Spatial Dependence of Extreme Rainfall and Development of Intensity–Duration–Frequency Curves Using Max-Stable Process Models

Abstract

The effective management of flood risk and urban drainage design hinges on a comprehensive understanding and accurate modeling of extreme rainfall variations, particularly in vulnerable areas. The study proposes to model spatial extreme rainfall across various durations in the Ganga River basin of India using max-stable processes (MSP). Incorporating geographical covariates like longitude, latitude, and elevation, 28 surface response models were constructed for location and scale parameters, with linear variations in marginal parameters while keeping the shape parameter constant across space. Various max-stable characterizations were evaluated using the Takeuchi information criterion (TIC) value and likelihood ratio test statistics, including Brown-Resnick, Smith, Extremal-t, Schlatter, and Geometric-Gaussian models with different correlation functions. The findings showed that the Brown-Resnick model consistently simulated well for shorter extreme rainfall for 3, 4, and 6-h and 36-h durations. The extremal coefficients revealed higher dependency between closer locations for most durations. In comparison with classical univariate extreme value theory (UEVT), the MSP exhibits a minimal overestimation in extreme rainfall intensity at New Delhi (by 13.6 mm/h) and Diamond Harbor (by 10.2 mm/h) stations for shorter durations, i.e., 2-h to 6-h range. Its estimations align within the uncertainty bounds of the identical and independent distribution (I.I.D) for longer durations. This suggests the importance of considering the strengths and limitations of M.S.P. and UEVT approaches for accurate rainfall intensity estimation, especially in flood risk management and urban drainage design. In data-sparse region/ungauged basins, where traditional methods like univariate UEVT may be limited due to the absence of observed rainfall data. The fitted max-stable processes MSP can serve as a valuable tool when relevant geographical covariates are known.