area, the tributaries often tend to come together and join
the main stream near the centre of the area (Parde, 1955). Consequently, the
separate runoff peaks generated by a heavy fall are likely to reach the main
stream in approximately the same locality at approximately the same time,
thereby resulting in a large and rapid increase in the discharge of the main
stream. If on the other hand, the catchment area is long and narrow, the
tributaries will tend to be relatively short, and are more likely to join the
main stream at intervals along its length. This means that, after a heavy
rainfall over the area, the runoff peaks of the lower tributaries will have left
the catchment before those of the upstream tributaries have moved very far
down the main stream. Elongated catchments are thus less subject to high
runoff peaks.
Synder (1938) suggested that one way to express the effective shape
of a catchment was to draw isopleths of travel time of the water above the
drainage outlet and to plot the area between isopleths against time. The
resulting curve would then express the shape of the catchment by giving the
increment of the area that is at any particular travel-time distant from the
outlet.
A second pertinent topographical factor is the slope of the catchment
area which, as has already been suggested, may affect the relative
importance of predominantly vertical movement of water by means
infiltration and the predominantly lateral movement of water by means of
interflow and over land flow, the former tending to be more important in flat
areas, the latter in steeply sloping areas. Furthermore, because the speed of
water movement will tend to increase with slope, runoff in steeply sloping
areas will reach stream channels quickly.
The shape of the runoff hydrograph depends not only on the speed
with which water gets into the stream channel but also on the speed with
which it moves down the channel to the outlet of the catchmnent. Channel
slope may therefore be as important as catchment slope and has frequently
yielded more significant correlations with runoff characteristics.
2.4.3.2 Geology
By its very nature, the geology of a catchment area will exert a
fundamental influence on runoff which will be felt in many ways. Two
aspects are, however, of chief importance – the type of rock in which the
catchment area has been eroded, and the main structural features of the area.
The influence of rock type on runoff may be seen in the close
relationships which often exist between geology and the texture of drainage.
Thus studies in Pennsylvania showed that high runoff peaks occurred in
shale and sandstone catchments while catchments having extensive, thick
limestone generated extremely low runoff peaks (White,1970). Where
subsurface water movement through limestone is very rapid, however,
runoff peaks may be substantially greater than in other geological areas.
2.4.3.3 Soil
The influence of soil type on infiltration characteristics and its
consequent effect upon the disposition of rainfall as either overland flow,
interflow or groundwater flow cannot be over-emphasized. Open-textured
sandy soils will tend to be associated with higher infiltration values than
fine-grained, closely compacted clay soils and will, therefore, tend to
generate smaller volumes of quickflow.
Soil profile characteristics are important in relation to their effects
upon infiltration and the generation of interflow. In particular, marked
reductions of hydraulic conductivity with depth, especially in the upper
horizons, facilitate the formation of interflow and, during prolonged rainfall,
the saturation of the soil surface and the generation of overland flow. On the
other hand, deep uniformly permeable soils tend to encourage continued
vertical infiltration and the dominance of baseflow over quickflow.
Hydrologists have for a long time reorganized the relationship
between the amount of runoff (especially quickflow) produced by a given
rainfall and the moisture content of the soil, expressed either as a direct
measurement or indirectly as an antecedent precipitation index. Earlier
workers, using Hortonian concepts, tended to ascribe this relationship to the
reduction of infiltration capacity which accompanies the increase of soil
moisture content. In the light of modern views on runoff formation,
however, it will be appreciated that, in general, the source areas within a
catchment will tend to expand as the catchment becomes wetter and that this
is a much more likely explanation of observed relationships between runoff
and catchment moisture indices.
2.4.3.4 Vegetation
The effect of vegetation on the distribution of runoff with time has
probably received more attention from hydrologists than the effect of any
other catchment factor and yet because of the complexity of the interaction
involved, there is still much confusion. The complexity of the problem
becomes evident when it is considered that the total effect of vegetation on
runoff is comprised of its individual effects on interception,
evapotranspiration, soil moisture movement (particularly in terms of
infiltration and interflow), and also the pattern of snow accumulation and
melt. By way of illustration, let us compare a forested and a non-forested
area on which all precipitation falls as rain and which are identical, apart
from vegetation differences. In the non-forested area, transpiration and
interception losses will probably be lower, thus producing wetter soils with a
reduced capacity for additional water storage, and thereby resulting in higher
volumes of dry season quickflow and higher instantaneous peak flows. In
the wet season, the storage capacity of the soils under both vegetation types
will be at a minimum so that the response of runoff to rainfall will be similar
from both areas. In a less direct way, vegetation may influence runoff
through its effect on soil type.
2.4.3.5 Drainage Network
The character of the drainage pattern is important because of the
extent to which it may reflect many of the physical characteristics of
catchment areas. In a catchment where sub surface storage and hydraulic
conductivity are low, the ground surface will be prone to saturation resulting
both from the downslope movement of interflow and the increase in
elevation of shallow water tables during and immediately after precipitation.
In this situation, the channel network will expand rapidly during
precipitation, or, stated in alternative terms, a large proportion of the
precipitation will be evacuated as overland flow. On the other hand, in a
catchment where subsurface storage and hydraulic conductivity are high,
deep infiltration will be encouraged, channel network expansion during
precipitation will be small, and only a small proportion of the precipitation
will be evacuated as overland flow. Consequently, the surface, topographic
expression of overland flow, i.e., interconnection depressions, hills and
valleys, will be correspondingly smaller.
A final point which can be made in connection with the influence of
the drainage network on runoff concerns the presence of lakes and swamps
in a catchment area. Where these occur, they tend to ‘absorb’ high runoff
peaks and thus to exert a moderating influence on the hydrograph, which is
particularly beneficial in catchments which generate large volumes of
quickflow.
2.4.4 Human Factors
There are very few areas of the world in which runoff is not affected
to some extent by the influence of man. In remote uplands, dams have been
constructed for water supply and hydro-electric power generations.
Elsewhere, former grasslands have been ploughed up, more land have been
forested, semi-desert areas have been irrigated, swamps have been drained,
and everywhere there has been a great increase in urbanization, and the
resulting spread of artificial, impermeable surfaces. In all these ways, the
response of catchment areas to rainfall and, consequently, the pattern and
distribution of runoff has been changed.
2.4.4.1 Hydraulic Structures
The flow of many of the world’s large rivers is controlled or modified
by dams and reservoirs which have been constructed for power, water
supply, or irrigation purposes. The effect of these structures has been similar
to that of natural lakes to the extent that flood peaks are normally ‘absorbed’
by the artificial lakes and subsequently gradually released. An additional
effect, in some instances, has been a marked diminution of flow, particularly
where multipurpose schemes are in operation in which the impounded water
is used not only for water supply and power but also for irrigation.
Streamflow may also be affected by artificial modifications to stream
prone to flooding. Such modifications commonly include channel
straightening and enlargement and the construction of relief and by-pass
channels in order to reduce both discharge and water levels at critical points.
2.4.4.2 Agricultural Techniques.
A second aspect of human influence on runoff may result from the
application of specific agricultural techniques and practices, particularly
where these cause a sudden change in catchment characteristics, e.g.,
vegetation cover. Some of these changes have been brought about
deliberately, as conservation measures; other changes have brought about
‘accidentally’ and sometimes initially surprising hydrological results. In
Russia, for example, experiments showed that autumn ploughing may
decrease runoff by as much as 45 percent, and a 20 percent reduction in
runoff resulted in some areas from the cultivation of virgin lands (Lvovitch,
1958). Again, Ayers (1965) reported that in southern Ontario ploughed soils
in good management yielded much less runoff during the winter months than
grass-covered areas.
Some of the most dramatic land use changes are those associated with
afforestation and deforestation, the hydrological effects of which continue to
engender considerable controversy. In general, it has been shown that runoff
is reduced when deciduous trees are replaced by conifers and increased
when forest is replaced by lower growing vegetation such as grass or crops.
2.4.4.3 Urbanization
The effects on runoff of the spread of settlement and ancillary features
such as roads, pavements, and airfields calls for serious attention. Over large
areas, infiltration capacity is considerably reduced, falling precipitation is
caught by rooftops and roads, and is passed through drainage systems which
have been designed to dispose of it into nearby streams as rapidly as
possible. The result is that, immediately below large urban areas, there tends
to be a marked and rapid build-up of surface runoff which will be
accentuated where slopes are steep. Increases in the magnitude of peak flows
are thus a result of partly an increase in the volume of quick flow and partly
of the more rapid movement of runoff which is possible in an urbanized
area. Apart from peak flows, urbanization also affects water quality and
wide range of other hydrological variables.
2.4.4.4 Severity of Flooding
In conclusion, it is of interest to note that it is largely the human
factors which have been discussed above which are believed to be
responsible for the apparent increased severity of floods during recent times.
Floods, which may be defined as unusually high rates of discharge often
leading to the inundation of land adjacent to the streams, are nearly always
the result of quickflow, rather than baseflow, and are thus usually caused by
intense or prolonged rainfall, snowmelt, or a combination of these factors.
Any increase in the severity of floods is, therefore, likely to be caused
by increased rainfall intensity, or duration, reduced infiltration capacity, or
the changed efficiency of the drainage network. There is some evidence to
suggest that storms are increasing in intensity; the effect of urbanization in
reducing infiltration capacities have already been noted and, in addition,
such factors as forest clearance and burning, accidentally or otherwise, of
large areas of peat moorland must also be taken into account. Finally, the
efficiency of drainage channels is likely to be impeded by bridges, levees,
flood walls, and similar structures, and although the individual effect of each
may be small, their combined effect in large built-up areas may be
surprisingly significant (Wisler and Brater, 1959).
