A Nonhomogeneous Markov Model for Daily Precipitation

Balaji Rajagopalan
Upmanu Lall
David G. Tarboton, Utah State University


This paper presents a one-step nonhomogeneous Markov model for describing daily precipitation at a site. Daily transitions between wet and dry states are considered. The one-step, 2 × 2 transition-probability matrix is presumed to vary smoothly day by day over the year. The daily transition-probability matrices are estimated nonparametrically. A kernel estimator is used to estimate the transition probabilities through a weighted average of transition counts over a symmetric time interval centered at the day of interest. The precipitation amounts on each wet day are simulated from the kernel probability density estimated from all wet days that fall within a time interval centered on the calendar day of interest over all the years of available historical observations. The model is completely data-driven. An application to data from Utah is presented. Wet- and dry-spell attributes [specifically the historical and simulated probability-mass functions (PMFs) of wet- and dry-spell length] appear to be reproduced in our Monte Carlo simulations. Precipitation amount statistics are also well reproduced.