New Proposal for maximum hydrological events fitting showing the ‘separation phenomenon’ with flexible TCEV Distribution

Hydrological extreme records in many regions in the world may include observations from different genesis and levels of extremeness forming a characteristic “separation phenomenon’ that limits the effectiveness of traditional distributions such as the Gumbel and log-Pearson Type III models, and in such mixed extreme populations, the Two-Component Extreme Value (TCEV) distribution is better suited. However, conventional fitting approaches tend to emphasize the abundant ordinary data because of the scarcity of right-tail observations, which results in inaccurate predictions of high quantiles. Nevertheless, accurate representation of the upper tail (i.e., the high-value ranges of the cumulative distribution function, CDF) is essential for flood risk evaluation and the design of hydraulic structures. To address this issue, this study introduces a new TCEV fitting approach (SR-MWS) aimed at improving right-tail performance. In the new proposal, the dataset is first approximated using a piecewise two linear regression, and the slope ratio between the two parts (R = S1/S2) is used to assess whether TCEV modeling is appropriate or not (if R > 1.5, the dataset is regarded as suitable for TCEV fitting). Following, three weighting strategies—linear, quadratic, and exponential—are applied sequentially to obtain the final TCEV parameters. A partitioned scoring framework is then used to select the most suitable weighting scheme, emphasizing the mid-to-upper CDF range F(x) ∈ [0.6, 1.0], which corresponds to return periods from about 2.5 years to more than 200 years, while also considering overall fit quality. Our results show that the proposed method yields more accurate estimates for extreme values than conventional techniques and exhibits consistent performance for both peak-flow and precipitation datasets. Beyond hydrological applications, it provides an automated and robust tool for modeling extreme events and supporting risk assessment in fields characterized by mixed-population data with a pronounced dog-leg structure.