Flood Frequency Analysis Using the Bivariate Logistic Model with Non-Stationary Gumbel and GEV Marginals

Flood frequency analysis is essential for designing resilient hydraulic infrastructure, but traditional stationary models fail to capture the influence of climate variability and land-use change. This study applies a bivariate logistic model with non-stationary marginals to eight gauging stations in Sinaloa, Mexico, each with over 30 years of maximum discharge records. We compared stationary and non-stationary Gumbel and Generalized Extreme Value (GEV) distributions, along with their bivariate combinations. Results show that the non-stationary bivariate GEV–Gumbel distribution provided the best overall performance according to AIC. Importantly, GEV and Gumbel marginals captured site-specific differences: GEV was most suitable for sites with highly variable extremes, while Gumbel offered a robust fit for more regular records. At station 10086, where a significant increasing trend was detected by the Mann–Kendall and Spearman tests, the stationary GEV estimated a 50-year return flow of 772.66 m3/s, while the non-stationary model projected 861.00 m3/s for 2075. Under stationary assumptions, this discharge would be underestimated, occurring every ~30 years by 2075. These findings demonstrate that ignoring non-stationarity leads to systematic underestimation of design floods, while non-stationary bivariate models provide more reliable, policy-relevant estimates for climate adaptation and infrastructure safety.