2.5 Variations of Runoff
Preceding discussions have shown that many factors combine to
influence runoff. So numerous are these factors, indeed, that all variations of
runoff are unique since no combination of all the variables are ever likely to
be repeated. However, certain general similarities and patterns may be
observed both in the spatial variation of annual runoff totals and in the
variation of runoff with time at one particular place.
2.5.1 Areal Variations
Areal variations of runoff are associated with varying runoff values
over a geographic sphere. An outstanding feature of this distribution is the
very low values representative of some regions where rainfall is low and
evaporative losses are generally high. At other regions, there could be high
values, and there is a fairly rapid transition between the areas of high and
low runoff.
2.5.2 Seasonal Variations
Most rivers show a seasonal variation in flow which, although
influenced by many factors, is largely a reflection of climatic variations and,
in particular, of the balance between rainfall and evaporation. The pattern of
seasonal variations which tends to be repeated year after year is often known
as the regime of the river or stream. Thus, equatorial rivers tend to have a
fairly regular regime, tropical rivers show a marked contrast between runoff
in the rainy and dry season, while in other climatic areas complications may
arise from the fact that precipitation falls as snow and does not, therefore,
contribute directly to runoff until melting occurs. In this way, river regimes
may be considered in relation to the climatic zones from which they
principally derive.
2.5.2.1 Simple Regimes
Simple regimes are those variations of river flow throughout the year
in which a simple distinction may be made between one period of high water
levels and runoff, and one period of low water levels and runoff. Such
regimes may result from one of several contrasting factors: thus, in many of
the oceanic areas of Europe, rainfall is fairly evenly distributed throughout
the year, but the peak of evapotranspiration during the summer months
results in low runoff during this season, in contrast to high runoff values
during the winter months when evapotranspiration is small. In tropical areas,
on the other hand, evapotranspiration tends to be uniformly high through the
year, so that the rainfall distribution is the main determinant of the river
regimes, with high runoff occurring as a result of the summer rains.
6-
5-
4-
3-
2-
1-
0
J F M A M J J A S O N D J
Time (months)
Fig2.3 Simple regimes hydrograph for a typical tropic rainfall
Runoff
(cu
mec
s)
2.5.2.2. Complex I regimes
Complex I regimes are characterized by at least four, and sometimes
as many as six, hydrological phases, although normally there are two low
runoff and two high runoff periods. In the case of European streams, the first
high runoff period, resulting perhaps from snowmelt, may occur in spring
and then be followed by a period of low runoff. Later in the year, a second
period of high water levels and runoff may occur in the summer as a result
of, say, convectional rainfall over a ‘continental’ area, or in autumn as a
result of Mediterranean storms, or in winter as the result of an excess of
rainfall over evapotranspiration in an oceanic area. This sequence results,
then, in two periods of peak runoff which are separated by two periods of
lower discharge, giving four distinct hydrological phases through the year.
2.5.2.3 Complex II regimes
Complex II regimes form the third and probably the most important
group in Parde’s classification and are found on most of the world’s large
rivers. Since these normally flow through several distinct relief and climatic
regions, and may receive the waters of large tributaries which themselves
flow over varied terrain, rivers comprising this group normally have a
simple or a complex I regime in their headwater reaches but, downstream,
are gradually influenced by a variety of factors such as snow or glacier melt,
rainfall, and evaporation regimes which may emphasize the trends found in
the headwater regime of which, because they work in opposite ways, may
cancel each other out.
2.6 Hydrograph
The hydrograph is a graph of discharge against time (i.e., specified
time). Discharge graphs are known as flood or runoff graphs. Each
hydrograph has a reference to a particular river site. The time period for
discharge hydrography may be hour, day, week or month.
Hydrograph of stream or river will depend on the characteristics of the
catchment and precipitation over the catchment. A hydrograph will assess
the flood flow of rivers hence it is essential that anticipated hydrograph
could be drawn for river for a given storm. A hydrograph indicates the
power available from the stream at different times of day, week or year. A
typical hydrograph is shown in the figure below.
A M J J A S O N D J F M A
Time
Fig. 2.4 A Typical hydrograph.
The main features of a hydrograph resulting from a single storm on a
basin are rising limb, a peak and a recession limb. Multiple peaks often
Rising Limb
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - -
Peak or crest
Point of inflexion
Point of inflexion
Recession Limb
Dis
char
ge
resulting from rain storms separated by periods of little or no rain or by areal
variation in storms are sometimes noticed.
The rising segment depends on the duration and intensity distribution
of rainfall and the antecedent condition of the drainage area. The peak of the
hydrograph represents the highest runoff in the drainage basin. It occurs at a
certain time after the rain has ended. The point of inflexion on the falling
segment is assumed to mark the time at which the surface inflow to the
channel system ceases. The recession represents the withdrawal of water
from the storage after all inflow of water from the storage into the channel
has ceased. It is more or less independent of the time variations, rainfall and
infiltration. It may be slightly dependent on area-rainfall distribution and it
depends heavily on the ground condition.
Generally, the hydrograph is used in computing storage and outflow
from reservoirs. Based on this research work, the concept of unit hydrograph
is of uttermost importance, as it offers opportunity of estimating runoff
discharge. This will be discussed extensively in later chapters.
2.6.1 Unit hydrograph method
The peak flow alone does not give sufficient information about the
runoff since it (peak flow) represents a momentary value. Therefore, it is
necessary to understand the full hydrography of flow. The basic concept of
unit hydrograph is that the hydrographs of runoff from two identical storms
would be the same. In practice, identical storms occur very rarely. The
rainfall generally varies in duration, amount and areal distribution. This
makes it necessary to construct a typical hydrograph for a basin which could
be used as a unit of measurement of runoff.
A unit hydrograph may be defined as the direct runoff hydrograph
corresponding to an effective unit precipitation (such as 1cm of rainfall) in a
specified time duration. The precipitation is assumed to occur uniformly
over the entire catchment. The important conditions implied in the above
definition must be effective;
(1) The precipitation must be effective.
Therefore, the total precipitation volume must equal the volume
indicated by the hydrograph curve. For the unit hydrograph, the direct runoff
corresponds to unity.
(2) The time of occurrence of the unit precipitation is a specified one.
This could be 3hrs, 4hrs, or 6hrs. For each time duration, the shape of the
unit hydrograph would be different. Also a 4-hr unit hydrograph corresponds
to an effective precipitation of 1/4cm/hr for 4hrs uniformly. Hence, it is
necessary to specify the duration of a unit hydrograph.
(3) The unit hydrograph is used to correlate the direct runoff with the
excess precipitation. Therefore, the resulting hydrograph does not include
the base flow.
The application of U.H method consists of two aspects;
(1) To arrive at the unit hydrograph of a suitable duration for the
catchment under consideration.
(2) To use the U.H derived for finding out the flood hydrograph
corresponding to any storm. For design purposes a design storm is
assumed which will with the help of the U.H give a design flood
hydrograph.
2.6.2 Construction of unit hydrograph.
The following steps are used for the construction of unit hydrograph:
(1) Choose an isolated intense rainfall of unit duration from past
records.
(2) Plot the discharge hydrograph for outlet from the rainfall records.
(3) Deduce the base flow from stream discharge hydrograph to get
hydrograph of surface records.
(4) Find out the volume of surface runoff which would correspond to
the area under the direct runoff hydrograph and convert this
volume into cm of runoff by dividing by the catchment area. This
runoff depth is the effective precipitation depth over the basin.
(5) Measure the ordinates of surface runoff hydrograph.
(6) Divide these ordinates by obtained run-off in cm to get ordinates of
unit hydrograph.
Thus for any catchment, unit hydrograph can be prepared once. Then
whenever peak flow is to be found out, multiply the maximum ordinate of
unit hydrograph by the runoff value expressed in cm. Similarly to obtain
runoff hydrograph of the storm of the same unit duration multiply the
ordinates of the unit hydrograph by the runoff value expressed in cm. If the
storm is of longer duration calculate the runoff in each unit duration of the
storm. Then super-impose the runoff hydrographs in the same order giving a
lag of unit period between each of them. Finally, draw a summation
hydrograph by adding all the overlapping ordinates. Generally, the
computations are done in a tabular form before the hydrograph is plotted.
The direct runoff depth or the effective precipitation depth is given
by;
Direct runoff depth = 0.36 X Σ0 X t
A (cm) …(2.1)
where;
Σ0 = Summation of DRO ordinates in cumecs
t = Time interval in hours between successive ordinates.
A = area of basin in km2.
The U.H ordinates will be
U.H ordinates = ordinates of DRO
depth of DRO ...(2.2)
Effective duration = 6 hours.
Unit
hydrograph
Peak
flow
Runoff hydrograph
Runoff time (hours)
Surf
ace
runoff
(m
3/s
)
Fig.2.5 showing how a runoff hydrograph is constructed from a unit
hydrograph.
2.6.3 Assumptions
The following assumptions have been made in the unit hydrograph
method:
(1) The base period of a direct runoff hydrograph corresponding to the
storm of the same duration but different intensities, is always
constant.
(2) The direct runoff hydrograph from a catchment corresponding to a
given period of rainfall reflects all the physical characteristics of
the basin lumped together. Hence, the unit hydrograph can be
viewed as the catchment response to an input precipitation of 1 cm
in same specified time.
(3) The principle of linearity applies. This means that the direct runoff
at any instant is directly proportional to the intensity of
precipitation.
