A bivariate rainfall frequency analysis framework in urban areas by coupling copula theory and stochastic storm transposition

Extreme rainfall is a critical “agent” driving flash floods in urban areas. In rainfall frequency analysis (RFA), however, storms are usually assumed to be uniform in space and fixed in time. Spatially and temporally uniform design storms and area reduction factors are oftentimes used in conjunction with RFA results in engineering practice for infrastructure design and planning. The consequences of such assumptions are poorly understood. This study examines how spatiotemporal rainfall heterogeneity impacts RFA, using a newly-introduced bivariate framework consisting of copula theory and stochastic storm transposition (SST). A large number of regionally-extreme storms with specific features—rainfall depth, duration, intensity, and level of intra-storm spatial organization—were collected. Rainfall intensity-duration-frequency (IDF) estimates exhibiting these bivariate features were then generated by synthesizing long records of rainfall via SST. The results show that dependencies exist among spatiotemporal storm characteristics. Bivariate frequency results exhibit smaller uncertainties but more complex physical meanings that the results from conventional methods. In particular, the highly spatially-organized storms play a leading role in frequency estimates.