Methods for Estimation of Flood Discharge
This article throws light upon the top six methods for estimation of flood discharge. The methods are: 1. Catchment-Run-Off Method 2. Empirical Formulae 3. Rational Method 4. Cross Sectional Area and Bed Slope 5. Area of Cross-Section and Velocity As Observed At Bridge Site 6. Available Records.
Method # 1. Catchment-Run-Off Method:
The catchment area is the command area of a river wherefrom the river gets the supply of water. The catchment area is computed from the contour map and the flood discharge is estimated from the “Run-off ” formula.
The rainfall is measured by rain gauges in millimetre. From the daily record of rainfall, annual rainfall for a zone is determined. The annual rainfall varies from place to place and therefore, the recorded rainfall for a considerable period, say fifty years, is very useful in getting the maximum rainfall recorded during this period.
The estimation of maximum flood discharge shall be based on this maximum recorded rainfall. Table 3.1 gives the rainfall record in different parts of the Indian Union for a period of 15 years (1935-1949).
ADVERTISEMENTS:
Run-off is defined as the proportion of water out of the total rainfall in the catchment area running to the water course, channel or river. It is needless to mention that the full quantity of rainfall does not reach the water course as some quantity is soaked in the soil to form the sub-soil water strata, some quantity is absorbed by vegetation, some quantity is evaporated and the rest only flows to the channel or river.
How the rain water reaches the channel or the river from the catchment area is shown in Fig. 3.1 and Fig. 3.2.
The catchment area of the stream or river upstream of the bridge site is obtained by marking the ridge line of the contour map and measuring the area enclosed by this ridge line with the help of a plan meter or tracing paper graphs.
ADVERTISEMENTS:
The possibility of intensive rainfall falling simultaneously over the entire area of a big catchment is less and therefore, a lesser percentage of run-off may be taken. Another important factor which determines the percentage of run-off is the shape of the catchment.
Fig. 3.1 and Fig. 3.2 show two types of catchment. In normal single catchment, the watershed is long and narrow having a number of short tributaries joining the main stream.
In such catchment, storms of shorter duration which cause the maximum flood discharge, will not reach the bridge site nearly at the same time and as such run-off in such catchment area will be less than that in a fan-like shape of catchment.
ADVERTISEMENTS:
In the latter case, the tributaries are longer and few in number and therefore, their run-off will reach the bridge site almost simultaneously causing thereby concentration of flow during storms of shorter duration. Hence, even if the catchment area, quantity, duration of rainfall etc. are the same for both types of catchment, the run-off at the bridge site will be more for fan shaped catchment than for normal single catchment.
Percentage run-off varies from 20 per cent to 70 per cent depending upon the shape and nature of the catchment. Porosity of soil; that is, whether sandy, clayey or rocky; degree of previous saturation; area covered by forest; presence of lakes, ponds, swamps, artificial reservoir etc.; determine the percentage run-off.
Therefore, while estimating the flood discharge from the catchment area, the aforesaid factors shall be duly taken into consideration.
ADVERTISEMENTS:
As discussed before, the run-off depends on the following factors:
(i) Degree of porosity and degree of saturation of the soil in the catchment area.
(ii) The shape and slope of the catchment area.
(iii) Obstacles to flow such as roots of trees, bushes etc.
(iv) Degree of vegetation.
(v) State of cultivation.
(vi) Amount of evaporation.
(vii) Intensity of rainfall; Run-off is more if the same amount of rainfall say 50 mm is within a very short period of, say, two hours than is spread for a larger period of, say, 24 hours in which case it is in the form of drizzling.
(viii) Total quantity of rainfall in the catchment area.