(4) The principle of superposition applies. This means that the
combined hydrograph of the successive rainfalls can be obtained
by finding the direct runoffs for each rainfall period separately and
then superposing all such hydrograph.
2.6.4 Limitations of unit hydrograph method.
The limitations of the application of the unit hydrograph method are
that:
(1) Its use is limited to areas about 5000sq. kilometers since similar
rainfall distribution over a large area from storm- to- storm is
rarely possible.
(2) The odd-shaped basins (particularly long and narrow) have very
uneven rainfall distribution. Therefore, unit hydrograph method is
not adopted to such basins.
(3) In mountain areas, the areal distribution is very uneven; even then
unit hydrograph method is used because the distribution pattern
remains same from storm to storm.
2.7 The estimation, prediction and forecasting of runoff
Ideally, all hydrological problems would be solved by the use of
measured data, thus obviating the necessity for estimation, prediction, and
forecasting. There are many circumstances, however, in which the use of
these techniques becomes necessary. Thus, for example, there may be a
deficiency of measured data for a particular area, but there may be the
possibility of extrapolating future runoff trends either from existing runoff
data relating to adjacent or nearby areas or from precipitation data.
Alternatively, measured data may be collected too late to be of any use. Such
is the case in areas where peaks of quickflow constitute a flood problem
which must be viewed and solved in the light, not only of hydrological
factors, but also of factors of settlement and communications, agriculture,
and economics. Inevitably, the relevant measured data cannot become
available until the flood peaks themselves have occurred and so, in these
circumstances, the need is for techniques for accurately forecasting the
volume and timing of quickflow peaks. Again, in areas where water supplies
for agriculture, industry, or domestic uses are likely to be limited at times of
low flow; the need is for accurate forecasts of the magnitude of dry-weather
flows, and the time occurrence of minimum flow.
The main requirements, therefore; are for techniques to forecast, for a
given point within a drainage basin, both the total volume of runoff and the
magnitude of the instantaneous peaks normally associated with sudden
increases of quickflow and also to forecast the timing and magnitude of the
minimum flows which are likely to be associated with decreasing volumes
of baseflow, particularly groundwater flow. Most of the techniques currently
in use were developed before the newer concepts of runoff formation, which
shall be presented in this chapter, had been accepted or, in some cases, had
even emerged. Interestingly, however, many of these methods yield
reasonable results despite being conceptually weak or even erroneous. Such
successes may be fortuitous but techniques are either highly empirical, and
are often applicable only to restricted areas, or else are based upon factors
which, although not directly cause-related to the patterns of runoff under
consideration, are themselves directly affected by the real runoff-forming
factors.
Although, in normal English usage, the terms forecasting and
prediction are clearly synonymous, they are sometimes used in a more
restricted sense by hydrologists. Thus, as Smith (1972) observed, prediction,
in this context, refers to the application of statistical concepts to long periods
of data, usually relating to extreme events, with a view to defining the
statistical probability or return period of a given magnitude of flow. In other
words, there is no indication of when this particular flow will occur.
Forecasting, on the other hand, refers to specific runoff events, whether
floods or low flows, and to the use of current hydro-meteorological data in
order to provide a forecast of the magnitude of the runoff event and also, in
many cases, of its timing. As far as possible, this distinction will be
preserved in the ensuring discussions.
There are many techniques of runoff prediction and forecasting. Some
of these are in widespread use, either because they work reasonably well
over a wide range of conditions or else are easy to apply. The use of other
techniques may be restricted to specific areas or to specific users, such as a
particular Government agency. Most methods have little merit and yield
poor results. It would clearly be impossible to deal with all methods or even
a representative selection of the better ones. Indeed, in the present context
this would not, in any case, be appropriate. Instead, the main lines of
approach to the problem of runoff prediction and forecasting will be briefly
reviewed in general terms and will be illustrated, where appropriate, by
specific examples.
2.7.1 Annual and Seasonal Runoff
Reasonably accurate estimates of annul and seasonal runoff totals for
given catchment areas may, in some cases; be made from annual or seasonal
rainfall totals, using a simple straight line regression between the two
variables. Normally, however, such simple correlations between rainfall and
runoff may be expected to yield forecasts of only token accuracy and
certainly for shorter periods of hours, days or even weeks, more refined
techniques must be used.
Some improvement on the simple rainfall-runoff relationship may be
derived from procedure such as that proposed by Thonthwaite (Thornthwaite
and Mather, 1957). It was shown that a reasonably accurate forecast of
monthly and even shorter period runoff totals for a small drainage basin in
eastern England could be obtained from a simple consideration of rainfall
and potential evapotranspiration values (Ward, 1972).
Finally, it may in some cases be appropriate to consider vegetation
type as an indicator of potential runoff. Satterlund (1967) investigated the
use of forest vegetation in this respect and concluded that, in relation to the
USA, the technique would be more useful where water supplies are scanty,
as in the south-west, and useful where a considerable excess of water over
plant needs is available, as in Southern Appalachia.
2.7.2 Peak Flows
It has earlier been shown that increases in runoff after rainfall or
snowmelt tend to be rapid, leading quickly to a short-lived or instantaneous
peak, which is followed by a rather longer period of declining runoff. Since
it is likely to be the peak flow which causes damage to structures, or
flooding of agricultural land adjacent to streams, the main problems of
forecasting and prediction concern the magnitude and timing of this peak,
and the frequency with which it is likely to occur, although, it may also be of
interest to know in advance, say, the total volume of runoff, and there length
of the period between the beginning and the end of quickflow. Several
techniques may be used, and in the ensuing discussion, these will be
considered. The choice of method will normally be determined by the
purpose for which it is required, by the available data, and by the area and
characteristics of the drainage basin. In relation to the last point, for
example, there is clearly a major difference between a drainage basin of
1km2, where the runoff-producing storm may cover the entire area, and a
basin of several thousands of square kilometers, where a flood peak
generated on a small headwater stream by an isolated thunder storm will
move down the drainage system and where the main problem is to forecast
its change in shape and magnitude as it does so.
2.8 Empirical Formulae
In this method an attempt is made to derive a direct relationship
between the rainfall and subsequent run-off. For this purpose, some
constants are established which give fairly accurate results for a specified
region. Virtually all methods of runoff prediction and forecasting contain an
element of approximation and empiricism; the heading of this section may
be considered misleading. However, as with equality, so with empiricism,
some methods are more empirical than others. The main weaknesses of such
methods are normally their non-generality and the difficulty of knowing the
exact conditions under which they may be used. One of the earliest and best-
known attempts to estimate peak flows was the so-called rational formula.
2.8.1 Rational Method
The Rational method is an empirical relation between rainfall
intensity and peak flow that is widely accepted by hydraulic engineers;
however, the origin of the method is unclear. In the United States, Kuichling
(1889) was the first to mention the method in the scientific literature, yet
some engineers attribute the principles of the method to Mulvaney (1851). In
England, the method is often referred to as the Lloyd-Davis method, which
was published in 1906 (Chow, 1964).
The Rational Method is based on the theory that, for a given storm
frequency, the maximum runoff rate results from a rainfall intensity of
duration equal to the time of concentration of the particular basin. The
simplicity of the equation is misleading because “the critical value of the
rainfall intensity, through the medium of concentration time, entails a
consideration of such factors as basin size, shape, and slope; channel length,
shape, slope, and conditions; as well as variation in rainfall intensity,
distribution, duration, and frequency; all of which can and should be
considered in determining its value” (National Resources Committee, 1939).
Virginia Department of Transportation (VDOT) (2002) recommends
use of the Rational Method for estimating the design-storm peak runoff from
small basins with area up to 200 acres(2ha) and for up to 300 acres(3ha) in
low-lying tidewater areas. The method uses an empirical equation that
incorporates basin and precipitation characteristics to estimate peak
discharges (Chow, 1964). The Rational Method is relatively simple to apply;
however, its concepts are sophisticated. Considerable engineering
knowledge is required to select representative hydrologic characteristics that
will result in a reliable design discharge (Virginia Department of
Transportation, 2002). Validation of the Rational Method is difficult because
direct measurement of some hydrologic characteristics used in the method is
not easily accomplished.
2.8.1.1 Assumptions of the Rational Method
The rational method assumes that (Merit, 1976):
(1) The maximum rate of runoff for a particular rainfall intensity occurs if
the duration of rainfall is equal to or greater than the time of concentration;
(2) The maximum rate of runoff from a specific rainfall intensity whose
duration is equal to or greater than the time of the rainfall intensity;
(3) The frequency of occurrence of the peak discharge is the same as that of
the rainfall intensity from which it was calculated;
(4) The peak discharge per unit drainage area increases and the intensity of
rainfall decreases as its duration increases;
(5) The coefficient of runoff remains constant for all storms on a given
watershed.
(6) Precipitation is uniform over the time or space;
(7) Precipitation does not vary with time or space;
(8) Time of concentration is relatively short and independent of storm
intensity;
(9) Runoff is dominated by overland flow;
(10) Basin storage effects are negligible. (U.S Geological Survey, 2005)
The rational formula is given by;
Q = 0.278 CIA …(2.3)
where,
Q is the quantity of runoff in (m3/s);
C is the coefficient of runoff;
I is the rainfall intensity in (mm/hr);
A is the tributary or catchment area in (km2)
For the application of the above formula, C, I and A must be known, and A
in (m2), then;
Q = CIA in (m3/s). (Agunwamba, 2001)
2.8.1.2 Rainfall intensity (I)
The Rational Method uses a rainfall intensity to represent the average
intensity for a storm of a given frequency for a selected duration (Viessman
and others; 1977). As noted, assumptions of the method include that the
rainfall intensity is constant over the entire basin and uniform for the time of
concentration. Of all the assumptions associated with the Rational Method,
the assumptions of constant, uniform rainfall intensity are the least valid in a
natural environment. However, the variability of rainfall intensity during a
storm and over a basin becomes less as the size of the basin decreases such
that these assumptions become more valid. The variability of rainfall
intensity in time and space is a major reason for an upper limit on basin size
when using the Rational Method to estimate peak flow.
