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close this bookHandbook for Agrohydrology (NRI)
close this folderChapter 2: Measurement of runoff
View the document(introduction...)
View the document2.1 Estimates of runoff
View the document2.2 Collecting runoff data
View the document2.3 Water level recording instruments
View the documentEquipment costs
View the documentAppendix A: Measurement of runoff

2.1 Estimates of runoff

Estimates of runoff are made for two reasons:

1. They are essential guides in the decision of which system of runoff measurement to use, either volumetric or continuous. After this decision has been made, these estimates must be used to determine the size and capacity (peak flow and flow volume) of the equipment.

2. If the measurement of runoff is not to be undertaken, then calculations must be made to estimate the design specifications of bunds, channels etc. that are to be used in the mechanics of water harvesting and field layouts.

2.1.1 Estimates Based on Previous Data

A project may be fortunate in succeeding previous work that has already undertaken runoff measurement. These data can provide a good starting point for the selection of appropriate equipment. For example "Will a 100 litre collection tank be large enough to collect runoff from a 50 m² plot when previous data show that a 50 litre tank was large enough for a 20 m² plot?". The answer in this case would probably be "Yes", but caution must be exercised. Comparisons of catchment size, land use, slope and rainfall must be made to ensure that these data can be used for the purpose of installation design. Generally, if a project is succeeding another it is likely that most of the physical conditions under which the new project will operate will be similar and catchment size may be the primary concern in estimating flow peaks and volumes. Catchment size is by no means the main influence on runoff amount, however.

Consider Table 2.1 below, data from a strip tillage experiment undertaken in semi-arid SE Botswana. All physical conditions for the plots, including rainfall for each season, were identical. In both seasons the smallest plots produced most runoff (both seasonal and event by event) and the conclusion may be drawn that catchment size exerts an influence on runoff, though this influence appears to be relatively small and is unlikely to cause serious problems in estimating probable runoff proportions, volumes or peak flows, by a simple ratio of previous to proposed catchments areas. The complete set of rainfal/runoff data relating to these plots is given in chapter 7, section 7.1.

Other research has shown that for small plots, runoff proportions (percentages, sometimes called "runoff efficiencies") tend to be larger for small catchments until the distance of flow is about 80 m. Thereafter it is assumed that runoff proportions remain the same for catchments with the same conditions.

Table 2.1: Runoff Proportion (%) versus Catchment Size (average of 2 replicates)

Other factors can be much more influential than catchment size. In the example above, the variation in runoff from catchments of the same size due to differences in rainfall between the seasons was as great as that due to plot size. It must be remembered that data from previous work may have been collected during historical periods with greater or lesser rainfall amounts and/or intensities than those of a new project, even though the location of the data collection site is the same. Variations in other catchment physical conditions, such as vegetation and crop cover, the level of which are determined by yet other environmental circumstances (especially rainfall and human activity), may also be important. The data in Table 2.2 shows runoff from the same-sized plots at the same site for three different rainfall seasons, each plot has a different kind and density of vegetation cover. The data are from a rangeland area of SE Botswana.

Table 2.2: Variation of Seasonal Runoff (%) with Vegetation Cover

Note that not only does vegetation cover type and extent determine runoff, but once again the difference in seasonal rainfall exerts a strong influence. In this case the season with most rainfall produced least runoff from all plots. This kind of comparison shows the influence of different, variable conditions on runoff.

The difficulties in estimating future runoff from past data are best overcome by a statistical analysis of the information: changes in catchment condition or rainfall pattern which affect runoff amount will be present in the data and will be accounted for.

The main design criterion of hydrological equipment is whether or not this equipment will cope with the largest individual runoff event in any given number of seasons. In experimental and equipment design, it is the balance struck between the cost of the over-design of equipment and the possibility of equipment failure during large storms, that is particularly important. A probability must be assigned to the occurrence of the particular design flow or peak that is selected. This can be done by several statistical methods the simplest of which is the annual maximum series, outlined below:

a. Theoretical Distributions

Runoff data are often matched to statistical distributions with known forms. Extrapolation can be made relatively simple where a good adherence to a statistical distribution can be found, but hydrological data may not conform, or different distributions may be more suitable in different geographical regions.

b. Partial Duration Series Methods

These methods do not evaluate the bulk of the data, but use a number of flows for each season that are greater than a selected runoff threshold. The pattern of these values is determined and linked to a statistical distribution from which flows of a specified return period can be extrapolated. The use of these methods is suitable when the number of seasons for which data have been collected is small, perhaps only 10 or less.

