Power-variance models for modelling rainfall

Abstract

Modelling rainfall presents difficulties: one is that rainfall is both continuous and discrete. The discrete component corresponds to exactly zero rainfall. Some researchers circumvent this by using two models - one for determining the presence and absence of rainfall, another for the rainfall amount. Here, we use power-variance (Tweedie) generalized linear models, which can explictly model continuous data with exact zeros. We demonstrate there is a basis for using these models; that the parameters, in some cases, lend themselves to a useful interpretation; and show the models fit the data well using monthly rainfall data from Charleville. We then model Australian annual rainfall, and develop a contour map for the power-variance model index parameter.