Fréchet and chi-square parametric expressions combined with Horton ratios to derive a synthetic unit hydrograph

Abstract

This paper explores the potential of using the density functions of the one-parameter chi-square distribution (1PCSD) and the two-parameter Fréchet distribution (2PFD) as parametric expressions for describing synthetic unit hydrographs (SUH) using geomorphological parameters of the catchment and, in particular, Horton ratios. To estimate the parameters of these two distributions, a simple analytical procedure is proposed. Finally, the suitability of these methods compared to the existing two-parameter gamma distribution (2PGD) method for SUH derivation is examined using limited field data conditions for two Indian catchments. Based on STDER criterion, 1PCSD is found to perform marginally better than 2PGD and 2PFD for Bridge catchment 253. However, for the Myntdu-Leska catchment, 2PFD performs marginally better than 2PGD and 1PCSD. The results indicate that the two density functions compared well with the popular 2PGD, indicating the equal potential of both for SUH derivation using Horton ratios.