Compatibility of Continuous Rainfall Occurrence Models With Discrete Rainfall Observations

Inferences about the underlying rainfall generating mechanism made through a model fitted to the sampled rainfall series at a particular time scale are meaningful only if they are invariant under the time scale of measurement at which the fitting of the model is made. Following the work of I. Rodriguez‐Iturbe et al. (1984), this assertion is tested by examining the compatibility of the Neyman‐Scott (N‐S) model for the continuous underlying rainfall with sampled realizations taken over intervals ranging from one hour to one day. The results suggest that the N‐S model is inconsistent at different time scales, and therefore mathematical descriptions of rainfall using this model are inevitably limited to the time scale of measurement at which a description of rainfall is sought. These findings are quite general, in that they apply to any model with rainfall deposited instantaneously at times described by a N‐S process, regardless of how the amounts associated with the events are distributed, and of the dependence structure of the amounts.