Approximations of Temporal Rainfall From a Multidimensional Model

The feasibility of representing the temporal structure of a multidimensional rainfall process with simpler stochastic models and a study of the effect of parameter robustness on the time scale is investigated here via performing controlled numerical experiments. A multidimensional representation for precipitation, given in the theory recently proposed by E. Waymire et al. (1984), is used for simulating rainfall in space and time. The model produces moving storms with realistic mesoscale meteorological features, e.g., clustering, birth and death of cells, cell intensity attenuation in time and space, etc. Two‐year traces of rainfall intensities at fixed gage stations were generated at intervals of 0.1 hours for three climates. These traces are then aggregated at different time scales ranging from 1 to 24 hours. First‐ and second‐order statistics are evaluated from the above series at each aggregation level and they are used for estimating the parameters of three one‐dimensional models of temporal rainfall at a point: (1) Poisson model with independent marks, (2) rectangular pulses with independent intensity and duration, and (3) Neyman‐Scott with independent marks. Only at very high levels of aggregation the compound Poisson model was able to reproduce the statistical structure of the simulated traces. The rectangular pulses model was found to have parameters which vary significantly with the time scale of aggregation and moreover, it leads to large distortions in the mean depth and duration of storm events. The Neyman‐Scott scheme proved to be the most stable model throughout the different time scales and it also reproduced quite well the average storm characteristics at the event level. None of these three models was able to reproduce in a satisfactory manner the simulated extreme value distribution of the multidimensional model.