Rainfall intensity is selected from an intensity-duration-frequency
(IDF) curve generated from point rainfall data collected in the local area.
This is, however, possible if both the duration (Tc) and the storm return
period (T) are known. These curves are generated by fitting annual
maximum rainfall intensities for specified durations to a Gumbel-probability
distribution, usually by plotting the data on extreme-value-probability paper
(Mckay, 1970). Figure 2.6 is an example of an IDF curve plotted on
arithmetic paper. The rainfall intensity is estimated by transferring the basin
time of concentration as duration in minutes through the desired storm
frequency curve in the same manner as shown in figure 2.6. For example, if
the hypothetical IDF curve in figure 2.6 is valid for the basin being analyzed
and it is determined that a basin has a time of concentration of 20 minutes,
then the rainfall intensity for the 25-year storm is 5.2 in/hour.
Oyebande and Longe (1990) obtained an empirical formula by using
Gumbel Extreme value distribution. In order to overcome the problem of
inadequate length of available records and poor aerial coverage of
hydrological data, data from individual stations of areas with similar rainfall
distribution were pooled together.
The equation obtained for rainfall intensity expressed in mm/hr is;
I = KTmtn
1-1
…(2.4)
where
K, m, and n1 are parameters dependent on the regions as classified in
Table 2.1;
T is the return period (yrs); and
t is the rainfall duration in (hrs).
If t<1, n1 is replaced by n2.
Table 2.1: Values of the parameters for computing rainfall intensity for
different regions.
Regions/stations Parameters
K M N1 N2
Group I
Port Harcourt, Calabar,
Umudike
54
0.26
-0.86
-0.38
Group II
Warri, Benin
47
0.28
-0.85
-0.38
Group III
Lagos, Ikeja, Oshodi
34
0.30
-0.89
-0.47
Group IVa
Oshogbo, Ondo, Ilora, Ibadan
40
0.28
-0.87
-0.51
Group IVb
Markudi, Enugu
38
0.32
-0.90
-0.48
Group VI
Bida, Ibi, Yola
38
0.32
-0.90
-o.52
Group VIIa
Lokoja, Minna
32
0.25
-0.90
-0.60
Group VIIb
Sokoto, Yelwa
33
0.27
-0.87
-0.61
Group VIII
Kano, Gusau, Zaria, Bauchi,
Samaru
33
0.32
-0.88
-0.60
Group IX
Potiskum, Maiduguri
32
0.30
-0.89
-0.59
Group X
Nguru, Karsina
30
0.32
-0.95
-0.64
Source: Oyebande and Longe (1990).
12-
11-
10-
9-
8-
7-
6-
5-
4-
3-
2-
50-yr
2-yr
5-yr
10-yr
25-yr
100-yr
Storm Frequency
RA
INF
AL
L I
NT
EN
SIT
Y, IN
CH
ES
PE
R H
OU
R
1-
0 10 20 30 40 50 60 70
Fig. 2.6 Hypothetical intensity-duration-frequency (IDF) curve. (plotted
from data provided by the U.S Geological Survey for small basins in Central
Virginia). (U.S.G.S, 2005).
The return period is chosen from 2 to 5 years, if damage due to
flooding is small, and from 20 – 100 years
when the damage is great (e.g when basements in commercial areas can be
flooded). Typical frequency (return) periods of storm sewers for different
districts are shown in Table 2.2 below (Agunmamba, 2001).
Table 2.2: Frequency periods of storm sewers for different areas.
Areas Frequency Period
Residential Areas 2-10 years
Commercial and high value district 10-50 years
Flood protection works 50 years
Urban roads 5 years
Source: Federal Republic of Nigeria Highway Manual Part 1.
2.8.1.3 Runoff coefficient (C)
The runoff coefficient, c is a dimensionless empirical coefficient
related to the abstractive and diffusive properties of the basin. Basin
abstractions including infiltration, depression storage, evapotranspiration,
and interception are lumped into the coefficient. Runoff diffusion is a
measure of the attenuation of the flood peak attributable to basin runoff
characteristics (Ponce, 1989). The runoff coefficient ranges between 0 and
1.0, where a value of 0 indicates that none of the rain falling on the basin
generates runoff, and a value of 1.0 indicates that all of the rain falling on
the basin generates runoff. A basin that has low land-surface slopes, high
infiltration rates, high ground-water storages, and extensive vegetation and
surface storage will have a low runoff coefficient. A steep basin with an
impervious surface, little vegetation, and no surface storage will have a high
runoff coefficient. Values of coefficient of runoff (C) for different vegetative
covers and slopes are given in Table 2.3.
Table 2.3: Runoff coefficient values for urban areas
Flat Rolling hilly
2-10% 10%
Pavement and roofs 0.90 0.90 0.90
Earth shoulders 0.50 0.50 0.50
Drives and walks 0.75 0.80 0.85
Gravel pavement 0.50 0.55 0.60
City business areas 0.80 0.85 0.85
Apartment dwelling areas 0.50 0.60 0.70
Normal Residential areas 0.40 0.50 0.55
Dense Residential areas 0.50 0.65 0.70
Lawn, sandy soil areas 0.10 0.15 0.20
Lawn, heavy soil areas 0.20 0.25 0.35
Grass shoulders 0.25 0.25 0.25
Side turfed slopes 0.30 0.30 0.30
Cultivated land (clay and loam) 0.50 0.55 0.60
Cultivated land (sand and gravel) 0.25 0.30 0.35
Industrial area 0.50 0.70 0.80
Parks and Cemeteries 0.10 0.15 0.20
Play grounds 0.20 0.25 0.30
Woodland and forests 0.10 0.15 0.20
Meadows and pasture land 0.25 0.30 0.35
Unimproved areas 0.10 0.30 0.30
Source: Federal Republic of Nigeria Highway Manual Part I ‘Drainage
Design’ section I.
2.8.1.4 Catchment Area (A)
This is the area contributing runoff into the drain. It is determined
from the topographical map by breaking the area into regular figures,
calculating each and summing up. A planimeter may also be used.
2.8.1.5 Design Computations
The VDOT (2002) design manual recommends use of the Rational
method for peak discharge design for acres up to 200 acres(2ha) except in
low-lying tide water areas where the method can be used for areas up to 300
acres(3ha). The form of the Rational Equation recommended by VDOT
(2002) is;
Q=Cf.C.I.A …(2.5).
where,
Q is the peak flow in (ft3/s),
Cf is the design storm frequency adjustment factor (dimensionless),
C is the runoff coefficient (dimensionless),
I is average rainfall intensity from an intensity-duration-frequency
curve for a duration equal to tc in (in/hour),
A is areas in acres,
Tc is time of concentration in minutes.
The only difference in this form of the Rational Equation and equation
(2.4) is inclusion of the storm frequency adjustment factor, Cf. Many
investigators have concluded – in contrast to the basic assumptions of the
Rational method – that the runoff coefficient varies with rainfall intensity
and duration (Ponce, 1989; Beadles, 2002; Pilgrim and Cordery, 1993), and
recommend that the runoff coefficient be adjusted for design of less frequent
floods. Values for Cf are selected from a chart, see fig. 4.10. A value of 1.0
is used when the combined value of C+Cf is greater than 1.0.
2.8.1.6 Time of Concentration
Time of concentration has several definitions. The minimum time
required after runoff begins for the entire basin to contribute flow to the
outlet is the definition preferred by the authors. Other definitions are the
time required for a particle of water to travel from the most hydraulically
distant point in the basin to the outlet (Wigham, 1970), and the time required
for a flood wave to travel from the most hydraulically distant point to the
outlet (National Resources Committee, 1939).
VDOT (2002) defines time of concentration as the time required for
water to flow from the hydraulically most distant point to the outlet.
Determination of time of concentration consists of combining flow times for
overland flow, channel flow, and conveyance flow in pipes, as appropriate,
at several locations within the basin. Overland flow computations should be
limited to approximately 200ft(61m) and either the Seelye method or
kinematic wave method used to compute flow times. For channel flow
computations, VDOT (2002) recommend use of the nomograph developed
by P.Z. Kirpich. No recommendations are given for determining flow time
through pipes.
The rainfall duration is assumed equal to the time of concentration
which is the time required for water to flow from the most remote part of the
area to the outlet. The time of the overland flow is influenced mainly by the
ground slope, surface cover and flow length.
The rainfall duration is assumed equal to the time of concentration
which is the time required for stormwater to flow from the most remote part
of the area to the outlet where measurements are being considered. The time
of overland flow is influenced mainly by the ground slope, surface cover and
flow length.
The time of concentration is the sum of the inlet time (ti) (time
required for runoff to gain entrance to the drain, assumed to vary from 1 to
20mins) and the flow time (tf) (time required by the stormwater to flow from
the beginning of the drain to the end). The time of concentration (mins) may
be expressed as,
Tc = 0.0078(L)0.77
(S)0.5
...(2.6)
where,
L is the flow path distance (ft) from the remotest part of the water
catchment to the drain outlet, while
S is the surface shape (slope).
