Parameter Estimation of Beta Distribution for Unit Hydrograph Derivation

Abstract

Traditionally used methods for developing a synthetic unit hydrograph (SUH) are well known for their limitations. In last few decades, use of probability distribution functions in developing SUHs has received much attention. In this study, the potentials of a three-parameter beta distribution are explored. Using a analogy between the three-parameter beta-distribution shape and the SUH shape, approaches are developed to evaluate the unknown parameters. Based on nondimensional analysis and optimization, a simple accurate relation is introduced to estimate the three parameters of the beta distribution that is useful for unit hydrograph derivation. The relation yields results closer to those obtained by an available trial and error procedure. The unit hydrographs from the proposed method fit observed hydrographs better than those from the widely used two-parameter gamma distribution. The potential of the approach is demonstrated using data from different catchments lying within and outside India. The methodology is found to work consistently better in most cases.