The Run-off available from a basin can be computed daily, weekly, monthly or yearly.
Following are the methods which can be used for finding out the run-off:
Method # 1. Run-Off by Using Empirical Formulae and Tables:
a. Run-Off Coefficient Method:
The volume of run-off can be directly computed approximately by using an equation of the form –
R = KP
where R is run-off, P is rainfall or precipitation and K, a constant depending upon the surface of the drainage area.
Truly speaking this equation cannot be rational, because the run-off not only depends upon the precipitation but also upon the recharge of the basin. This equation gives more and more reliable results as the imperviousness of the drainage area increases and the value of K tends to approach unity.
This formula is used in the computation of run off from small areas, especially for urban areas where the percentage of imperviousness of the area is quite high. This method should be avoided for rural areas and for major storms. The values of K for different conditions may be taken as given in Table 6.1.
Mr. T.G. Barlow carried out his studies of catchments in U.P. He suggested coefficients of run-off for different catchments as follows. He classified different catchments in five class as A, B, C, D and E.
These coefficient are to be further multiplied by coefficient given below to convert them to suit the different conditions of rain fall. These coefficients also had been given by Mr. T.G. Barlow.
b. Strange’s Tables and Curves:
Mr. W.L. Strange carried out his experiments in South India. He classified the catchments into three categories, namely – good, average, and had. He also had taken initial surface conditions for each catchment as dry, damp and wet. Daily run-off for dry, damp and wet conditions for different intensities of rainfall is given in Table 6.4.
Mr. Strange also gave curves relating rainfall and run-off and conditions of the basin both on daily and yearly basis. These curves have been reproduced in Fig. 6.10.
c. Empirical Formulae:
Run-off can be approximately computed by using empirical formulae.
Some of the formulae in most common use have been given as follows:
In all the empirical formulae given here R and P are respectively run-off and precipitation and both have been considered in centimetres. T is mean temperature in 0° F.
In Lacey’s formulae S represents catchment factor and F, monsoon duration factor. The values of S for catchments A, B, C, D and E as classified by Mr. T.G. Barlow are respectively 0.25, 0.60, 1.0, 1.70 and 3.45. The value of F is taken as 0.45, 1.0 and 1.5 for very short, standard, and very long duration rainfalls respectively.
Method # 2. Run-Off by Using Infiltration Characteristics:
The process, whereby water enters the surface strata of the soil and thus moves downward towards the water-table is known as infiltration. In fact when water falls on the soil, a small part of it is first of all absorbed by the top thin layer of soil so as to replenish the soil moisture deficiency. After this any excess water moves downward where it is trapped in the voids and becomes ground water.
The amount of stored ground water mainly depends upon the number of voids present in the soil. The number of voids further depend upon the size, shape, arrangement, and degree of compaction of the soil. Hence different soils will have different number of voids and hence different capacities to absorb water. The maximum rate at which a soil in any given condition is capable of absorbing water, is called its infiltration capacity.
It is evident that rain water will enter the soil at full capacity rate only during the periods when rainfall rate exceeds the infiltration capacity. When the rainfall intensity is less than the infiltration capacity, the prevailing infiltration rate is approximately equal to the rainfall rate. Hence the actual prevailing infiltration rate may be equal to or less than the infiltration capacity. This actual prevailing rate at which the water is entering the given soil at any given time is known as infiltration rate.
If the rainfall intensity exceeds the infiltration capacity the difference is called as the rainfall excess rate. This excess water is first of all accumulated on the ground as surface detention and then flows over land into the streams. The water below the water-table is known as the ground water and the water above the water-table is known as soil moisture.
When a graph is drawn between infiltration capacity and duration of rainfall in hours we get a curve known as infiltration capacity curve. Infiltration capacity is very high at the beginning of a rainfall. As the duration of rain goes on prolonging tire infiltration capacity also goes on decreasing. After a certain period (of the order of 1 to 3 hours) the infiltration capacity tends to become constant.
