A stochastic rainfall model that can reproduce important rainfall properties across the timescales from several minutes to a decade

Abstract

A stochastic rainfall model that can reproduce various rainfall characteristics at timescales between 5 min and one decade is introduced. The model generates the fine-scale rainfall time series using a randomized Bartlett-Lewis rectangular pulse model. Then the rainstorms are shuffled such that the correlation structure between the consecutive storms are preserved. Finally, the time series is rearranged again at the monthly timescale based on the result of the separate coarse-scale monthly rainfall model. The method was tested using the 69 years of 5-minute rainfall data recorded at Bochum, Germany. The mean, variance, covariance, skewness, and rainfall intermittency were well reproduced at the timescales from 5 min to a decade without any systematic bias. The extreme values were also well reproduced at timescales from 5 min to 3 days. The past-7-day rainfall before an extreme rainfall event, which is highly associated with the extreme flow discharge was reproduced well too. The rainstorm shuffling approaches introduced here may be adopted as a standard procedure in combination with any Poisson cluster rainfall model. The methods are simple and parsimonious, yet significantly reduce the systematic underestimation of rainfall variance at coarse scales, and improve the reproduction of skewness, and extreme rainfall depths values at a range of time-scales, thereby addressing well-known shortcomings of Poisson cluster rainfall models.