Modelling daily rainfall with climatological predictors: Poisson-gamma generalized linear modelling approach

Generalized linear models (GLMs) are used in understanding the impact of predictors on a dependent variable. The aim of this study is to fit GLMs to daily rainfall totals using potential predictors. First, the appropriate probability distributions within a specific family, the Tweedie family, were determined for daily rainfall totals from four stations of Peninsular Malaysia from 1983 to 2012. Within the Tweedie family, the Poisson Gamma (PG) distribution was found appropriate to model both components: occurrence (dry/wet days) and amount (rainfall totals on wet days) of rainfall simultaneously. Then, the PG-GLMs were fitted to rainfall data with a sine term, a cosine term, lagged rainfall, NINO3.4 and Southern oscillation index (SOI) as predictors. Finally, the models were compared using the Likelihood ratio test and the Akaike information criterion. Initially, considering the cyclic pattern of rainfall data, models with only sine and cosine terms (the base model) were fitted. Then the lagged rainfall and climatological variables were added each time to the base model. Diagnostic QQ plots indicate that the models fit the data well. The models were fitted using the first 60% of data and validated using the remainder. The models capture the various characteristics of observed datasets reasonably well. Including single climatological variables in the model significantly improves the fit compared to the base model with lagged rainfall (except for the south-east coastal station, Mersing), however, including both climatological predictors in the same model does not improve the model significantly. The model with SOI is only favoured for the east coastal station, Kuala Terengganu, and the model with NINO3.4 fits better to the inland and west coastal stations. The models are useful in understanding the impact of the studied climatological variables and to predict the amount and probability of rainfall.