Annual Maximum Series

This method, which is a particular kind of partial duration series, selects the largest event of each year or season, tabulates them in order of magnitude and from this list derives a flow peak with a probability of occurrence and return period. To extrapolate for large events, the data may be plotted as in Figure 2.1 below on log-normal probability paper. This is a very simple and straightforward method, its main limitation is that it requires a large number of years' data to be useful, as it selects only the greatest flow from any season.

Figure 2.1: Annual Maximum Series, Runoff versus Probability

These methods of estimation of design flows are discussed in detail in Chapter 8, Data Analysis.

2.1.2 Theoretical Estimates of Flow

A great deal of research has been undertaken to develop hydrological models that can predict runoff peak flows and volumes. The majority, however, are not suited to general use. Sometimes they are too complex but most frequently they are limited by the geographical localities and hydrological conditions within which the data were collected. Many models are regression models and their value is difficult to assess outside their own particular circumstances.

Presented here are five models that can be used to predict peak flows and three models that are suitable to estimate runoff volumes. They are suitable for use with a wide range of catchment sizes and conditions. These methods of estimation have certain drawbacks: they can be relatively inaccurate because they make simplifying assumptions. They demand the availability of some primary data such as catchment physical characteristics and rainfall. However, they have been used for some time in a variety of environments with success and are based on measurements from a great number of catchments, with a wide range of physical characteristics. Peak Flows

Peak flows determine the design specifications of structures such as bunds, channels, bridges and dams. Peak flows also determine the capacity of the control sections of flow-through measurement systems and the collection pipes and transfer conduits of volumetric collection vessels. Some estimate of peak flows must be made before the design of these systems can be completed.

Design peak flows are linked to particular return periods, such as the maximum flow in 5, 10, 25, etc. years and design specifications are a balance between economic cost and the prevention of failure of the structure. Where no serious damage will result, for example on field bunds, a low return period ( say 5 or 10 years ) can be used. The 10 year return period is commonly used for agricultural purposes . Where serious damage or the loss of life is involved, then designs for large return periods, perhaps 50 or 100 years, are necessary. The return period most appropriate to the objectives of the project should be decided upon.

a. Rational Method

The Rational Method which estimates peak flows, is a simplified representation of the complicated process whereby rainfall amount and intensity, catchment conditions and size as well as human activity, determine runoff amount, but it is suitable where the consequences of the failure of structures are limited. The method is usually restricted to small watersheds of less than 800 ha and is based on the rainfall/runoff assumptions of the hydrograph below.

Figure 2.2: Hydrographic Basis of the Rational Method

The equation to calculate peak flows is:

q = 0.0028 CirA where (2.1 )

q = peak flow in m³ s-1
C = the runoff coefficient
ir = maximum rainfall intensity in mm h-1 for the desired return period and the "time of concentration" of the catchment, Tc.
A = area of the watershed in hectares (1 ha = 10,000 m²)

The rainfall intensity is assumed to be uniform for the period and over the whole catchment for a time at least as great as the time of concentration of runoff, (Tc).

Values of Coefficient C

The value of C is the ratio of the peak runoff rate to the rainfall intensity and is dimensionless. It represents the proportion of rainfall that becomes runoff and is determined, to a large extent. by catchment conditions. Work by the US Soil Conservation Service has enabled the influence of many of these conditions to be expressed in various values of C. Examples of these C values are given in Tables 2. 3 for the USA (temperate region' 700-1000 mm average annual rainfall) and 2. 4 below for Malawi in central southern Africa (sub-tropical region' average annual rainfall variable. from < 400 mm to > 1000 mm). Different hydrological conditions according to soil groups are accounted for.

Table 2.3: Coefficient C values for USA

Values of coefficient 'C' for Malawi are given in Table 2.4:

Table 2.4: Coefficient C values (Malawi)

Rainfall intensity, ir

The rainfall intensity value used in the Rational Method is selected according to the desired return period for the design of the structure under study. The duration of the rainfall intensity is, for the purpose of the Method, said to be equal to the time of concentration of the runoff, Tc.

