We develop a doubly stochastic point process model with exponentially decaying pulses to describe the statistical properties of the rainfall intensity process. Mathematical formulation of the point process model is described along with second-order moment characteristics of the rainfall depth and aggregated processes. The derived second-order properties of the accumulated rainfall at different aggregation levels are used in model assessment. A data analysis using 15 years of sub-hourly rainfall data from England is presented. Models with fixed and variable pulse lifetime are explored. The performance of the model is compared with that of a doubly stochastic rectangular pulse model. The proposed model fits most of the empirical rainfall properties well at sub-hourly, hourly and daily aggregation levels.

Several Markov modulated Poisson process (MMPP) models are developed to describe winter season rainfall with parsimonious parameter use. We propose a methodology for determining the best form of seasonal model for fine-scale rainfall within a MMPP framework. Of those proposed here, a model with a fixed transition rate is shown to be superior over the other MMPP models considered. The model is expanded to include covariate data for sea-level air pressure, relative humidity, and temperature using reanalysis data over 14 years from the coordinates covering the Bracknell rainfall collection site in England. Results are compared using the likelihood ratio test and the second-order properties of aggregated rainfall.