Probabilistic Forecasting of Peak Discharges Using L-Moments and Multi-Parameter Statistical Models

Abstract

Given the global rise in magnitude and frequency of extreme events due to climate change, accurately determining these values—typically through frequency analysis—is especially important. The article analyzes the particular aspects of three probability distributions of 4 and 5 parameters in flood frequency analysis (FFA) using the L-moments as a parameter estimation method. Aspects regarding the behavior of the five-parameter Wakeby, four-parameter generalized Pareto and four-parameter Burr distributions are highlighted in generating the maximum flow values in the area of low annual exceedance probabilities characteristic of rare and very rare events. After applying these distributions to four case studies, it was found that for the 10,000-year return period event, the relative error between multi-parameter distributions is under 20%—a more than acceptable margin given the extremely low exceedance probability. However, its importance depends on the use of the generated values, which in some cases can lead to excessive costs in establishing structural flood protection measures (urban planning), which can be avoided. It also highlights possible negative consequences (material and human lives) regarding the risk associated with these analyses that can lead to an under-dimensioning of this infrastructure.