Formulation for Predicting Flood Peaks Using a Skewed Chi-Square Distribution

Abstract

Floods remain one of the most devastating natural disasters, causing significant human, economic, and ecological losses worldwide. Accurate prediction of flood peaks is therefore essential for effective water resource management, urban planning, and disaster mitigation. However, modeling flood peak data is challenging because such observations are nonnegative, highly skewed, and often exhibit heavy-tailed characteristics. Traditional symmetric probability models, such as the normal distribution, fail to capture this behavior. In contrast, the skewed chi-square distribution, particularly its scaled and noncentral variants, offers a mathematically flexible and practically interpretable framework for modeling positively skewed hydrological extremes. This paper develops a statistical formulation for flood peak prediction based on skewed chi-square modeling, including parameter estimation, return level analysis, and diagnostic validation. To complement simulation-based evaluation, an empirical study using annual flood-peak records from a Midwestern U.S. catchment (1950–2020) was conducted with data obtained from USGS and NOAA archives. The real data analysis confirms that the scaled noncentral chi-square distribution accurately captures the strong right skewness and heavy tails observed in hydrological extremes, outperforming traditional gamma and lognormal models. The proposed approach aims to bridge the gap between theoretical distributional modeling and real-world flood risk assessment.