The Categorisation of Rainfall

Abstract

There are two mechanisms by which episodes of precipitation are generated, namely, that for rain and that for showers. At any one time and place only one, or neither, of these can be operating and, whichever one it is, it will persist for some time compared to the time scale of variations of rain rate within the episodes. The variations of rate are captured by the breakpoint representation of rainfall in which the times when one steady rate switches to another are recorded together with the rates themselves which will, of course, be zero in dry periods The longer dry periods during which the probability of rain is zero delineate rainfall events during which, even though there are dry intervals, the probability of rain is positive. These events consist of episodes which are defined by the operating mechanism. However, the data available consist only of rain rates and durations and there is no explicit information attached to each data point regarding the mechanism that was operating at that point. Any such information is implicit in the variation of rates and period lengths which differs between rain and showers with the latter, in general, being shorter and heavier than rain. The model adopted was that the breakpoint dataset derives from a mixture of the mechanisms and the EM algorithm and a discriminant analysis were used to attach a mechanism label to each data point. The most difficult problem encountered with the data involved the distinction between low intensity and zero rainfall in short periods. This was circumvented by developing versions of the EM algorithm which could be used with a truncated dataset where the lower rate data were removed. These versions of the EM algorithm proved to be as powerful at the original one with tight confidence intervals around parameter estimates and little prior knowledge of the parameter values being required even though the algorithm is an iterative one which requires initial values. Thus the statistics relating to the precipitation mechanisms were solidly established. However, in general, there were large overlaps in the ranges of data that could be attributed to each mechanism and, consequently, the discriminant analysis contained many misclassifications. These could be rectified to a certain extent by using the persistence of the mechanisms but better results are expected by replacing the static mixture model by a dynamic hidden Markov model.