A Recursive Multi-Scaling Approach to Regional Flood Frequency Analysis

Abstract:

In the past few decades, hydrologists considered the hypothesis of self-similarity to perform frequency analysis of extreme hydrologic events (e.g., extreme rainfall, floods) for arriving at estimates of the events at ungauged/sparsely gauged sites. The hypothesis states that the estimates of an extreme hydrologic event at a specified space scale are related to estimates of the event at another space scale through scaling relationship. Shortcomings associated with conventionally used simple- and multi-scaling approaches based on the hypothesis would be discussed. Following this, a new scaling approach developed based on the self-similarity hypothesis (referred to as Recursive Multi-scaling (RMS) approach) would be presented. Its advantages over the conventional simple- and multi-scaling approaches would be demonstrated in the context of regional flood frequency analysis. The RMS approach involves (i) identification of a separate set of attributes corresponding to each of the sites (being considered in the study area/region) in a recursive manner according to their importance, (ii) utilizing the identified attributes to construct effective regional regression relationships to estimate statistical moments (SMs) of peak flows, and (iii) using the SMs as the basis to estimate parameters of flood frequency distribution, and flood quantiles corresponding to different return periods. Effectiveness of the RMS approach in arriving at flood quantile estimates for ungauged sites would be demonstrated in the conventional and L-moment frameworks through leave-one-out cross-validation experiment on watersheds in Indiana State, USA. Error in quantile estimates is quantified in terms of various performance measures such as relative-bias (R-bias) and relative root mean square error (RRMSE). The results indicate that the proposed RMS approach outperforms index-flood based Region-of-Influence approach, simple- and multi-scaling approaches and a multiple linear regression method in yielding quantile estimates with significantly low errors.