Simulation of the entire range of daily precipitation using a hybrid probability distribution

Underestimation of extreme values is a widely acknowledged issue in daily precipitation simulation. Nonparametric precipitation generators have inherent limitations in representing extremes. Parametric generators can realistically model the full spectrum of precipitation amount through compound distributions. Nevertheless, fitting these distributions suffers from numerical instability, supervised learning, and computational demand. This study presents an easy-to-implement hybrid probability distribution to model the full spectrum of precipitation amount. The basic idea for the hybrid distribution lies in synthesizing low to moderate precipitation by an exponential distribution and extreme precipitation by a generalized Pareto distribution. By forcing the two distributions to be continuous at the junction point, the threshold of the generalized Pareto distribution can be implicitly learned in an unsupervised manner. Monte Carlo simulation shows that the hybrid distribution is capable of modeling heavy tailed data. Performance of the distribution is further evaluated using 49 daily precipitation records across Texas. Results show that the model is able to capture both the bulk and the tail of daily precipitation amount. The maximum goodness-of-fit and penalized maximum likelihood methods are found to be reliable complements to the maximum likelihood method, in that generally they can provide adequate goodness-of-fit. The proposed distribution can be incorporated into precipitation generators and downscaling models in order to realistically simulate the entire range of precipitation without losing extreme values.