Method # 2. Empirical Formulae:
The flood discharge can be evaluated by using various empirical formulae involving area of the catchment and some coefficient depending upon the location of the catchment.
i) Dicken’s Formula
This formula (originally devised for Northern India but can now be used in most of the states of India with the modification of the value of the coefficient C) is given by:
Illustrative Example 1:
The area of a catchment is 800 sq.km. The area is located in Western India within 150 km. from coast. Estimate the maximum flood discharge by using the various empirical formulae and compare the flood discharges:
This formula is applicable for Madras (Tamil Naidu) State only and as such gives low value which is not considered
Comparison of flood discharges worked out by various empiral formulae:
Method # 3. Rational Method:
If R is the total rainfall in cm for a duration of T hours then the mean intensity of rainfall, I in cm per hour taken over the total duration of the storm is given by
I = R/T (3.6)
For a small time interval, t, the intensity of rainfall, i, may be more as may be evident from Fig. 3.3 since the mean intensity for a small time interval, t, is more than the mean intensity for the whole time period, T.
The relation between i and I may be shown as:
Where C is a constant and may be taken as unity for all practical purpose.
If t = one hour and corresponding i is taken as i„ and the value of I is taken from equation 3.6
From equation 3.9, io (One hour rainfall) can be worked out if the total rainfall R and duration of the severest storm are known. It is advisable to consider a number of heavy storms spread over a prolonged period and io may be calculated for each case and the maximum value of U shall be taken as the one hour rainfall of the region for the estimation of flood discharge.
From a record of the Meteorological Department, Govt. of India, the values of io for various places of the Indian Union are reproduced in Table 3.2:
Time of concentration is defined as the time taken by the run-off to reach the bridge site from the furthest point of the catchment which is termed as the critical point.
Since the time of concentration is dependent upon the length, slope and the roughness of the catchment, a relationship is established with these factors as below:
Where Tc = Concentration time in hours.
H = Fall in level from the critical point to the site of the bridge in meters.
L = Distance from the critical point to site of the bridge in Km.
The values of H and L can be found from the contour map of the catchment area.
The critical intensity of rainfall, Ic, corresponding to the concentration time, Tc, is derived from equation 3.9 considering I = Ic corresponding to T = Tc.
Estimation of Run-off:
One centimeter of rainfall over an area of one hectare gives a run- off of 100 cu. m per hour. Therefore, a rainfall of Ic cm per hour over an area of A hectare will cause a run-off of 100 A Ic cu. m per hour.
If losses due to absorption etc. is considered then the run-off is given by :
Q = 100 PICA cu.m per hour
= 0.028 PICA cu.m/sec (3.12)
Where P = Coefficient depending on the porosity of soil, vegetation cover, initial state of saturation of soil etc.
The values of P for various conditions of the catchment area arc given in Table 3.3:
In addition to the coefficient, P, another coefficient, f, is introduced in the formula for calculating the run-off. As the catchment area gets larger and larger, the possibility of reaching the run-off to the bridge site simultaneously from all parts of the catchment is less and less and as such the value of f is gradually reduced as the catchment area is increased.
Table 3.4 gives the value of f in equation 3.13 derived from equation 3.12 with the introduction of the coefficient, f, therein.
Q = 0.028PfIc A cu.m /sec. (3.13)
Illustrative Example 2:
The catchment area of a river is 800 Sq. Km. and is composed of sandy soil with thick vegetation cover. The length of the catchment is 30 Km. and the reduced levels of the critical point and the bridge site are 200 m and 50 m respectively.
Find out the peak storm discharge by the Rational Method assuming that the rainfall in 5 hours is 20 cm. What will be the peak discharge if the catchment area is of clayey soil lightly covered or of steep but wooded rock?
Maximum peak run-off, from equation 3.13
Q = 0.028 PflcA cu.m/sec
In the present case for catchment area composed of sandy soil with thick vegetation,
A = 800 sq.km = 80,000 hectares ; P from table 3.3 = 0.10 ; f from table 3.4 = 0.60 ; Ic = 2.98 cm/hour
... Q = 0.028 PfIcA = 0.028 x 0.10 x 0.60 x 2.98 x 80,000 = 400 cum/sec.
When the catchment area is of clayey soil lightly covered, P from table 3.3 = 0.50, values of A, f and Ic remaining as before.
... Q = 0.028 PfIcA = 0.028 x 0.50 x 0.60 x 2.98 x 80,000 = 2003 cum/sec.
In case of catchment area with steep but wooded rock, P from table 3.3 = 0.80
... Q = 0.028 PfIcA = 0.028 x 0.80 x 0.60 x 2.98 x 80,000 = 3204 cum/sec.
