RELEVANT ASPECTS OF FLOOD FREQUENCY ANALYSIS

Abstract

Flood is one of the pervasive natural disasters. Every year, numerous catastrophic flood events affect the fragile ecosystem, human lives, and other properties worldwide. Out of multiple available methods for estimating peak floods, flood frequency analysis (FFA) finds a widespread application. The present study explores some significant aspects of FFA. The annual maximum series (AMS) sampling method considers the maximum discharge of each year, i.e., the annual flood value. The first part of the study has a significant focus on selecting a basin-scale model for at-site flood frequency analysis using AMS by systematically evaluating probability distributions using some statistical measures and a few relevant catchment and flow properties. The proposed methodology is applied to the Mahanadi River basin in India. Generalized Extreme Value (GEV) distribution is selected as the basin-scale model based on a descriptive statistical ranking method followed by its test for predictive ability through bootstrap sampling. The distribution parameters are correlated with a few hydrological and physiographic characteristics of the watershed through regression analysis. Flood flow values estimated at the gauging sites considering the site-wise best distribution and the basin-scale standard model are also compared. The marginal difference of error between them further supports applying a standard model for the entire basin despite site-wise different models. The graphical approach of FFA deals with displaying ranked data on a probability paper based on their probability of occurrence. This probability of occurrence given by one minus its cumulative probability is predicted using a plotting position (PP) formula. There have been several schools of thought about selecting a suitable PP based on the objective of investigation and the choice of distribution-free or distribution-specific formulas. The second part of the research further details this continuing debate on PPs for GEV distribution. An attempt is made to derive unbiased PP for various subranges of the shape parameter of GEV. The derived formulas are compared with other PPs based on root mean square error, the relative bias between theoretical reduced variates and reduced variates obtained from plotting positions, and the sum of squared error in the top five reduced variates. The proposed formula performs better in a broader range of shape parameters. Graphical comparison of all these PPs on GEV probability paper for synthetically generated data set doesn’t show any significant difference. The formulas are further applied to the annual maximum series (AMS) at different gauging sites of the Mahanadi River basin in India, and error statistics are calculated between the observed and predicted AMS. The detailed analysis reveals that even though the unbiased PP proposed in the present study possesses the minimum error and bias between the reduced variates, the practical application of all PPs is almost similar for graphical analysis. Also, the distribution-free PPs perform relatively better for predicting flood flow values. The partial duration series (PDS) sampling in FFA represents a complete flood generating process by dual modeling of flows above a specific truncation level. One distribution is for modeling the arrival of peaks, and the other for the magnitude of those exceedances. The present study adds a new dimension to this area of research, where the principle of maximum entropy (POME) theory is used to locate the optimum threshold in a PDS. After satisfying the independence criteria of peaks and some graphical analysis, suitable distribution models are fitted, and the respective entropy function is calculated. The optimum threshold is selected where the combined entropy of both the models of a PDS is the maximum. The proposed methodology is applied to the Waimakariri River at the Old Highway Bridge site in New Zealand. Various return period quantiles are estimated, and their predictive ability is tested by bootstrap sampling. Overall the study shows that the entropy approach can be used as an alternative that considers both models of a PDS while selecting the optimum threshold. This study also investigates another aspect of entropy applications where an entropy based approach is proposed as a goodness of fit measure for threshold selection in the GP/PDS modeling of flood frequency analysis. The proposed methodology is initially applied to synthetically generated data series from mixture distribution with varying sample length and shape parameters. The performance of this approach is also evaluated at two gauging sites, i.e., the Canterbury Regional Council’s gauging station on the Waimakariri River at Old highway bridge site, New Zealand, and the River Thames at Kingston in the United Kingdom. Various statistical error criteria and graphical measures such as mean residual life plot; parameter stability plots assess the performance of PDS models along with a non-parametric bootstrap sampling for defining the 95% confidence intervals. Such graphical and analytical results from the simulation study and the study areas indicate that entropy can become an alternate tool for threshold detection of PDS models in flood frequency analysis.