Revised Dicken’s method for flood frequency estimation of Upper Ganga basin

Highlights

• Use of Empirical formulas for a number of potential sites is common where insignificant data or no data is available for estimating the flow statistics.

• Dicken’s formula is one such empirical formula but despite its simplicity and applicability it is not capable of yielding flood volume at different desired frequency.

• In the present study an attempt has been made to modify the Dicken’s coefficient so as to accommodate the frequency component in flood estimation for Upper Ganga Basin.

• Regional flood frequency curve has been analyzed using probability weighted method, Index flood method, General extreme value and Wakeby distribution .Best fit distribution is decided, based on annual maximum discharge peak (ADF), Efficiency (EFF) and Standard Error (SE) parameters.

• Prediction accuracy of flood frequency analysis using the Revised Dicken’s formula is found to be above 85% while results show General Extreme Value to be the best fit distribution for the Upper Ganga basin.

Abstract

Flood discharge and its frequency is an important input to many infrastructure development, management and decision making models. However, for a number of potential sites, the data used for statistical analysis of flood discharge and its frequency, are either insufficient or unavailable. In such a situation, empirical formulae are the only alternative method to provide an estimate of design flood. Dicken’s formula is one of such empirical formulae used by practicing field engineers for flood estimation. In spite of its simplicity and applicability, Dicken’s formula is not capable of yielding flood volume at different desired frequency. In the present study an attempt has been made to modify the Dicken’s coefficient so as to accommodate the frequency component in flood estimation. For this purpose, observed flood discharge data sixteen gauging points of Ganga basin have been used to develop regional flood frequency curve, using probability weighted method, Index flood method, General extreme value and Wakeby distribution. Modified Dicken’s coefficient C_T shows a sharp gradient for sub-catchments draining up to 5000 Km². Further, C_T value, ranges from 0.834 to 6.924. The C_T –values are lower when calculated by Index Flood method while these are higher by Wakeby method. In all of these methods, C_T –values do not approach the values of 11 or 14 as suggested for northern Indian catchments. An analysis of flood volume corresponding to C_T –values of 11 or 14, reveals that these values yield high flood volume that correspond to return period of more than 1000 years and 3000 years respectively. These values are certainly very high for any rational design. Best fit distribution is decided, based on annual maximum discharge peak (ADF), Efficiency (EFF) and Standard Error (SE) parameters. Prediction accuracy of flood frequency analysis using revised Dicken’s formula is found to be above 85% for the best-fit distribution. General Extreme Value is found to be the best fit distribution for the Upper Ganga basin.

Introduction

Design of any important developmental project, for example small hydropower projects or other hydraulic structures, requires data of flood magnitudes and their frequencies. Suitable methodology to be adopted for estimation of design flood for a project depends upon importance of the project, economic and safety consideration, data availability and computational facilities etc. An accurate assessment of the river flow is essential for estimating the design discharge for any hydraulic projects at the proposed site. Increasing trend in one or more flood characteristics have led researchers around the globe to find a way for more reliable flood prediction measures (Hall et al.,2014, Vormoor et al., 2016, Kundzewicz, 2019). However, for a number of potential sites, there is either insignificant data or no data which can be used to estimate the flow statistics. Regional flood frequency analysis in ungauged basins have been a subject of interest. Various methods like L-moments method and annual maximum series of mean daily streamflow has been used for reliable prediction of flood quantiles in various countries (Smithers and Schulze, 2001, Hosking and Wallis, 2005, Kumar and Chatterjee, 2005, Malekinezhad and Zare-Garizi, 2014, Hailegeorgis and Alfredsen, 2017). Empirical formulas are the only alternative method to provide an estimate of the design flood in ungauged catchment and as such various empirical formulae have been devised for different regions of the country (Acreman, 1985, Commission, 1980, Greenwood et al., 1979, Huq et al., 1986). Most of these empirical formulae involve one or two physical characteristics for estimation of the flood peaks. These formulae are essentially the regional formulae based on statistical correlation of the observed peaks and important catchments and climatologic characteristics. However, in the present form, these formulae are not capable of providing flood estimates for a desired return period (Commission, 1980).

One of the empirical formula adopted for moderate size North Indian catchments is Dickens formula, which is given as

$$Q=C{A}^{0.75}$$

where Q is flood volume in cumecs, A is catchments area in Sq. Km., and C is the Dickens coefficient, whose values for various regions are given in Table 1.

The coefficient C is chosen from the given range for the specific regions. In spite of its simplicity and applicability, Dicken’s formula is not capable of yielding flood volume at different desired frequency.

In this paper, a methodology is being presented for the computation of revised coefficient of the Dickens formula, to estimate design flood of different return period, by relating the frequency curves developed for hydro meteorologically homogeneous regions by fitting probability weighted moments (PWM) based Index flood method, General extreme Value (GEV) and Wakeby distributions to the data of 16 gauging sites of Ganga basin in Himalayan region. The floods of different return periods are computed for four test catchments for validation of the revised Dickens formula. This revised Dicken’s empirical formula will enhance its practical utility for computation of flood volume for Upper Ganga basins.