A graph or set of graphs can be drawn, to determine the maximum rainfall intensity for a particular return period and a particular rainfall duration (equal to Tc for the purposes of the Method). Such graphs demand the availability of many years of data, as they represent the line of best fit through a group of data points drawn from a wide range of rainfalls and their intensity measurements. Extensive records are especially necessary for long duration-intensity periods, which are not experienced frequently. Obviously, the climates of geographical regions will vary and even local differences can be great where a country shows a marked variety of topographic form. Areas of uniform rainfall characteristics should be provided with unique sets of rainfall intensity graphs. Figure 2.3 shows the manner in which these graphs are drawn.

A simple alternative way to calculate the return period of the maximum rainfall intensity for a specific duration, where data are too sparse to plot graphical relations, is shown below in Table 2.5 using 10 years' hypothetical example data. Where extrapolation is concerned, it should be remembered that the accuracy of estimation is related to the quantity of available data and the length of record. Note that in Figure 2.3, the lines defining Tc/Intensity relations are lines of best fit obtained from many storm data.

Figure 2.3: Example Graphs of Return Period, Intensity and Duration (which = Tc)

Example return periods used widely for different structures are: Field structures, 5-10 years; Gully control and Small farm dams, 20 years; Large farm dams, 50 years.

List the data as follows (duration in mins, intensity in mm h-1, m is order number of the item in the array). The rainfall intensity is the maximum intensity recorded that season or year, for the particular duration. The return period, in descending order of magnitude, of the rainfall intensity in years - (n+1)/m., where n is the number of years of record. Note that in the example Table 2.5 below, the exact values for the 5 and 10 year returns must be interpolated from the table and the values are given in bold type. Although the relation between intensity and duration is in fact curvilinear, linear interpolation does not lead to important inaccuracies. Making the time steps between the durations smaller, increases accuracy.

Table 2.5: Annual Maximum Series (Hypothetical Example Data.)

Intensities for the same return period increase with shorter duration (and Tc). It is also clear from the example above, that long records of data are necessary to obtain rainfall intensity values associated with long return periods as well as long durations and this may be a limiting factor with work in developing countries where records are frequently short. Great care must be exercised in using data that are imported from other regions, if local data are not available.

Time of concentration, Tc

The time of concentration (Tc) is the time by which water from most distant parts of the catchment has reached the outlet. The following formula has been developed to estimate Tc., with example values given in Table 2.6.

Tc = 0.0195 L0.77 S-0.385 where (2.2)
Tc is in minutes
L the maximum length of the catchment in m, and S = slope of the catchment in m m-1 over the total length L

Table 2.6: Values of Tc using Formula 2.2

The time of concentration, when calculated from equation 2.2 or obtained from Table 2.6, can be used to obtain the desired maximum rainfall intensity, depending on return period.

Figure 2.4: Time of Concentration, Tc, for Catchment Areas 0 - 36 Hectares

Equation 2.2 is not universally accepted and alternatively, the time of concentration can be found by dividing the measured length of flow by the estimated flow velocity. Manning's formula can be used to estimate flow velocities, although the estimation of flow velocity using Manning's formula can be a complex matter for large catchments where changes in channel form, size, slope and roughness can vary greatly and where the evaluation of these characteristics may be difficult. Figures 2.4 (above) and 2.5 (below) give values of Tc for a range of catchment areas, slope categories and qualities of protection. In all cases, it is important to calculate runoff peaks for the catchment conditions most likely to produce them, so that maximum peak flows are estimated: for example before cultivated land has been ploughed and before dense natural vegetation has regrown on non cultivated areas.

Figure 2.5: Time of Concentration, Tc, for Catchment Areas 40 - 200 Hectares
Source: Land Husbandry Manual, Ministry of Agriculture and Natural Resources, Malawi

Worked Example

A catchment of 15 ha is composed of 5 ha of permanent pasture (Soil Group B) and 10 ha of row crop in poor condition (Soil Group C). What peak flow is to be expected from a 1 in 5 year storm? The maximum flow length is 610 m, with a gradient of 2%.

