## METHODOLOGY frequency are carried out by different

METHODOLOGY 5.1 GENERAL The analyses of flood frequency are carried out by different methodology.

Different statistical methods and with the help of software HEC-SSP the analyses has been done to find out maximum probable flood for different return period. 5.2 METHODS OF FLOOD FREQUENCY ANALYSIS The Various methods of finding flood of different frequencies can be classified in two main types i.e., I) Empirical Methods, II) Statistical Methods and Statistical Software Package.

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5.2.1 Empirical Methods Empirical Methods are listed below, 1) Fullers Formula 2) Creagers Equation 3) Correlation with Mean Flow – R. S.

Varshneys Relation 4) Percentage Increase Method of Design Flood. The empirical formulae to determine peak flow should be employed only when there is insufficient available hydrologic information for performing the detailed and precise analysis. The main in drawback of the method is due to the uncertainty involved in the subjective decision of the hydrologist on the factor of safety to be adopted. Moreover, no indication is available regarding the probable frequency of the maximum recorded floods or maximum historical flood on the stream under consideration. The empirical methods will not be discussed here, as these methods involve various constants which are difficult to predict.

The results of these methods are also quite approximate. 5.2.2 Statistical Methods If the entire flood peaks of all the years of records of a basin are arranged in the order of their magnitude, they are found to constitute a statistical arrangement, which may be arranged in a frequency curve. Most of the distributions encountered in hydrology are pronounced skew.

The flood frequency curves are also skew and therefore an additional parameter is involved in their calculations. Various techniques have been evolved to develop graphical or mathematical means of solving this difficulty of skewness and to fit the observed data to smooth frequency curves. The means of deriving the frequency curves are explained without going into details of theoretical consideration involved. Statistical Methods are listed below, Return Period About 100 Years 1) Normal Frequency Evaluation Graphical Method 2) California Methods B) Large Return Periods 3) Fosters Method Type-I III 4) Hazens Method 5) Gumbels Method (Using Frequency Factors) 6) Gumbles Method (Statistical Approach) 7) Powels Method 8) Ven Te Chows Method 9) Log-Normal Method 10) Log Pearson Type-III Method 5.3 NORMAL FREQUENCY EVALUATION GRAPHICAL METHOD (RETURN PERIOD LESS SAY ABOUT 100 YEARS) This is the simplest and easiest method of drawing frequency curve. According to law of probabilities, the possible percentage of future floods that will equal or exceed a given flood Q may be obtained by the following relation.

QUOTE (5.3.1) Where, p Calculated possibilities of future flood i.

e. in 100 year how many times this magnitude of flood will be exceeded. m the number of years during the period of record that a flood was equaled or exceeded. n total no of years of record. After calculating p, QUOTE (5.3.2) Where p Calculated possibilities of future flood i.e.

in 100 year how many times this magnitude of flood will be exceeded. m no of years the discharge Q was exceeded. I Future flood frequency i.e. after how many years Q will be exceeded. An estimate of the probable frequency of flood flows of the Sabarmati River at Dharoi Dam has been made in Table 5.1 and frequency curve is shown in Fig 5.1.

According to Normal Frequency Evaluation Graphical Method the lowest magnitude of flood 118 is came in every year and calculated possibilities of it is 100 and the highest magnitude of flood 13186 is came once in 21 year and calculated percentage possibilities of it is 3.45. Table 5.1 Calculations for Probability Plotting of Sabarmati River by Normal Frequency Evaluation Graphical Method from 29 year data at Dharoi Dam (1978 to 2006). Normal Frequency Evaluation Graphical MethodSr. No.Peak Flow in cumecNo of OccurrencesSummation of Occurrencesp100m/nI100/p1118129100.001.

00224412896.551.04334712793.101.07439312689.661.12561112586.

211.16665912482.761.21768412379.

311.26870912275.861.32973212172.411.381096212068.971.

4511103911965.521.5312104511862.071.6113117911758.621.7114140011655.

171.8115151011551.721.

9316158511448.282.0717169911344.832.

2318204511241.382.4219394111137.932.

6420518811034.482.902158911931.

033.222259461827.593.632361611724.144.142470481620.694.832573311517.

245.802678341413.797.252778741310.349.67287881126.

9014.502913186113.4529.00 Fig. 5.

1 Frequency curve for Normal Frequency Evaluation Graphical Method. 5.4 CALIFORNIA METHODS 5.

4.1 Modified California Method The flood frequency f in100 years is based upon the following equation. QUOTE (5.

4.1) 5.4.2 Modern California Method Here the equation for the flood frequency is given by the equation. QUOTE (5.4.2) Where m rank of the flood n total no of years of record f in 100 years no. of times the flood is likely to exceed y.

According to California Method the value of f indicates that in 100 years no of times the flood is likely to exceed. The lowest magnitude of flood 118 is come in 98.2759 in 100 years by Modified California Method and by Modern California Method it is 96.

6667. The highest magnitude of flood 13186 is come in 1.7241 in 100 years by Modified California Method and by Modern California Method it is 3.

