An improved relative frequency method for flood season partitioning

Partitioning the flood season into multiple sub-seasons holds significant theoretical and practical importance in water resources management and hydrology. While the relative frequency method offers an objective approach to eliminate subjective bias in flood season partitioning, its traditional scheme evaluation using the Euclidean distance is prone to suboptimal segmentation. This limitation arises because the Euclidean distance overlooks the statistical dependence between sub-seasons and their varying variability, potentially leading to biased results. This study improves the traditional RF method by introducing the Mahalanobis distance. Utilizing the Mahalanobis distance in the optimization process offers two advantages: (a) it adaptively normalizes the evaluation space using the covariance matrix estimated from bootstrap replicates, which automatically accounts for the correlation structure among sub-season flood frequencies; and (b) it reduces sensitivity to the varying variability ranges of sub-seasons in the membership degree space. Consequently, it provides a more precise characterization of flood frequency distribution and accurately identifies periods of high flood risk. Subsequently, the precision and reliability of the proposed method were rigorously validated using Monte Carlo simulation. Finally, applying the method to the Lhasa River Basin yielded the following sub-season partition: Pre-flood season: 1-Jun to 1-Jul; Main flood season: 2-Jul to 12-Aug; Post-flood season: 13-Aug to 30-Sep.