From Table 2.6 or equation 2.2, Tc = 12 minutes

From Table 2.5 (hypothetical illustration), Rainfall intensity 73.0 mm h-1

Runoff coefficient C for permanent pasture (Group B, 5 ha ) = 0.14

Runoff coefficient C for poor row crop (Group C, 10 ha) = 0.71 therefore weighted value of C for whole water shed - 0.52 substituting in equation 2.1:

q = 0.0028 × 0.52 × 73.0 × 15 = 1.6 m3 s-1

b. Cook's Method

Developed by the USCS, this method essentially provides a simpler and more generalised, but similar approach to the estimation of peak flows to the Rational Method. Catchment size and conditions are accounted for. Table 2.7 gives catchment condition details.

Table 2.7: Values () for Catchment Conditions Cook's method

Catchment conditions are assessed and the numerical values assigned to each are added together. For example, if conditions are those in the right column of Table 2.7, a total value of 25 would be found and peak flows could be expected to be low, the exact size depending on catchment area. The conditions of a particular catchment will probably be found to be listed in different columns, but the relief condition is most heavily weighted and, in general, the four columns list conditions that describe "type" catchments. It was found generally that for African conditions, surface storage had little effect and a different set of values for catchment conditions were determined, as presented in Table 2.8. Soil type and drainage conditions were found to be especially important.

Table 2.8: Catchment Condition Values for African Conditions

When a total of catchment condition values is made, the peak flow is estimated using Table 2.9, below.

Table 2.9: Peaks Flows (m³ s-1) According to Catchment Condition Total Values and Area Using 10 Year Probability High Intensities for Tropical Storms

c. TRRL (UK Transport and Road Research Laboratory) Model

Work in East Africa, by the UK Transport and Road Research Laboratory has led to a model designed to overcome two serious problems associated with data in many developing countries: that rainfall/runoff correlations can only be developed using large amounts of data and that extremes in the data are rare. The US SCS method was found not to give acceptable results for East African conditions.

The concept of a "contributing area" (CA) is used to avoid the use of a uniform coefficient throughout the catchment. Early rain fills the initial retention (Y) and runoff et this stage is zero. A lag time (K) was incorporated to account for routing on larger catchments. Total Runoff Volume was found to be defined by:

Q= (P-Y) CA · A · 103 (m³ s-1) where (2.3)

P = storm rainfall (mm) during time period equal to base time of the hydrograph.
Y = initial retention (mm)
CA = contributing area coefficient
A = catchment area (km²)

The average flow QM is given by:

QM = 0.93 · Q/ 3600 · TB where (2.4)

TB is the hydrograph base time (hours)

Initial Retention (Y)
A value of 5 mm for Y was found to be appropriate for arid and semi-arid conditions.
A value of 0 mm for Y was found to be appropriate for wet zone areas.

Contributing Area (CA)

Soil type, slope, land use and catchment wetness were found to be the most influential factors in determining catchment contributing area. The design value is of the form:

CA = CS CW CL where (2.5)

CS = a standard value of contributing area coefficient for grassed catchment at field capacity.
CW = catchment wetness factor
CL = land use factor

Lag Time (K)

Lag time was found only to have a relation with vegetation cover.

Base time of the hydrograph (TB)

Simulation studies showed that TB could be found from the equation:

TB = Tp + 2.3 K + TA where (2.6)
TA = 0.028L / QM0.25 S0.5 where (2.7)

L = main stream length (km)
QM = average flow during base time (m³ s-1)
S = average mainstream slope
K = lag time
Tp = rainfall time

The value of QM can be estimated, through a trial and error iteration of equation 2.6, with TA initially being zero. Below are the tables necessary to estimate the various runoff factors.

Table 2.10: Standard Contributing Area Coefficients, CS (wet zone areas, short grass cover)

Table 2.11: Catchment Wetness Factor, CW

The table (2.13) gives rainfall time (Tp) for East African 10 year storms as a guide. The values for the localities under study can be obtained from local data if available.

Table 2.12 Land use factors, CL Catchment Lag times, K

Table 2.13 Rainfall time, Tp, for East African 10 year storms

Procedural steps for calculation

- Measure catchment area, land slope and channel slope.

- Establish catchment type and from Table 2.12 Lag time K.

- Establish soil type and using land slope, estimate standard contributing area coefficient, Cs. from Table 2.10.

