Stochastic models for daily rainfall in the Western Pacific

Several stochastic models of rainfall occurrence and daily rainfall amount have been applied to data sets, of 18–20 years duration, for 22 islands in the Western Pacific. The models for rainfall occurrence were first- and second-order Markov chains, the truncated negative binomial distribution, and the truncated geometric distribution; each was applied with parameters determined independently for each month, and with parameters assumed to vary smoothly through the year according to a Fourier series. The models tested for daily rainfall amounts were the Weibull distribution, a mixed exponential distribution, the two-parameter gamma distribution, a skewed normal distribution, the kappa distribution, and the Srikanthan-McMahon model. The rainfall data were classified according to the number of adjoining wet days, and the models tested with all data grouped together, solitary wet days fitted separately from other wet days, and each class of data fitted separately. The results of these tests showed that this classification improves model fitting, in spite of the additional number of parameters required. For several months of the year, there are significant differences between the distributions of rainfall amounts for the three classes. However, for 18 of the 22 stations, the Srikanthan-McMahon model outperformed all others, and successfully simulated the differences between the rainfall classes.