Flood analysis using negative binomial and Generalized Pareto models in partial duration series (PDS)

Abstract

Two flood analysis estimation schemes, based on, respectively, partial duration series (PDS) and annual maximum series (AMS), are compared. The PDS model assumes a Generalized Pareto (GP) distribution for modeling the flood exceedances above threshold corresponding to a generalized extreme value (GEV) distribution for annual maxima. As a generalization of the common assumption of the Poisson distribution (PD) to count the occurrences of peaks over threshold in the PDS models, the advantage of negative binomial (NB) distribution is explored in this study. The T-year event estimator for the annual maximum distribution corresponding to the parent PDS model is formulated for producing AMS samples consistent with PDS samples which are used in simulations. The performance of the two models in terms of the uncertainty of the T-year event estimator is evaluated in the cases of estimation with the method of probability weighted moments (PWM). In a similar way, the performance of the derived PDS/NB-GP model is compared with the existing PDS/PD-GP model in terms of uncertainty of T-year event estimator using simulation and field data. The results show the T-year event estimate using PDS/NB-GP model yields lower variance compared to PDS/PD-GP models for most cases. However both the models perform similarly at higher return periods more than 300 years, using the ratios of the variance of T-years estimate as an index, and the ratio decreases with an increase in mean number of annual exceedances above threshold (l). From the results it is observed that both AMS and PDS models yield the same variance when l varies from 1.4 to 1.65. However, in case of NB distribution the PDS and AMS models gives the same variance of q(T) when variance (r2) is 1.5 times the mean number of annual exceedance above threshold. The performance of the PDS models and the corresponding AMS models using the available data of Dee (at Cairnton) shows the PDS/NB-GP model to be marginally better at return periods lower than 50 years.