Comparison of Generalized Extreme Value, Log Normal and Weibull Distributions for Assessment of Low-Flow

Abstract

Assessment of low-flow is an important aspect for water quality management, reservoir storage design, determining minimum release policy and safe surface water withdrawals. For which, the annual minimum d-day average flow is generally adopted procedure for characterizing the low-flow in a stream, which can be obtained by averaging the flow using moving average method for ‘d’ consecutive days viz., 7-, 10-, 14- and 30- days. This paper presents a study on comparison of three probability distributions such as Generalized Extreme Value, 2-parameter Log Normal (LN2) and Weibull adopted in estimation of low-flow for river Cauvery at Kollegal gauging site. The parameters are determined by three methods viz., method of moments, maximum likelihood method and L-Moments (LMO), and are used for estimation of low-flow. The adequacy of fitting probability distributions adopted in low-flow frequency analysis is evaluated by quantitative assessment through Goodness-of-Fit (viz., Chi-Square and Kolmogorov-Smirnov) and diagnostic (viz., correlation coefficient and root mean squared error) tests, and qualitative assessment using the fitted curves of the estimated low-flow. The results of quantitative and qualitative assessments indicate that LN2 (LMO) is better suited amongst three distributions adopted in estimation of 7-, 10-, 14- and 30- day low-flows for river Cauvery at Kollegal site.