Therefore, it may be noted from the illustrative example that the peak run-off is very much dependent on the nature of the catchment, other factors remaining the same and varies from 400 cum/sec to 3204 cum/sec when the degree of porosity and absorption of the catchment area is very high or very low.
The Rational Method is, therefore, very realistic and considers all relevant factors which regulate the peak run-off. The empirical formulae do not consider these factors except some adjustment in the value of the coefficient C and therefore, are not very much realistic.
Method # 4. Cross Sectional Area and Bed Slope:
By this method the discharge is calculated from Manning’s formula,
Where A = the area of cross section of the stream measured from H.F.L
n = the rugosity co-efficient.
R = the hydraulic mean depth and equal to the ratio of cross-sectional area, to wetted perimeter, P
S = the bed slope of the stream measured over a reasonably long distance.
In a stream having non-erodible banks and bed, the shape and the size of the cross-section remain practically the same during a flood as at normal times and therefore, the normal cross-section and the perimeter may be used in calculating the discharge.
But in a stream flowing through alluvium region, the cross-sectional area and the perimeter may change during highest floods due to the scouring of the banks and the bed and as such in estimating the maximum flood discharge, the depth of scour has to be ascertained first and the values of the cross-sectional area and the perimeter may then be calculated by taking levels of the bed at certain intervals.
The value of the rugosity co-efficient depends on the nature of the bed and the bank of the stream and proper care is required to be taken in selecting the right value of this co-efficient in order to get the correct discharge. Some values of the rugosity co-efficient, n, are given in table below for various types of surface conditions.
Illustrative Example 3:
A river has the bed levels at the highest flood at certain intervals as shown in Fig. 3.4. The R.L. of the lowest beds at 500 m upstream and 500 downstream are 107.42 m and 105JO m respectively. Calculate the maximum flood discharge if the river has fairly clean, straight banks but having some weeds and stones.
Solution:
Area of cross-section A at H.F.L. may be found out by dividing the area into strips such as BPC, PCDO, ODEN etc.:
The wetted perimeter P at H.F.L. is the bed line BCDEFGHI which is the summation of the length of line BC, CD, DE etc. These length may be worked out as below (See Fig. 3.5):
Bed slope, S, is the level difference of the lowest bed at 500 m upstream and 500 m downstream divided by the distance.
Method # 5. Area of Cross-Section and Velocity as Observed at Bridge Site:
The area of cross-section is measured by taking a series of levels of the river at H.F.L. at certain intervals. The velocity in this case is determined at site by direct measurement of the velocity in place of theoretical calculation from bed slope etc.
To measure the velocity directly, the river is divided into few sections width wise and then the velocity for each section is determined by surface float placed at the centre of each section.
The time taken by the float to cover a fixed distance is noted by a stop watch and the distance travelled by the float divided by the time taken is the surface velocity of the stream. Such surface velocity is to be determined for each section and weightage average value is obtained for the purpose of flood discharge estimation.
The velocity is least in the vicinity of the bed and banks and mean at the centre line of the stream at a point 0.3 d below the surface where, d, is the depth of water (see Fig. 3.6). If V, is the velocity at surface, Vb is the velocity at bottom and Vm is the mean velocity then their relationship may be established in the following equation,
Vm = 0.7 Vs= 1.3 Vb (3.15)
After the determination of the mean velocity of the stream, the flood discharge is obtained by;
Q = AVm (3.16)
Method # 6. Available Records:
In some cases it may be possible to have the maximum flood discharge measured at weir or barrage sites. This value may be compared with the theoretical worked out value and a final value may be selected. The flood discharge thus obtained, though very realistic, suffers from one drawback viz. the age of the record, since the weirs or the barrages are mostly of recent construction.
The flood discharge shall preferably be the maximum of 100 years’ recorded value for important bridges and 50 years’ recorded value for less important bridges. The terms “100 years’ value” and “50 years’ value” are defined as momentary peak discharge which occur “on the average” once in 100 years or once in 50 years.
The phrase “on the average” means all the peak discharges as observed over a period of 100 years or 50 years as the case may be and average of the peaks is taken.