These parameters are determined from the topographical map of the
project area. After metric conversion of L to meters,
Tc = 0.01947(L)0.77
(S) 0.5
… (2.7)
Tc and T are known, I can be determined from a rainfall duration
curve (e.g., fig. 4.9). where T is the storm return period in years. In some
areas where these graphs do not exist or cannot be produced because of lack
of data, it is usual to use rainfall-duration curves of other areas of similar
rainfall distribution.
The time of concentration, Tc and rainfall intensity may also be
computed using Izzard method (1946). That is,
Tc = 526.423bL1/3
(CrI)2/3
…(2.8)
The equation is valid only for laminar flow conditions where the product. IL
is less than 3871.
The coefficient b is expressed by
b = 2.8 X105 I Cr
S1/3
…(2.9)
The parameter Cr is the retardance coefficient with values 0.07 for
smooth asphalt surface, 0.012 for concrete pavement, 0.017for Tar and
gravel pavement and 0.060 for dense blue grass turf. Obtaining I using the
Izzard method (equation 2.8) involves trial and error since Tc is expressed as
a function of I.
Empirical relationships between rainfall duration and I also exist. For
instance,
I = a
t + b … (2.91)
where a and b are locality constants; a = 1846 and b = 3.6 for eastern part of
Nigeria.
For t>12 mins.
I = Co
ts …(2.92)
Typical value are s = ½ and Co = 446.
2.8.2 Khosla’s Formula:
R=P-4.811T …(2.93)
where,
R = annual runoff in (mm)
P = annual rainfall in (mm)
T = mean temperature in degree centigrade
2.8.3 Inglis Formulae for hilly and plain areas:
For hilly region
R = 0.88P – 304.8 ... (2.94)
For plain region,
R = (P – 177.8) X P
2540 ...( 2.95)
2.8.4 Lacey’s Formula:
R = P
1+3084F
PS ….(2.96)
where,
R = monsoon runoff in (mm)
P = monsoon rainfall in (mm)
S = catchment area factor
F = monsoon duration factor.
Values of S for various types of catchment area given below;
Types of catchment Values of S
Flat, cultivated and black cotton soils. 0.25
Flat, party cultivated, various soils. 0.60
Average catchment. 1.00
Hills and places with little cultivation 1.70
Very hilly and steep, with hardly any cultivation. 3.45
Values of F for various durations of monsoon are given below;
Class of monsoon Values of F
Very short 0.50
Standard length 1.00
Very long 1.50
2.8.5 Statistical Method
Hazen (1914) was one of the first to apply statistical methods to low
flow forecasting. As with peak flows, statistical methods are based on the
assumption that conditions recorded in the past will be repeated in the future
so that the reliability of these methods has inevitably improved considerably
since Hazen’s initial work simply because of the availability of longer and
more widespread flow records (Hudson and Hazen, 1964). Forecasting
procedures may be concerned with evaluating the minimum flow which is
likely to occur in the most severe drought conditions but are more frequently
concerned with estimating the probability of occurrence of low flows of a
given magnitude and with the duration of flows below a certain threshold
value.
An elementary but useful method is to plot a runoff duration curve,
either for the catchment whose low flow is to be predicted, or for adjacent
catchments, if no runoff records are available for the area in question.
An estimate of the frequency with which a given magnitude of runoff
may be exceeded in the future is based upon consideration of the recorded
historical pattern of runoff events. Unfortunately, the duration of runoff
records is normally so short that it is difficult to extrapolate them with a high
degree of reliability. In essence the main problem is that flood frequency
estimation involves the estimation of the tail of a probability distribution
curve from a sample of values which usually does not include values within
this tail (Melentijevich, 1969). However, statistical methods of extreme
value frequency analysis have been designed to extract the maximum
information from the recorded data and to evaluate the likely nature of the
distribution of the parent population from which the sample has been drawn
(Bruce and Clark, 1966).
Various methods of plotting extreme value data and of drawing
frequency curves through the plotted points have been devised, including
several types of special plotting paper on which the data will plot as a
straight line and are therefore, easier to extrapolate (Bruce and Clark, 1966).
One of the simplest and most practical methods of computing flood
frequency is as illustrated in Table 2.3 and Fig. 2.7. In this hypothetical
example the problem is to predict the likelihood of a certain sized runoff
peak occurring during a specified time, on a stream whose flow has been
measured for, say, 24 years. Using the annual maximum series, the peak
flows recorded during that period are arranged in descending order of
magnitude and the recurrence interval and probability are determined as
shown in Table 2.3. If the size of the peak flow and the probability are then
plotted on log-probability paper, as shown in fig. 2.7A, it will be seen that an
approximately straight line is described, which it is possible to extend in
order to predict floods with probability factors, within or outside the range
represented by the sample data. Alternatively, runoff may be plotted against
recurrence interval on semi-logarithmic coordinates as shown in fig. 2.7B.
Mathematical analyses have demonstrated that the mean annual flood has a
recurrence interval of 2.33 years, i.e., on average, the annual maximum flow
will exceed the mean maximum flow once every 2.33 years, and this
recurrence interval is indicated by the broken line.
This type of technique is quite successful provided that a long
sequence of recorded data is available. Where, however, the records are brief
or intermittent there is a considerable danger that the sample data will be
inadequate, and that extrapolations based upon them will be grossly
inaccurate. One frequently used method of reducing sampling error is
regional analysis, whereby data from within homogeneous area, or from
adjacent similar areas, are combined to increase the sample size, and thus to
improve the quality of the result (Alexander, 1963; Satter lund, 1967). A
homogeneity test was developed by Langbein (1947) to define a
homogeneous region and various methods of regional analysis have been
developed, including the construction of regional flood frequency curves
(Dalrymple, 1960).
Table 2.3 Probability and recurrence interval calculated from a 24 year
annual maximum series for a hypothetical stream
Runoff Peak
(cumecs)
Order number
(m)
Probability m_
n+1
(Percent)
Recurrence Interval
n+1
m (years)
150000 1 4 25.00
135000 2 8 12.50
126000 3 12 8.33
117000 4 16 6.25
114000 5 20 5.00
108000 6 24 4.17
105000 7 28 3.57
102000 8 32 3.13
100500 9 36 2.78
96000 10 40 2.50
93000 11 44 2.27
91500 12 48 2.08
87000 13 52 1.92
84000 14 56 1.79
81000 15 60 1.67
79500 16 64 1.56
78000 17 68 1.47
75000 18 72 1.39
72000 19 76 1.32
70500 20 80 1.25
66000 21 84 1.19
63000 22 88 1.14
57000 23 92 1.09
51000 24 96 1.04
where n is the number of years o record and m is the rank of the item in the
array.
300 -
200 -
150 -
100 -
50 -
30 - Runoff
in c
um
ecs
(thousa
nds)
-
10 -
99.99 99.8 98 80 50 20 2.0 0.2 0.0
Probability (percent)
Fig. 2.7A Log-Probability graph of peak flows listed in Table 3.4
220 -
200 -
180 -
160 -
Runoff
in c
um
ecs
140 -
120 -
100 -
80 -
60 - Q2.33
1 2 3 5 10 20 30 50 100 200 300
Recurrence interval (return period) in years
Fig. 2.7B Recurrence interval graph of peak flows listed in Table 2.3.
2.9 Direct Measurement of runoff.
The reliability of many hydrological measurements, e.g., rainfall and
evapotranspiration, depends upon the representativeness of the catchment, in
the case of rainfall, or the loss, in the case of evapotranspiration, from a very
small sample area. Only a minute part of the total volume of rain falling on a
catchment area, for example, is caught by even an extremely dense network
of gauges, and yet large varieties of rainfall over small distances is usually
recorded.
In the case of measurements of runoff, however, inaccuracies
resulting from this type of sampling do not occur, since the total volume of
streamflow which passes a given point may be measured. If the measuring
device is located at the lowest point in a catchment area, and providing there
is no leakage of underground water across the divides, it may be assumed
that all the streamflow from the catchment area will pass the measuring
point. From this point of view, therefore, runoff data should be more reliable
than any other of the basic hydrological data.
2.9.1 Velocity – area method
The velocity-area method comprises three related operations. The first
involves the determination of the height or stage of the stream surface; the
second the determination of the mean velocity of the stormwater flow in the
stream channel; and the third the derivative of a known relationship between
stage and the total volume of discharge.
The discharge of a stream, i.e, the total volume of water flowing past a
given point in a known unit of time, is the product of the cross-sectional area
of the stream and the speed with which the water is flowing. Provided that
the stream bed and banks have been accurately surveyed at the point of
measurement, only data on the storage of the stream is needed to enable the
cross-sectional area of the water in the stream channel to be rapidly
calculated. Thereafter, the volume of discharge may be readily calculated if
the mean velocity of the current is known.
The measurement of current velocity in streams and rivers is normally
accomplished by means of a current meter. Alternatively, current velocities
may be determined directly using deflecting vanes, pitometers or floats or
may be estimated by means of one of the commonly used theoretical flow
equations for the steady flow of water in open channels such as that
proposed by Manning (1889) or Chezy.
