A copula-based multisite rainfall frequency analysis: a case study on the Lanyang watershed in Taiwan

Frequency analysis is a widely used method in hydrology; however, the conventional approaches to frequency analysis do not consider the spatial dependence between stations. This study proposes a novel approach for multisite frequency analysis using the copula method. This approach uses the framework of pair copula construction to extended bivariate copula functions for multivariate analysis, allowing for non-homogeneous marginal distribution and spatial dependence. Our approach was applied to analyze hourly rainfall in Taiwan’s Lanyang watershed from 1996 to 2011, constructing the multisite rainfall distribution to estimate the frequency of extreme rainfall events. The results showed the nonlinear relationships and distinct frequency distributions of rainfall across the study area due to changes in elevations. Based on the copula-based multisite rainfall distribution, the study simulated extreme rainfall events at multiple sites with predetermined frequencies, preserving the spatial characteristics of rainfall more accurately than previous methods. This approach avoids potential underestimation and overestimation of hourly rainfall intensity at specified return periods resulting from assumptions of homogeneity and spatial independence. This study also evaluated possible multisite rainfall combinations at a given frequency using Monte-Carlo simulation. These simulations characterized spatial uncertainties in design multisite rainfall, providing critical information for water resources management and hydrological design.