A Hybrid Stochastic Rainfall Model That Reproduces Rainfall Characteristics at Hourly through Yearly Time Scale

Abstract

A novel approach of stochastic rainfall generation that can reproduce various statistical characteristics of observed rainfall at hourly through yearly time scale is presented. The model uses the Seasonal Auto-Regressive Integrated Moving Average (SARIMA) model to generate monthly rainfall. Then, it downscales the generated monthly rainfall to the hourly aggregation level using the Modified Bartlett-Lewis Rectangular Pulse (MBLRP) model, a type of Poisson cluster rainfall model. Here, the MBLRP model is fine-tuned such that it can reproduce the fine-scale properties of observed rainfall. This was achieved by first generating a set of fine scale rainfall statistics reflecting the complex correlation structure between rainfall mean, variance, auto-covariance, and proportion of dry periods, and then coupling it to the generated monthly rainfall, which were used as the basis of the MBLRP parameters to downscale monthly rainfall. The approach was tested at the 29 gauges located in the Midwest to the East Coast of the Continental United States with a variety of rainfall characteristics. The results of the test suggest that our hybrid model accurately reproduces the first through the third order statistics as well as the intermittency properties from the hourly to the annual time scale; and the statistical behaviour of monthly maxima and extreme values of the observed rainfall was well reproduced as well.