2.9.2 Weirs and Flumes
On streams where a physical obstruction in the channel is permissible,
e.g., small tributaries and drainage channels which are not used for
navigation, discharge may be accurately measured by means of a weir or
flume. These are rigid structures whose cross-sectional area is closely
defined and stable and which, therefore act as a permanent control. Since the
velocity of falling water (or indeed of any other substance) depends solely
on the height of fall and the acceleration due to gravity (i.e., V2 = 2gh), and
since the acceleration due to gravity is constant, it follows that, in order to
measure accurately the velocity of a stream, it is only necessary to cause the
water to fall (as over a weir or through a flume), and to measure the head of
water by means of a continuous recorder at an appropriate point. Insofar as
this basic theory of measurement is concerned, the only significant
difference between weirs and flumes is that there is a loss of head (and of
kinetic energy) over the weir, whereas there is a considerable recovery of
head (preservation of kinetic energy) in the case of the flume.
There are two main types of weirs, which are; sharp-crested and
broad-crested, the former being more commonly used where precise
measurement is required. One important advantage of the flume is that it is
self-cleansing because of the high velocity through and below the control
section. Because of this, it is particularly suited to discharge measurement in
silt and debris-laden water.
CHAPTER THREE
METHODOLOGY
The studys for which the available data were obtained was aimed at
estimating runoff discharge using the unit hydrograph method, rational
method, Khosla and Inglis formulae. For the present case, the aim is to
compare the results of these methods with the measured peak discharge at
the catchment outlets. The available data was obtained from series of field
measurements through the use of the current meter and the meter rule, to
determine the velocity and depth of flow respectively.
3.1 Gauge Stations
The catchment area was divided into four sub-areas. This was done
such that the time of concentration increases from one sub-area to the next.
Thus the times of concentration for the sub-areas I, II, III and IV are 30min,
33min, 36min and 40min respectively. Thus, in the first 30min, only the sub-
area I contributes the discharge at outlet. In the next 3min, both the areas I
and II contribute, and so on. Hence, each sub-areas contributes to the total
discharge from the catchment during the entire storm period.
Runoff then can be computed from the discharge and time as in the
hydrograph method.
3.2 Empirical Formulae
In this method an attempt is made to derive a direct relationship
between the rainfall and subsequent run-off. For this purpose some constants
are established which give fairly accurate result for a specified region.
Virtually all methods of runoff prediction and forecasting contain an element
of approximation and empiricism; the heading of this section may be
considered misleading. However, as with equality, so with empiricism, some
methods are more empirical than others. The main weaknesses of such
methods are normally their non-generality and the difficulty of knowing the
exact conditions under which they may be used. One of the earliest and best-
known attempts to estimate peak flows was the so-called rational formula.
3.3 Velocity – area method
The velocity-area method comprises three related operations. The first
involves the determination of the height or stage of the stream surface; the
second is the determination of the mean velocity of the water flowing in the
stream channel; and the third the derivative of a known relationship between
stage and the total volume of discharge.
The discharge of a stream, i.e, the total volume of water flowing past a
given point in a known unit of time, is the product of the cross-sectional area
of the stream and the speed with which the water is flowing. Provided that
the stream bed and banks have been accurately surveyed at the point of
measurement, only data on the storage of the stream is needed to enable the
cross-sectional area of the water in the stream channel to be rapidly
calculated. Thereafter, the volume of discharge may be readily calculated if
the mean velocity of the current is known.
The measurement of current velocity in streams and rivers is normally
accomplished by means of a current meter. Alternatively, current velocities
may be determined directly using deflecting vanes, pitometers or floats or
may be estimated by means of one of the commonly used theoretical flow
equations for the steady flow of water in open channels such as that
proposed by Manning, (1889).
3.4 Unit hydrograph method
The peak flow alone does not give sufficient information about the
runoff since it (peak flow) represents a momentary value. Therefore, it is
necessary to understand the full hydrography of flow. The basic concept of
unit hydrograph is that the hydrographs of runoff from two identical storms
would be the same. In practice, identical storms occur very rarely. The
rainfall generally varies in duration, amount and areal distribution. This
makes it necessary to construct a typical hydrograph for a basin which could
be used as a unit of measurement of runoff.
0
1
2
3
4
5
6
0 3 6 9 12 15 18 21 24 27 30
Time (Hrs)
3Hrs-Unit-Hydrograph
0
0.05
0.1
0.15
0.2
0.25
0 3 6 9 12 15 18 21 24 27 30
Times (Hrs)
Dis
ch
arg
e (
cu
me
cs
)
(cu
me
cs
)
Fig. 4.1: A 3-hr Effective Duration of Storm
Hydrograph
STATION I D
isc
harg
e (
cu
me
cs
)
CHAPTER FOUR
RESULTS AND ANALYSIS
4.1 Unit Hydrographs
Fig. 4.2: A 3-hr Unit Hydrograph
3Hrs-Storm Hydrograph
0
1
2
3
4
5
6
0 3 6 9 12 15 18 21 24 27 30
Time (Hrs)
Dis
ch
arg
e (
cu
me
cs
)
3-Hrs-Unit Hydrograph
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 3 6 9 12 15 18 21 24 27 30
Time (Hrs)
Dis
ch
arg
e (
cu
nm
ec
s)
Fig. 4.4: A 3-hr Unit Hydrograph
STATION II
Fig. 4.3: A 3-hr Effective Duration of Storm
Hydrograph
STATION III
3-Hrs storm Hydrograph
0
1
2
3
4
5
6
0 3 6 9 12 15 18 21 24 27 30
Time (Hrs)
Dis
ch
arg
e (
cu
me
cs
)
3-Hrs Unit Hydrograph
0
0.02
0.04
0.06
0.08
0.1
0.12
0 3 6 9 12 15 18 21 24 27 30
Time (Hrs)
Dis
ch
arg
e (
cu
me
cs
)
Fig. 4.6: A 3-hr Unit Hydrograph
Fig. 4.5: A 3-hr Effective Duration of Storm
Hydrograph
STATION IV
3-Hrs Storm Hydrograph
0
1
2
3
4
5
6
0 3 6 9 12 15 18 21 24 27 30
Time (Hrs)
Dis
ch
arg
e (
cu
me
cs
)
3-Hrs Unit Hydrograph
0
0.01
0.02
0.03
0.04
0.05
0.06
0 3 6 9 12 15 18 21 24 27 30
Time (Hrs)
Dis
ch
arg
e (
cu
me
cs
)
Fig. 4.8: A 3-hr Unit Hydrograph
Fig. 4.7: A 3-hr Effective Duration of Storm
Hydrograph
4.2 Rational Formula
Intensitiy -Duration Frequency Curve
0
50
100
150
200
250
300
350
400
450
500
30 60 90 120
Duration of Rainfall (min)
Rain
fall
in
ten
sit
y (
mm
/hr)
2-Yr rainfall intensity (mm/hr)
5-Yr rainfall intensity (mm/hr)
10-Yr rainfall intensity (mm/hr)
100-Yr rainfall intensity(mm/hr)
Fig.4.9: Intensity-Duration Frequency (IDF) curve of Nsukka campus.
The catchment area was obtained from the topographical map, I from
fig. 4.9 while C was obtained from a table (Agunwamba, 2001). These
values and the corresponding discharges obtained from the rational formula
are given in Table 4.1.
Table 4.1 Discharge obtained from Rational formula.
STATION Area, A
(km2)
Rainfall
Intensity, I
(mm/hr)
Coefficient of
Runoff,C
Discharge
(cumecs)
I 0.765 220 0.40 18.715
II 0.573 210 0.40 13.381
III 0.383 200 0.40 8.519
IV 0.191 190 0.40 4.035
DESIGN STORM FREQUENCY ADJUSTMENT FACTOR [Cf]
The maximum rainfall intensity, Imax = 446.2 mm/hr. Using a storm frequency
adjustment factor (Cf) of 0.30 for the maximum storm intensity (since runoff
coefficient varies with rainfall intensity and duration and constitute about
30% of basin losses) (VDOT, 2002).
Cf=Ip X 0.30 …(4.1)
Imax
where, Ip = peak storm intensity for the year.
Year Ip (mm/hr) Imax (mm/hr) Cf
1973 446.20 446.20 0.30
1981 439.70 ,, 0.30
1974 429.60 ,, 0.29
1979 404.20 ,, 0.27
1980 373.30 ,, 0.25
1972 372.70 ,, 0.25
1971 364.90 ,, 0.25
1978 364.90 ,, 0.25
2007 327.66 ,, 0.22
1975 327.30 ,, 0.22
2008 326.02 ,, 0.22
2006 313.94 ,, 0.21
1982 312.90 ,, 0.21
1976 306.70 ,, 0.20
1977 251.20 ,, 0.17
1983 241.20 ,, 0.16
0.30 –
0.20 –
0.1 –
0 20 40 60 80 100 120 140 160 180 200 220
Mean Annual Rainfall Intensity
(mm/hr)
Des
ign
sto
rm-f
req
uen
cy a
dju
stm
ent
fact
or
(Cf)
Fig. 4.10: Design storm frequency adjustment factor chart
Design Computations
The modified rational formula is given by;
Q = 0.278 Cf CIA
where, Cf = design storm frequency adjustment factor (obtained from chart)
Table 4.2 Discharge obtained by the various methods.
STATION Modified
Rational
method
Khosla’s
Formula
Inglis Formula Velocity
Area
method
(measured)
Cf Discharge
(cumecs)
T
(oC)
Discharge
(cumecs)
P
(mm)
Discharge
(cumecs)
Discharge
(cumecs)
I 0.17 3.182 25.5 0.861 220 0.032 0.188
II 0.18 2.409 25.5 0.773 210 0.024 0.144
III 0.19 1.619 25.5 0.684 200 0.015 0.102
IV 0.19 0.767 25.5 0.596 190 0.008 0.050
0
0.5
1
1.5
2
2.5
3
3.5
1 2 3 4
Stations
Dis
ch
arg
e (
cu
me
cs
)
Modified Rational Formula
Khosla
Inglis
Measured
Unit Hydrograph
Fig. 4.11: A graph of Discharges against Station for all the methods used.