- Establish antecedent rainfall zone and catchment wetness factor, CW, from Table 2.11.

- Use Table 2.12 to estimate land use factor, CL.

- Calculate contributing area coefficient by: CA = CS · CW · CL

- Find initial retention Y (0 or 5 mm).

- Using Table 2.13 or local data find rainfall time, Tp.

- Calculate design storm rainfall to be allowed for during time interval TB hours (P mm).

- Runoff volume is given by:
Q = CA · (P - Y) · A · 103 (m³).

- Average flow is given by:
QM=0.93 Q/3600 · TB

- Recalculate base time using
TB = Tp + 2.3 K + TA where TA = 0.028 L/ QM0.25 S0.5

- Repeat steps 6 to 9, until QM is within 5% of previous estimate.

- Design peak flow, QP is given by:
QP = F · QM where the peak flood factor, F is 2.8 when K < 0.5 hour and 2.3 when K is > 1.0 hour.

Worked Example
What is the 10 year peak flow of a catchment with the following details? Area 5 km²; Land slope 3%; Channel slope 1%; Channel length 2 km; Soils with slightly impeded drainage; Good pasture. 10 year daily point rainfall of 80 mm.

From Table 2.12, Lag time K

= 1.5 hrs

From Table 2.10 Standard contributing area coefficient CS

= 0.38

From Table 2.11, Catchment wetness factor CW

= 0.5 (dry zone ephemeral)

From Table 2.12, Land use factor CL

= 1.0

Therefore. design CA = 0.38 · 0.5 · 1.0

= 0.19

Initial retention Y

= 0 mm

From Table 2.13, TP

= 0.75 hrs

Using equation 2.6 with TA = 0

TB = 0 75 +2.3 .1.5

= 2.59 hrs

Rainfall during base time is given by

RTB = TB/24 (2.33/ TB + 0.33 )n · R10/24

where R10/24 = 10 year daily rainfall
and n = 0.96 (Table 2.13)
Therefore R2.59 = (2.59/24 · 24.33/ 2.92)0.96 · 80 = 72.2 mm

An areal reduction factor is used to take account of the fact that rainfall depths are smaller over catchment areas than they are at spot measurement points.

The Areal Reduction Factor (ARF) was found to be = 1 - (0.04 · TB-0.33·A0.55)
which for the value of A and TB = 0.93, thus:

Average rainfall P

= 72.2 · 0.93

= 67.5 mm.

The Runoff volume Q = CA (P - Y ) · A · 103

= 0.19 (67.5 - 0) · 5.103

= 64.13 × 10.3 m³.

QM = 0.93 · Q/3600 · TB

= 6.40 m³ s-1

First iteration of TA = 0.028 L/ QM0.25 S0.5

= 0.04 hrs

The value of TA (very small) indicates that no re-calculations of TB, the Rainfall time and QM are necessary.

Therefore the design flood is:

QP = F · QP where the flood factor F is 2.3 (as K is > 1 hour).
Therefore the Peak Bow QP - 2.3 · 6.4 = 14.72 m³ s-1

d. US Soil Conservation Service Method

This method is founded on the rainfa/runoff relation for the triangular hydrograph illustrated below in Figure 2.6. It is important to note that the method is used to calculate the peak flow of a known runoff event volume or to calculate the peak flow for an expected or desired runoff event volume. A specific discharge must be designed for. Knowledge of rainfall intensity is not needed. Peak flow is defined by:

q = 0.0021QA/Tp where (2.8)

q = runoff rate (peak flow) in m³ s-1
Q = runoff volume in mm depth (the area under the hydrograph)
A = area of water shed in ha
Tp = time to peak in hours, defined by:

Tp = D/2 + TL where (2.9)

D = duration of excess rainfall
TL = tune of lag, which is an approximation of the mean travel time and can be obtained from the nomograph below, Figure 2.7. Alternatively, Time of lag = 0.6 × Time of concentration which is the longest travel time of the runoff (not the time to peak as in the Rational Method).

Figure 2.6: The US SCS Triangular Hydrograph

Figure 2.7: Lag Time and Time of Concentration, US SCS Method

Source: US SCS Hydrology, National Engineering Handbook, 1972

Worked Example Determine the peak flow from a 10 ha catchment with a 0.5 hour storm that produced a runoff volume of 7 mm . Time of lag is 0.1 hours.

