Large-scale spatial variability of rainfall through hidden semi-Markov models of breakpoint data

The breakpoint format for rainfall data records the rain rate and the times when the rain rate changes. A Markov model was chosen so that the 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". A suitable structure for the model was chosen and fitted to breakpoint data sets from widely spaced localities within New Zealand. At all locations, wet and dry states could be put into two groups such that one (i.e., rain) was characterized by longer periods of lighter precipitation with few dry breaks, while the other (i.e., showers) had shorter but generally heavier periods of precipitation with often long dry breaks in between. The large-scale spatial variability of the rainfall climatology was assessed through model statistics with the frequency of events and the amounts-from and durations-of rain, as distinct from showers, being found to be the most variable. Also, usually only one episode of rain and one of showers constituted a precipitation event.