4.3 Relationship between Estimated and Measured Runoff
Discharge
Qe = 17.6Qm – 0.135 ---------------------------- Rational Formula
Qe = 1.115Qm ----------------------------------- Unit Hydrograph Method
Qe = 1.93Qm + 0.494--------------------------- Khosla’s Formula
where, Qe = Estimated runoff discharge at the catchment.
Qm = measured runoff discharge at the catchment.
From the results obtained above, the unit hydrograph method gave
the best estimation of the runoff discharge when compared with other
methods, for all the sub-catchments. Only the Inglis formula gave discharge
estimates below the observed discharges at each of the sub-catchments. It is
therefore not suitable for these catchments.
CHAPTER FIVE
CONCLUSION AND RECOMMENDATION
5.1 CONCLUSION
This project work reviewed and compared the different methods
of runoff discharge estimation for drainage design. The design of a drainage
structure requires hydrologic analysis of precipitation amount and duration,
peak rate of runoff, and the time distribution of runoff from a given basin.
Many hydrologic methods are available for estimating peak flows from a
basin, and no single method is applicable to all basins. Although, of all the
methods reviewed, the unit hydrograph method gave a much closer
estimation of the basin peak flows, it is however not widely applied owing to
the disadvantages of non-availability of runoff data for a minimum of
25years for a particular catchment and the cost for obtaining such data.
Although, the Khosla’s formula proved relatively effective in the estimation
of the basin peak flow, it is however, limited in application since basin
hydrological characteristics vary significantly from catchment to catchment.
The rational formula, though it over-estimates, is commonly used
to estimate the design-storm peak discharge. The advantages of this method
are its simplicity in application, relative availability of data and low cost of
obtaining these data. Once a basin rainfall intensities for a minimum of 25
years are available, the rational formula can then be applied. With the
modification in the rational formula, it is therefore considered appropriate
for the estimation of runoff discharge in many basins particularly in regions
were sufficient hydrologic data are not available.
5.2 RECOMMENDATIONS
(1) The unit hydrograph method is recommended for a basin whose
runoff data are available for a minimum of 25 years.
(2) Where these data are insufficient, the improved rational formula
can be applied.
(3) In applying the modified rational formula, effort should be made
to obtain the design storm frequency adjustment factor (Cf) chart peculiar to
the region of interest.
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APPENDIX I
Rainfall intensity of the University of Nigeria, Nsukka Campus.
Rainfall intensity for the year 2006.
Month Rainfall intensity
(mm/hr)
No. of rain (days)
January 36.32 1
February 4.06 2
March 103.12 4
April 51.05 5
May 243.83 16
June 259.60 16
July 213.86 21
August 195.58 19
September 190.50 25
October 313.94 19
November 1.54 1
December - -
Mean Rainfall Intensity = 146.67mm/hr.
2007
Month Rainfall intensity
(mm/hr)
No. of rain (days)
January - -
February 9.91 1
March 39.12 4
April 121.66 8
May 193.55 11
June 327.66 16
July 62.99 14
August 323.60 17
September 169.67 19
October 267.20 18
November 55.12 4
December - -
Mean Rainfall Intensity = 157.05mm/hr.
APPENDIX II
2008.
Month Rainfall intensity No. of rain (days)
(mm/hr)
January - -
February - -
March 61.23 4
April 143.30 11
May 254.01 12
June 186.43 15
July 246.10 14
August 203.20 19
September 326.02 22
October 198.63 11
November 8.38 2
December 10.93 2
Mean Rainfall Intensity = 163.82mm/hr.
1983
Month Temperature
(oC)
Wind
speed
(km/day)
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min.
January 30.0 18.0 223.0 4.7 20.0 0.0
February 34.0 20.0 156.9 5.7 54.0 0.0
March 35.0 21.0 168.3 3.2 51.7 0.0
April 35.0 21.0 183.9 5.2 68.8 13.7
May 31.0 19.0 156.1 1.5 78.0 114.9
June 28.0 19.0 133.6 0.8 86.0 168.5
July 27.0 18.0 122.0 0.6 89.0 158.3
August 26.0 18.0 96.7 1.0 92.0 102.4
September 28.0 18.0 67.6 1.4 67.0 241.2
October 29.0 17.0 75.6 2.0 79.0 55.8
November 31.0 19.0 96.8 1.8 75.0 33.1
December 31.0 18.0 99.3 1.9 67.0 11.2
Mean Rainfall intensity = 99.90 mm/hr.
APPENDIX III
1982
Month Temperature
(oC)
Wind
speed
(km/day)
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min.
January 32.0 21.0 127.0 6.5 40.0 17.3
February 33.0 22.0 149.7 5.9 59.0 55.7
March 32.0 22.0 157.8 6.1 51.0 56.4
April 32.0 22.0 169.2 6.3 76.0 83.4
May 30.0 21.0 114.1 5.4 81.0 217.2
June 27.0 20.0 119.8 4.2 86.0 225.4
July 27.0 19.0 113.8 3.1 90.0 312.9
August 26.0 19.0 136.3 2.3 90.0 180.9
September 27.0 19.0 88.5 2.5 88.0 228.5
October 28.0 19.0 97.8 4.3 65.0 303.1
November 30.0 18.0 99.8 6.6 64.0 19.0
December 32.0 18.0 108.5 6.7 66.0 0.0
Mean Rainfall intensity = 154.53 mm/hr
1981
Month Temperature
(oC)
Wind
speed
(km/day)
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min.
January 31.0 19.0 142.5 6.0 45.0 4.8
February 34.0 24.4 172.8 6.2 68.0 0.0
March 33.0 23.0 186.3 5.4 75.0 53.7
April 33.0 23.0 196.3 6.1 73.0 26.2
May 31.0 22.0 145.0 5.0 89.0 286.9
June 29.0 22.0 147.0 4.9 83.0 84.3
July 27.0 21.0 146.7 3.1 80.0 184.7
August 27.0 21.0 132.9 2.6 81.0 271.7
September 28.0 21.0 98.4 2.6 77.0 439.7
October 29.0 21.0 102.2 4.8 76.0 234.3
November 30.0 19.0 111.7 6.8 64.0 32.5
December 32.0 19.7 107.2 7.3 61.0 0.0
Mean Rainfall intensity = 161.88 mm/hr
APPENDIX IV
1980
Month Temperature
(oC)
Wind
speed
(km/day)
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min.
January 33.0 21.0 137.4 7.6 63.0 0.0
February 34.0 23.0 146.8 4.9 68.0 7.6
March 33.0 23.0 177.5 5.7 68.0 63.5
April 32.0 23.0 175.1 5.7 60.0 118.7
May 30.0 23.0 133.2 5.2 82.0 146.8
June 29.0 22.0 138.2 5.3 84.0 182.9
July 27.0 22.0 128.9 3.2 88.0 346.6
August 27.0 21.0 114.6 3.3 91.0 362.3
September 28.0 21.0 85.6 3.4 84.0 373.3
October 29.0 21.0 91.9 4.5 82.0 190.3
November 30.0 21.0 92.9 6.1 76.0 38.6
December 30.0 20.0 139.3 6.6 58.0 0.0
Mean Rainfall intensity = 183.06 mm/hr
1979
Month Temperature
(oC)
Wind
speed
(km/day)
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min.
January 33.0 20.0 131.4 8.2 56.0 0.0
February 32.0 23.0 149.3 6.2 76.0 48.8
March 33.0 23.0 147.1 5.1 73.0 23.9
April 33.0 23.0 174.8 0.0 73.0 100.6
May 30.0 22.0 126.0 5.6 80.0 198.5
June 29.0 22.0 144.7 4.8 83.0 135.6
July 28.0 21.0 148.3 3.4 85.0 326.2
August 27.0 21.0 150.6 2.7 90.0 404.2
September 28.0 21.0 96.8 4.1 82.0 300.7
October 29.0 21.0 100.6 5.1 82.0 269.5
November 30.0 23.0 98.2 6.1 81.0 57.0
December 31.0 18.0 127.4 7.8 47.0 0.0
Mean temp. = 25.5 oC, mean rainfall intensity 186.5 mm/hr.
APPENDIX V
1978
Month Temperature
(oC)
Wind
speed
(km/day)
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min.
January 32.2 20.0 110.3 8.8 33.0 0.3
February 33.9 23.3 101.2 6.8 45.0 17.1
March 32.8 22.8 106.8 7.1 50.0 51.6
April 30.6 21.7 95.5 5.5 67.0 245.9
May 30.0 21.7 82.0 6.5 70.0 364.9
June 28.3 20.6 85.6 5.1 73.0 242.4
July 26.7 20.6 101.7 3.0 77.0 167.8
August 27.2 21.1 97.9 3.4 77.0 178.3
September 28.0 21.0 124.4 3.2 76.0 217.3
October 30.0 21.0 105.3 5.0 76.0 217.3
November 30.0 19.0 116.6 8.3 74.0 39.0
December 31.0 20.0 105.3 8.2 68.0 6.1
Mean Rainfall intensity = 150.26 mm/hr
1977
Month Temperature
(oC)
Wind
speed
(km/day)
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min.