Substituting in equation 2.9,
Time to peak, Tp = 0.5/2 + 0.2 · 0.35 hours
Peak Bow, q = 0.0021 × 7 × 10 / 0.35 = 0.42 m³ s-1 or 420 l s-1

e. Izzard's Method

The previous techniques have been developed to estimate runoff rates from catchments ranging in size from a few hectares to several hundred hectares. However, agrohydrological experiments frequently make use of very small runoff plots only tens of square metres in area. This is for two reasons. First, they are easy to replicate and many such plots can be placed in a small area to study a range of catchment conditions. Second, they can be used conveniently to look at interventions that work on a small scale and which are intended to be installed within the boundaries of individual fields. In these circumstances, a method developed to estimate runoff from sheet flow and limited channel flow may be more appropriate. Izzard made extensive experiments with flows from various surfaces, over relatively small areas. He found that the overland flow hydrograph could be drawn as a composite of the two dimensionless curves illustrated by Figure 2.8 and peak flow is found when q/qe = 0.97 and t/te = 1.0. and is given by

qe, the flow at equilibrium = iL/ 3.6 × 106 whereh (2.10)

i = rainfall rate in mm hr-1 and L= length of flow surface (in m) for a portion of the flow surface that is 1 metre wide.

For the purposes of calculating only the peak flow, it is not necessary to enter into the relations between the other runoff parameters which allow the construction of the overland flow hydrograph and the calculation of total flow volume. This is discussed below in the section on runoff volumes.

Peak flow, qp in m³ s-1 = 0.97 (i L /3.6 × 106)

Worked example
What is the peak flow of runoff from a 25 m wide strip catchment length 10 m, as the result of a rainfall with a maximum intensity of 60 mm hr-1?

Using formula 2.10, Peak flow 0.97 × 60 × 10 × 25 × 1000 / 3.6 × 106 = 4.0 l s-1. Runoff Volumes

It is necessary to estimate the size of likely runoff volumes as accurately as possible, as they will determine whether volumetric or continuous data collection methods must be used. If the former is selected, these estimates will ensure that the design of collection tank size is suitable. Tanks that are too small will be over-filled, data will be lost during large runoff events. This will be a great set-back because obtaining information about large runoff volumes and the probabilities associated with them is critical for agricultural planning purposes. The over-design of collection tanks incurs unnecessary expense and can lead to difficulties of installation.

For water harvesting schemes, it is necessary to estimate the size of runoff volumes that catchments are likely to shed. Over-estimation of runoff volumes can lead to serious under-supplies of supplementary water, whereas volumes much larger than those expected can result in flooding and the physical destruction of crops and structures. It is important to stress once more, however, that the methods for calculating runoff volumes shown below, can only provide estimates.

a. US Soil Conservation Service Method

This method is applied to small agricultural watersheds and was developed from many years of data obtained in the United States, though it has been used successfully in other regions. The Method is based on the relations between rainfall amount and direct runoff. These relations are defined by a series of curvilinear graphs which are called "Curves". Each curve represents the relation between rainfall and runoff for a set of hydrological conditions and each is given a "Curve Number", from 0 to 100. The equation governing the relations between rainfall and runoff is:

Q = (P-0.2S)2 /P+ 0.85S where (2.11)

Q = direct surface runoff depth in mm
P = storm rainfall in mm
S = the maximum potential difference between rainfall and runoff in mm, starting at the time the storm begins.

The parameter S is essentially composed of losses from runoff to interception, infiltration, etc.

The US SCS calculates S by:

S = (25,400 / N) - 254 where (2.12)

N is the "Curve Number", from 0 to 100. Curve Number 100 assumes total runoff from the rainfall and therefore S = 0 and P = Q.

Values of curve numbers for different hydrological and agricultural conditions are given in Tables 2.14 and 2.15. Note that the values for these tables are separated on the basis of antecedent soil moisture condition, that is the state of "wetness" of soils prior to rainfall. The basic assumption for this separation is that wet soils shed a higher proportion of rainfall as runoff than dry soils and therefore the same soil will have a higher curve number when wet, than when dry.

