A Unified Generalized Extreme Value Distribution Framework for Estimating Lake Reference Nutrient Conditions with Confidence Intervals: A Case Study of Hongze Lake, China

The scientific determination of reference conditions for lake nutrients is fundamental for establishing ecologically sustainable nutrient criteria. This study developed a novel method for determining lake reference nutrient conditions based on generalized extreme value distribution theory. The method establishes a unified framework by integrating Weibull, Gumbel, and Fréchet distributions. It was applied to estimate the reference nutrient conditions in Hongze Lake, the fourth-largest freshwater lake in China. The results indicated that the extreme value sequences of total nitrogen (TN) and total phosphorus (TP) followed the generalized extreme value distribution, thereby confirming the method’s feasibility. The recommended reference conditions for TN and TP in Hongze Lake were 0.65 mg/L and 0.031 mg/L, respectively, with 95% confidence intervals of 0.56–0.74 mg/L for TN and 0.026–0.035 mg/L for TP. The proposed method could avoid the artificial errors associated with data grouping in descriptive statistical methods and assist in formulating adaptive water management strategies by providing confidence intervals for reference nutrient concentrations. The spatial distribution of the reference TN and TP concentrations across various watersheds in China revealed that the eastern watersheds exhibited higher reference concentrations of TN and TP compared to the western watersheds. This study provides valuable insights for developing nutrient criteria for lakes, contributing to the sustainable management of water quality in regional lake ecosystems.