Combined Effects of the Southern Oscillation Index and the Pacific Decadal Oscillation on a Stochastic Daily Precipitation Model*

The combined effects of the Southern Oscillation index (SOI) and the Pacific decadal oscillation (PDO) on a second-order Markov chain mixed exponential daily precipitation model were determined for 15 stations in Nevada, Arizona, New Mexico, and Washington. The linkage between these monthly indices and daily precipitation was investigated by perturbing logits of Markov chain transition probabilities and the mean of the mixed exponential distribution by linear functions of a time-lagged SOI and concurrent PDO. The combination of linear coefficients and lags that resulted in the maximum log-likelihood functions was identified, and the Akaike information criterion (AIC) was used to determine the best model. The SOI effect was consistent with previous studies in that negative SOI (El Niño) leads to more frequent precipitation and greater amounts of precipitation given a wet day in Nevada and the Southwest, with the opposite effect in the northwest. SOI and PDO interactions were most significant for the Nevada stations where a positive PDO increases both the probability of a wet day for three transition probabilities and also increases the mean of wet-day precipitation. The PDO had little effect for the monsoonal (Arizona and New Mexico) stations except for Hobbs, New Mexico, where a positive PDO would increase the mean depth on a wet day. The Washington stations showed an increase in the frequency and mean depth of precipitation given a positive SOI, but PDO had little effect. Identification of combined SOI–PDO effects allows more realistic simulations of daily precipitation and provides insight into the reliability of short records.