Table 2.14: Curve Numbers for Soils and Catchment Condition, Antecedent Soil Moisture Condition II

Table 2.15: Curve Numbers for Soils and Catchment Condition.

Local conditions, especially rates of evapotranspiration, should be considered to assess whether the categorisation of antecedent soil moisture conditions I to II should be modified. For example, soils in a region with summer rain and a summer growing season may fall within category 1, despite a previous 5-day rainfall of 40 mm. Similar soils with a winter growing season and the same antecedent rainfall could fall into category III.

One difficulty in using the US SCS method is the derivation of the value the rainfall parameter P. This parameter is usually defined as a specific return period storm of a known duration, for example "the 12 hour rainfall with a return period of 50 years", expressed in mm. Rainfall P is calculated from a relatively complex linear relation with several rainfall duration and return period factors. In the US, these data are easily available and can be obtained from published maps and although regional variations in the relations defining the rainfall intensity parameter exist to cover climatic variation, there are serious difficulties in transferring this kind of information to other geographical areas. In developing countries it is unlikely that such comprehensive data will be available. Even if they were, the work involved in converting raw data into a series of useful tables, graphs or maps would be beyond the scope of most projects where all that is sought is an estimate of runoff.

As an alternative, long-term daily rainfall is usually available even in countries with only basic meteorological information. The 24 hour rainfall is a frequently-used value and in these circumstances, it is best to use a simple estimate of rainfall that can be obtained from a listing of annual maxima, such as shown in Table 2.5. For example the 10year return daily (assume it to be the 24 hour) rain could be used in equation 2.11 to calculate runoff. Relations between daily and other period rainfall can be established by regression analysis where records exist. When available, local records should be used even if they are less amenable to sophisticated treatment

Table 2.16: Antecedent Soil Conditions

Worked example

Given that the 25 year return rainfall is 85 mm, calculate the total runoff volume from a catchment of 46 ha, of which 13 ha are poor pasture (soil group A), 25 ha are contoured under small grain crops with poor treatment (soil group C) and the remaining 8 ha are fallow (soil group B). Antecedent soil moisture condition 1.

Subarea A (ha)

Soil Group

Land Use

Curve No. N




Pasture, poor condition





Small grain, poor condition








Total N×A =


Therefore the weighted curve number = 3207 /46 = 69.7

From S = (25,400 / 69.7) - 254 = 110 mm

From equation 2.11 Q = (85 - 0.2x 110)2 / 85 + (0.8 × 110) = 22.9 mm over the catchment (1mm on 1 ha = 10 m³)

The total runoff, Q = 22.9 × 10 × 46 = 10,534 m³

b. TRRL Model

Reference to this model is made for an alternative method of calculating runoff volume later in this chapter.

c. Izzard's method

The use of work by Izzard for the calculation of peak flows was discussed earlier, in the relevant section. The results can also be used to calculate flow hydrographs and volumes and is especially useful for small runoff plot calculations.

Izzard found that the time to equilibrium,
te =2 Ve /60 qe where (2.13)

te is the time to which flow is 97% of the supply rate and Ve is the volume of water in detention at equilibrium. The volume Ve in cubic metres was found to be:

Ve =kL1.33 i0.33/ 288, where (2.14)

i is in mm hr-1 and L, the length of the strip is in m. k was found experimentally to be given by:

k = 2.76 × 10-5 i + c / s0.33 where (2.15)

s is the slope of the surface and c is given in Table 2.17.

The average depth over the strip is = Ve/L = kqe0.33 (2.16)

Figure 2.8: The Dimensionless Hydrograph according to Izzard

Table 2.17: give values of the surface retardance coefficient c for various surfaces. Table 2.17 Surface Retardance 'c'

Note that for low slopes and small rainfall intensities, the value of c is relatively important.

Procedure to calculate runoff volume

- Values of te and qe can be calculated from equations 2.13 and 2.10, respectively.
- With te and qe known, the plot of the rising limb of the overland flow hydrograph, plotted as q (volume) against t (minutes) can be found from Figure 2.8.
- The recession curve of the hydrograph can be plotted using the factor B which is:

B = 60qeta/VO where (2.17)

VO is the detention volume given by equations 2.15 and 2.16, taking i = 0 and ta is any time after the end of rain.

- When the hydrograph is drawn, the runoff volume is the area under the hydrograph.