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

Flood frequency analysis is a key tool for estimating return levels, which are essential for reducing human and economic losses. However, the non-stationarity introduced by climate change and land-use changes demands models that explicitly account for these dynamics. In this study, a bivariate logistic model with non-stationary marginals is applied to improve estimation accuracy. Eight stations from a homogeneous region in the state of Sinaloa, Mexico—each with over 30 years of instantaneous maximum discharge records—were analyzed. Stationary and non-stationary Gumbel and General Extreme Value (GEV) distributions were compared, along with their bivariate combinations (Gumbel–Gumbel, Gumbel–GEV, GEV–Gumbel, and GEV–GEV) using the proposed methodology. Results indicate that the non-stationary bivariate GEV–Gumbel distribution provides the best fit according to the log-likelihood function.