A simple scheme to adjust Poisson cluster rectangular pulse rainfall models for improved performance at sub-hourly timescales

Abstract

Although sub-hourly rainfall temporal characteristics play an important role in occurrences and magnitudes of urban flash floods, most stochastic rainfall models struggle to reproduce them when rainfall information is not available at sub-hourly timescales. This study suggests a simple approach to modifying Poisson cluster rectangular pulse rainfall models to resolve this issue. In this model, the original rectangles representing a rain cell are replaced by a bell shape that is mathematically represented as y = sin(2)(x). Such an alteration no longer makes it possible to obtain closed form expressions for the various rainfall statistics for model parameter calibration. Based on an assumption that this alteration would hardly alter the hourly and supra-hourly statistics, we calibrated the parameters of a rectangular pulse model with these statistics (from 1 to 32 h) and transplanted the same parameters to the sine-squared pulse model to generate 500 years of 5-minute rainfall. Importantly, this parameter transplant procedure does not require any sub-hourly information so that it amounts to a downscaling algorithm for the generation of sub-hourly rainfall. Our results show that both models reproduced well the rainfall mean, variance, autocovariance, proportion of dry periods, and extreme values at hourly to 72-hour timescales. However, the sine-squared pulse model performed significantly better at sub-hourly time scales. The same 500 years of synthetic rainfall data and 69 years of observed rainfall data were then used as input of a dual-drainage urban watershed model developed for a frequently flooded urban area of Seoul. While the traditional rectangular pulse model significantly underestimated the flooded area, the new sine-squared pulse model successfully reproduced the flooded area caused by the observed rainfall.