When Infiltration Capacity Curve (I.C.C.) is superimposed on the rainfall intensity pattern, the resultant amount will represent run-off. Hatched area in Fig. 6.11 represents the rate of run-off. This method of computing run-off can be used very easily if the rainfall rate never falls below the infiltration capacity rate.
But natural rains are sometimes below and sometimes above the prevailing infiltration capacity and thus distort the capacity-time curve. It is generally assumed that the infiltration capacity at any time is determined by the mass infiltration which has occurred upto that time. Thus if a rain begins at low rate and the rainfall during the first hour is two-third of the infiltration die capacity rate at the end of the hour will be taken as the capacity that would have prevailed at 2/3 hrs and not at one hour.
This method of computing run-off is used for small catchments having uniform characteristics. The rate of run-off and volume of run-off can be determined by deducting infiltration from the rain-fall.
The infiltration capacity curve as shown in Fig. 6.11 cannot be used for computing run-off from large basins. It is, because, in large basins the infiltration capacity as well as rainfall rate vary from point to point. Moreover sub-surface flow (interflow) will also be substantial.
Since this water-flow is a part of infiltration, it will not normally be included in the run-off compute by using infiltration capacity curve determined on a small test plot. Run-off volumes for large areas are computed using infiltration indices. W and ɸ are the two commonly used indices.
W-index in the average infiltration rate or the infiltration capacity averaged over the whole storm period and is given as follows:
W-index = P – R / Tr
where P = Total precipitation or rainfall.
R = Total run-off.
Tr = Duration of rainfall in hours.
ϕ-index may be defined as the average rate of loss of precipitation such that the volume of rainfall in excess of that rate will be equal to the volume of direct run-off ϕ-index can also be stated as the rate of rainfall above which the rainfall volume equals the run-off volume. ϕ-index can be represented as shown in Fig. 6.12.
ϕ and W-indices will be equal for a uniform rainfall but may not be equal for non-uniform rainfalls.
However for rains which are reasonably uniform or for heavy rains, these two indices are found to be nearly equal. The run-off coefficient k can be determined as follows if W-index is known,
k = p – W – index / p
Where
p = rate of rainfall or rainfall intensity.
Method # 3. Rational Method of Estimating Run-Off:
This method is a very useful method for evaluating the peak rate of run-off. This method is based on the fact that if a rainfall is applied to an impervious surface at a constant rate, the resulting run-off from the surface would finally reach a rate equal to the rate of rainfall.
In the beginning only a certain amount of water will reach the outlet, but after sometime, the water will start reaching the out let from the entire area and in this case the run-off rate would become equal to the rainfall rate.
The time required to reach this equilibrium condition is known as time of concentration and the peak rate of run-off would be equal to the rate of rainfall. This is the basis of the rational method.
The peak rate of run-off can be estimated using the following formula:
Method # 4. Run-Off by Using Unit Hydrograph:
Hydrograph:
It is graphical relation between discharge or flow, against time at a particular point of a stream or river. Hydrograph represents the time distribution of total run-off at the point of measurement. As volume of run-off, discharge or flow, is obtained by multiplying discharge with time, the area under the hydrographs gives the volume of flow during that period.
The hydrographs have three types of flows:
(i) Surface run-off or water flowing in the stream or river.
(ii) Sub-surface storm flow i.e. infiltrated water in the top layers of soil. This water reaches the streams within short time. It is also known as inter-flow or influent stream.
(iii) Ground water flow or water contributed as underground flow from the ground water reservoir fed by infiltration from previous rainfall and also some by the storm in question.
At the start of any hydrograph, there is contribution to the run-off from the ground water reservoir accumulated in the soil during previous rainfall. Due to fresh rainfall when water level in the streams rises, they contribute water to the ground water. The contribution of ground water to surface flow may be represented by the dotted line in Fig. 6.14.
Because it is not possible to determine, the actual shape of dotted line curve and also since in any major flood rise, the ground water table contribution is a small percentage of the total flow, it is sufficient to assume this line as straight line. The surface run off is above this line whereas ground water flow lies below this line.