January 27.6 21.7 141.5 5.8 51.0 9.4
February 32.8 22.2 154.7 6.1 61.0 3.3
March 33.3 22.8 180.4 2.9 62.0 42.7
April 32.2 23.3 181.8 4.6 74.0 31.8
May 31.1 22.2 186.2 6.3 77.0 143.3
June 28.3 21.1 176.4 4.7 85.0 140.3
July 27.2 20.6 170.1 4.0 86.0 239.2
August 26.7 20.6 163.2 3.3 89.0 131.3
September 27.8 21.1 126.2 3.2 81.0 251.2
October 28.9 21.7 112.8 5.6 82.0 187.7
November 35.0 20.6 129.4 8.9 63.0 0.0
December 31.1 18.9 170.1 8.9 48.0 13.7
Mean Rainfall intensity = 108.54 mm/hr.
APPENDIX VI
1976
Month Temperature
(oC)
Wind
speed
(km/day)
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min.
January 31.1 19.4 162.6 6.4 57.0 0.0
February 31.1 22.2 193.0 6.1 78.0 134.5
March 30.6 22.2 177.9 5.8 80.0 32.2
April 30.6 22.2 170.3 5.1 82.0 123.1
May 28.9 21.7 153.3 4.1 82.0 212.3
June 28.3 20.4 155.6 5.4 84.0 124.6
July 26.1 20.0 174.5 3.0 91.0 117.6
August 26.1 20.6 171.4 2.5 90.0 104.4
September 27.8 21.1 154.0 3.8 86.0 268.5
October 27.8 21.1 138.0 3.4 86.0 306.7
November 29.4 21.1 142.8 6.2 78.0 46.2
December 31.1 20.6 137.9 6.2 73.0 59.4
Mean Rainfall intensity = 139.05 mm/hr.
1975
Month Temperature
(oC)
Wind
speed
(km/day)
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min.
January 31.1 18.3 191.0 5.3 37.0 0.0
February 32.8 22.2 185.3 6.8 63.0 1.5
March 32.2 22.8 205.8 5.0 75.0 55.8
April 31.1 22.8 190.2 7.2 74.0 68.4
May 29.4 21.1 158.6 6.1 81.0 205.0
June 28.9 21.1 173.7 4.5 83.0 211.7
July 27.2 20.6 168.0 3.5 88.0 146.1
August 26.1 20.6 197.3 3.6 88.0 150.5
September 26.7 20.0 156.6 3.3 86.0 327.3
October 28.3 20.6 130.5 4.5 81.0 187.9
November 29.4 21.7 135.5 5.6 76.0 20.5
December 30.6 17.8 170.3 5.3 37.0 31.6
Mean Rainfall intensity = 127.85 mm/hr.
APPENDIX VII
1974
Month Temperature
(oC)
Wind
speed
(km/day)
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min.
January 30.6 18.9 152.8 4.9 53.0 0.0
February 32.8 21.7 178.3 6.4 64.0 29.7
March 32.8 27.2 201.6 4.6 72.0 38.4
April 31.1 21.7 185.5 6.0 78.0 134.6
May 29.4 21.1 158.6 4.9 78.0 254.0
June 28.3 21.1 161.9 4.5 79.0 186.6
July 27.2 20.6 162.0 3.1 86.0 178.4
August 27.2 21.1 189.0 3.1 86.0 132.4
September 27.2 20.6 163.2 3.9 85.0 429.6
October 28.3 20.6 148.0 4.5 84.0 301.3
November 30.6 20.6 148.0 6.9 73.0 1.8
December 30.6 18.3 182.0 4.8 48.0 0.0
Mean Rainfall intensity = 168.68 mm/hr.
1973
Month Temperature
(oC)
Wind
speed
(km/day)
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min.
January 31.7 21.7 158.2 4.7 66.0 8.1
February 33.3 23.3 180.1 6.4 70.0 2.2
March 33.3 23.3 210.1 5.8 65.0 25.1
April 32.2 22.8 187.9 4.7 72.0 96.0
May 30.0 21.7 163.6 5.5 78.0 267.7
June 28.3 21.1 155.3 3.4 84.0 326.6
July 27.8 21.1 180.2 3.7 84.0 103.5
August 27.8 21.1 212.2 4.2 86.0 165.7
September 27.8 23.9 138.3 3.3 85.0 446.2
October 28.9 20.6 127.5 3.5 81.0 200.3
November 31.1 19.4 137.6 5.8 61.0 50.8
December 30.6 21.7 145.7 4.6 76.0 33.3
Mean Rainfall intensity = 146.79 mm/hr.
APPENDIX VIII
1972
Month Temperature
(oC)
Wind
speed
(km/day)
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min.
January 31.7 20.0 152.8 5.4 71.0 21.5
February 32.2 22.8 178.3 6.0 84.0 31.0
March 31.7 22.8 200.0 2.8 54.0 41.4
April 30.0 21.7 185.5 4.5 80.0 161.0
May 30.0 21.7 156.9 6.2 68.0 172.5
June 28.3 21.1 164.7 4.6 83.0 216.6
July 27.8 21.1 145.5 3.9 85.0 100.9
August 26.7 20.6 116.9 3.2 88.0 163.0
September 27.2 21.1 134.1 3.1 87.0 372.7
October 28.3 20.6 123.9 5.5 81.0 201.6
November 31.1 18.9 130.7 8.7 64.0 0.0
December 31.1 20.0 160.3 8.7 62.0 19.6
Mean Rainfall intensity = 136.53 mm/hr.
1971
Month Temperature
(oC)
Wind
speed
Sunshine
(hours)
Humidity
(%)
Rainfall
(mm/month)
Max. Min. (km/day)
January 31.1 20.0 150.7 5.1 57.0 0.0
February 32.2 22.2 176.7 6.9 73.0 10.2
March 32.2 22.2 200.0 6.5 74.0 21.9
April 31.1 22.2 183.9 6.6 76.0 120.1
May 31.0 21.0 156.9 6.3 80.0 206.0
June 27.8 20.6 162.3 3.3 83.0 251.5
July 26.7 20.6 162.5 3.1 88.0 288.5
August 26.1 20.6 187.4 3.6 90.0 364.9
September 27.2 20.0 161.5 4.1 86.0 321.9
October 28.9 21.1 146.4 6.0 82.0 160.0
November 31.1 20.6 146.4 6.7 67.0 0.0
December 31.1 19.4 180.4 4.5 51.0 4.1
Mean Rainfall intensity = 174.91mm/hr
Unit Hydrograph Data
Run-off Discharge, UNN, July 2009
STATION 1
Time (hrs) Run-off (cumecs)
0 0.5
3 1.1
6 2.3
9 3.0
12 5.5
15 3.5
18 2.3
21 1.8
24 1.2
27 0.9
30 0.5
Time (hrs) Run-off
(cumecs) (1)
Base flow
(2)
Ordinate of DRO
(3) = (1) - (2)
Ordinate of U.H
(4) = (3) ÷ 24.14
0 0.5 0.5 0 0
3 1.1 0.5 0.6 0.02
6 2.3 0.5 1.8 0.07
9 3.0 0.5 2.5 0.10
12 5.5 0.5 5.0 0.21
15 3.5 0.5 3.0 0.12
18 2.3 0.5 1.8 0.07
21 1.8 0.5 1.3 0.05
24 1.2 0.5 0.7 0.03
27 0.9 0.5 0.4 0.02
30 0.5 0.5 0 0
ΣO = 17.10
Run-off (cumecs)
Time (hrs) Station II Station III Station IV
0 0.5 0.5 0.5
3 1.0 0.9 0.8
6 2.1 2.1 2.0
9 3.0 2.8 2.7
12 5.2 5.1 5.0
15 3.2 3.1 3.0
18 2.1 2.0 2.0
21 1.6 1.5 1.4
24 1.1 1.1 1.0
27 0.7 0.6 0.6
30 0.5 0.5 0.5
Ordinate of U.H
Time (hrs) Station II Station III Station IV
0 0.0 0.0 0.0
3 0.017 0.010 0.004
6 0.055 0.039 0.019
9 0.086 0.055 0.028
12 0.161 0.111 0.057
15 0.092 0.063 0.032
18 0.055 0.036 0.019
21 0.038 0.024 0.011
24 0.021 0.014 0.006
27 0.007 0.002 0.001
30 0 0 0
Velocity – Area Data
STATION I
Table 4.11; Velocity Measurement
S/No. Rev. Time (s) Rev/time (n) Depth of
flow
1 327 30 10.90 300
2 591 60 9.85 310
3 339 30 11.30 300
4 316 30 10.53 280
5 321 30 10.70 310
STATION II
Table 4.12: Velocity Measurement
S/No. Rev. Time (s) Rev/time (n) Depth of
flow
1 321 30 10.70 220
2 310 30 10.33 240
3 312 30 10.40 250
4 316 30 10.53 240
5 307 30 10.23 250
Width of drainage = 1000mm
Discharge, Q = 0.144 cumecs
STATION III
Table 4.13: Velocity Measurement
S/No. Rev. Time (s) Rev/time (n) Depth of
flow
1 300 30 10.00 210
2 305 30 10.17 200
3 311 30 10.37 190
4 308 30 10.27 200
5 302 30 10.07 200
Width of drainage = 1000mm
Discharge, Q = 0.102 cumecs
STATION IV
Table 4.14: Velocity Measurement
S/No. Rev. Time (s) Rev/time (n) Depth of
flow
1 165 30 5.50 150
2 200 30 6.67 130
3 178 30 5.93 160
4 202 30 6.73 160
5 152 30 5.07 150
Width of drainage = 1000mm
Discharge, Q = 0.050 cumecs