3333. The probable flood frequency has been estimated for the Sabarmati River. The calculations are shown in Table 5.2 and frequency curve is shown in Fig 5.2 and 5.

3. Fig 5.2 Frequency Curve for Modified California Method Fig. 5.

3 Frequency Curve for Modern California Method 5.5. FOSTERS METHOD So long as the problem under consideration deals with return periods considerably less than the period of record, one may obtain a reasonable trust worthy estimate of flood frequency by interpolation. When floods approaching or transcending the maximum of record must be considered, it becomes extremely important to know the exact nature of statistical distribution with which we are dealing. H. A. Foster (1924) suggested the case of Pearsons skew function for fitting observed flood data.

Pearson adopted the general differential equation, QUOTE (5.5.1) Where x is the deviation of the variable X, J the frequency corresponding to x, a is a constant f(x) which is a function of x. Standard Deviation QUOTE (5.5.

2) And the coefficient of skew, QUOTE (5.5.3) The coefficient of skew must be adjusted for the size of sample by, QUOTE (5.5.4) And QUOTE (5.5.

5) Equations 5.5.4 and 5.5.5 are used for Foster Type III ( Hazen) and Foster Type I respectively. Factor K corresponding to various percentage frequencies and the computed coefficient of skew can be selected from Table 5.3 and 5.4 for foster type III and type I respectively.

These factors K multiplies by the coefficient of variation and added to the mean of X define the frequency curve. Table 5.3 Skew curve Factors for Foster Type III Curve CsFrequency Percent9995805020510.10.

010.0010.00010.0-2.33-1.

64-0.840.000.841.642.333.093.

734.274.760.

2-2.18-1.58-0.85-0.030.

831.692.483.084.164.845.

480.4-2.03-1.51-0.85-0.060.

821.742.623.

674.605.426.240.

6-1.88-1.45-0.86-0.090.801.

792.773.965.

046.017.020.8-1.74-1.

38-0.86-0.130.781.832.904.255.486.

617.821.0-1.59-1.31-0.86-0.

160.761.873.034.545.

927.228.631.2-1.

45-1.25-0.85-0.190.

741.903.154.826.377.

859.451.4-1.32-1.18-0.84-0.220.

711.933.285.116.

828.5010.281.6-1.19-1.11-0.82-0.250.

681.963.405.397.

289.1711.121.8-1.08-1.03-0.80-0.

280.641.983.505.667.759.8411.962.

0-0.99-0.95-0.78-0.310.612.

003.605.918.2110.5112.

812.2-0.90-0.89-0.75-0.330.

582.013.706.20—2.4-0.83-0.82-0.

71-0.350.542.013.786.

47—2.6-0.77-0.

76-0.68-0.370.512.013.876.73—2.8-0.

71-0.71-0.65-0.380.472.023.956.99—3.

0-0.67-0.66-0.

62-0.400.422.

024.027.25— Table 5.4 Skew curve Factors for Foster Type I Curve CsFrequency Percent9995805020510.10.010.0010.

00010.0-2.08-1.64-0.920.000.921.

642.082.392.532.592.620.2-1.

91-1.56-0.93-0.050.

891.722.252.662.832.

943.000.4-1.75-1.47-0.93-0.

090.871.792.422.

953.183.553.

440.6-1.59-1.

38-0.92-0.130.851.852.853.

243.593.803.920.8-1.44-1.

30-0.91-0.170.

831.902.753.554.004.

274.431.0-1.30-1.21-0.89-0.210.801.

952.923.854.424.754.431.2-1.

17-1.12-0.86-0.

250.771.993.094.154.

835.255.501.4-1.

06-1.03-0.83-0.290.732.033.254.455.

255.756.051.6-0.

96-0.95-0.80-0.320.692.073.404.755.

255.756.051.8-0.87-0.87-0.

76-0.350.642.103.545.

056.086.757.202.0-0.

80-0.79-0.71-0.

370.582.133.675.356.507.257.

80 The calculation for the mean, standard deviation and the coefficient of skew are shown Table 5.5. Table 5.5 Frequency analysis computations for Sabarmati River by Fosters Method Type I and III Standard Deviation QUOTE And the coefficient of skew QUOTE Adjusted coefficient of skew For Foster Type III ( Hazen), Factors corresponding to various percentage frequencies and the computed coefficient of skew 1.

084432 are taken from Table 5.4. These factors multiplied by the standard deviation and added to the mean value define the frequency curve.

Similarly, The adjusted coefficient of skew for foster type I curve is given by, For Foster Type I, And the factor K is taken from Table 5.4 Table 5.7 Calculation for the flood frequencies Fosters Type I curve Fig.

5.4 Frequency Curve for Fosters Type III Method Fig. 5.5 Frequency Curve for Fosters Type I Method The calculation for the mean standard deviation and the coefficient of skew are the same as in the Fosters method (Type III). The calculation for the flood frequencies by Hazens method are shown in Table 5.9.

Fig 5.6 shows the curve fitting for the expected flood peaks for the Hazens Method. Table 5.