A range of Markov chain models have been used in the past to describe rainfall occurrence. Gamma distributions are commonly used for modeling rainfall amounts. These are all examples of generalized linear models. This unified view allows a regression-type approach to be used to fit and test alternative models. The approach is illustrated by fitting first- and second-order Markov chains in which the transition probabilities vary with time of year to data from sites in Jordan, Niger, Botswana and Sri Lanka. Gamma distributions with parameters varying with time are also fitted.