Sampling properties of parameter estimators for a storm field rainfall model

A statistical model of rainfall fields has been developed. The model parameters can be estimated from radar and rain gage data. The radar data are used only to estimate the spatial features of the model. The rain gage data are used to estimate the magnitude of rainfall. The parameter estimators are based on the method of moments and are shown to be consistent and asymptotically normal. To investigate the small sample properties of the estimators a Monte Carlo simulation experiment has been conducted. The results indicate that for certain combinations of the true rainfall field parameters the estimation procedure leads to biased results. The model has an attractive feature in that a simple statistic can be precomputed which indicates the feasibility of the model to represent a given rainfall data set. In case the statistic indicates infeasibility of the model it is difficult to distinguish whether the proposed model is not appropriate or the data sample is too small.