A Hybrid Index-Flood and Non-Stationary Bivariate Logistic Extreme-Value Framework for Flood Quantile Estimation in Data-Scarce Mexican Catchments

Regional flood frequency analysis (RFFA) is a cornerstone for estimating design floods at ungauged or data-scarce sites by pooling information within hydrologically homogeneous regions. This study proposes and evaluates a hybrid RFFA framework that integrates the Index-Flood (IF) technique with a bivariate logistic extreme-value model whose marginal distributions are formulated under both stationary and non-stationary assumptions. Non-stationarity is incorporated through a covariate-dependent location parameter, using time and large-scale climate indices—the Pacific Decadal Oscillation (PDO) and the Southern Oscillation Index (SOI)—as explanatory variables. The proposed approach is applied to two contrasting hydrological regions in Mexico—RH10 (Sinaloa) and RH23 (Chiapas Coast)—to assess its performance under differing climatic and hydrological regimes. Model adequacy and stability are evaluated using likelihood-based goodness-of-fit criteria (log-likelihood and Akaike Information Criterion) and a leave-one-out (jackknife) cross-validation scheme embedded within the IF regionalization workflow. Results indicate that non-stationary bivariate formulations dominate model selection at most stations and yield stable regional growth curves, providing robust and engineering-relevant performance under cross-validation. Overall, the proposed framework offers a conservative and operational pathway for regional flood quantile estimation that bridges local data scarcity and regional hydrological characterization in environments influenced by climate variability and long-term change.