Several types of empirical expressions have been developed from time to time to predict peak rate of runoff from agricultural watersheds.
Some of the most common expressions are described below:
1. Rational Method:
The oldest and the most famous hydrological model of predicting peak rate of runoff is the rational formula, expressed as:
q = CIA â€¦(3.2)
where, q = peak runoff rate, cfs (cubic feet per second),
C = runoff coefficient dependent upon the drainage basin characteristics. It represents the ratio of peak runoff rate to the rainfall intensity in a watershed.
A = watershed or drainage area, acres
I = rainfall intensity, inches per hour for the design return period, and for a duration equal to the time of concentration of the watershed.
In M.K.S. system the Rational formula is expressed as:
q = CIA/360 â€¦(3.3)
where, q is expressed in cubic meters per second, I in mm per hour, and A in hectare.
The value of I in the Rational formula can be computed using Eq. (3.1) with t equal to the time of concentration of the watershed.
A modified form of rational formula for Ambala Siwaliks has also been suggested as under:
q = CIA0.73
where, q = runoff, cusecs
C = runoff coefficient
I = rainfall intensity for the duration equal to the time of concentration, inches per hour A = area of catchment, acres
In metric units this equation is expressed as:
Q = 0.778 x CIA0.73/360 â€¦(3.4)
where, I is in mm per hour and A is in ha.
The value of C under different conditions is given in Table 3.4.
If the watershed is composed of various soil types under various land uses, it is necessary to estimate weighted C for computing runoff from the entire watershed.
Weighted C for watershed can be calculated using the relation:
C = A1C1 + A2C2 + A3C3 + â€¦/A â€¦(3.5)
where,A1,A2,A3, etc. = areas in ha under various land uses and soil types
C1, C2, C3, etc. = corresponding values of runoff coefficient for A1, A2, A3, etc.
A = Total area of watershed, ha
The time of concentration of a watershed is the time required for water to flow from the most remote point of the area to the outlet, once the soil has become saturated and the minor depressions have filled. It is assumed that when the duration of a storm equals the time of concentration, all parts of the watershed are contributing simultaneously to the discharge at the outlet.
The time of concentration of a watershed can be computed from the relation:
t = 0.0078 L0.77 S-0.385 â€¦(3.6)
where, t = time of concentration, min
L = maximum length of flow, ft.
S = watershed gradient, feet/foot.
It is the difference in elevation between the outlet and the most remote point divided by the length L.
In metric system, the following expression can be used.
t = 0.01947 L1.155 H-0.385 â€¦(3.7)
where, t = time of concentration, minutes
L – maximum length of flow, m
H = elevation difference between most remote point and outlet, m
The time of concentration of watersheds of various lengths of flow and gradients, as calculated by Eq. 3.6, have also been given in Table 3.5.
A reasonable estimate of time of concentration can also be obtained by dividing the distance from the most remote point to the outlet of the area by the average velocity, as given in Table 3.6, for the conditions of broad and almost flat waterways.
The Rational method is based on the following assumptions:
(a) The rainfall must occur at a uniform intensity for a duration at-least equal to the time of concentration of the watershed.
(b) Also, the rainfall must occur at a uniform intensity over the entire area of the watershed.
2. Cook’s Method:
Cook’s model, for estimating runoff rate from a small agricultural watershed (up to about 400 ha), is based on the watershed characteristics related to runoff.
In this method, the runoff characteristics of a watershed are examined under the following four categories:
(c) Vegetal cover, and
(d) Surface storage.
Based on the observations of peak flood from various agricultural watersheds, numerical values have been assigned to the various conditions of relief, infiltration rate, vegetal cover and surface storage, as given in Table 3.7.
The âˆ‘W of the numerical values assigned to the watershed characteristics is first obtained. Runoff curves as shown in Fig. 3.3 are then entered with the drainage area and the âˆ‘W and a value of peak runoff for a 10 year return period is obtained.
This peak runoff value is modified for frequency and geographic rainfall characteristics by the formula:
qâ€™ = PRF
where, q’ = peak anticipated runoff rate for a specified geographic location and return period
P = peak runoff rate from a watershed of given size and hydrologic characteristics, assuming a 10 year recurrence interval and a rainfall factor of 1.0 (Fig. 3.3)
R = geographic rainfall factor (Fig. 3.4) dimensionless.
F = return period factor (Fig. 3.5, dimensionless) (F = 1.0 for a 10 year return period storm) For accurate estimation of peak runoff rate by Cook’s method, the value of q’ should be multiplied by a shape factor which accounts for various lengths and widths of the watershed (Table 3.8).
3. Flood Frequency Analysis Method:
This method is based on the record of a number of years of runoff/flood data from the watershed under study. These records are then used to constitute a statistical array which defines the probable frequency of recurrence of floods of given magnitude. Extrapolation of the frequency curves helps to predict flood peaks for a range of return periods.
4. Other Methods:
In addition to above, a number of empirical formulae of the form given below have been developed to describe the magnitude of extreme floods.
q = KAx â€¦(3.9)
where, q = magnitude of the peak runoff
K = a coefficient dependent upon various characteristics of the watershed,
A = area of the watershed
x = a factor, determined from field observations