Mesoscale spatial variation of rainfall through a hidden semi-Markov model of breakpoint data

Abstract

Spatially, rainfall is very variable, and a common problem is that for a particular point of interest no observations are available. So a spatial model is required to provide suitable estimates at such points. The problem is further compounded by the many questions that can be asked regarding rainfall, with each question generally needing a particular spatial model for a particular data type. The approach here is through a temporal model of high temporal resolution rain rate data such that the spatial variability of rainfall is then, in part, that of the parameters of the model. Other aspects entailing contemporary differences in rainfall from point to point are not dealt with; only those based on long-term point statistics are considered. The breakpoint format of rainfall data, which records the rain rate and the times when it changes, implicitly provides high temporal resolution rainfall information in a highly compressed form. A Markov model was chosen so that its states could be aligned with the different physical processes that occur in the atmosphere and are associated with rainfall. However, the data consist only of rain rates and durations with no labels indicating the prevailing process for each datum; thus the states in the model are "hidden." The model was fitted to data from 20 locations in central New Zealand, and its parameters were then mapped using a thin-plate smoothing spline and verified through simulations of artificial breakpoint data sets and the subsequent extraction of a few statistics for which independent spatial variations were available. Thus, through similar simulations at any arbitrary point a set of model parameters is available, and many rainfall questions can be answered. The model, being physically based, also provides some insights into rainfall processes.