On the proper order of Markov chain model for daily precipitation occurrence in the contiguous United States

Markov chains are widely used tools for modeling daily precipitation occurrence. Given the assumption that the Markov chain model is the right model for daily precipitation occurrence, the choice of Markov model order was examined on a monthly basis for 831 stations in the contiguous United States using long-term data. The model order was first identified using the Bayesian information criteria (BIC). The maximum-likelihood estimates of the Markov transition probabilities were computed from 100 boot-strapped samples and were then used to generate 50-yr precipitation occurrence series. The distributions of dry-and wet-spell lengths in the resulting series were then compared with observations using a two-sample Kolmogorov-Smirnov (K-S) test. The results suggest that the most parsimonious model, as identified by the BIC, usually (in approximately 68% of the cases) reproduced the wet-and dry-spell length distributions. However, the K-S test often indicated a second-order model when the BIC indicated a first-order model. In a smaller number of cases, the BIC indicated a higher-order model than the K-S test. In both cases, the differences were found to be due to the distribution of wet spells rather than dry spells. It is concluded that models chosen on the basis of the BIC may not adequately reproduce the distributions of wet and dry spells for some locations and times of year.