Modeling distribution of temporal sampling errors in area-time-averaged rainfall estimates

In this paper, the authors examine models of probability distributions for sampling error in rainfall estimates obtained from discrete satellite sampling in time based on 5 years of 15-min radar rainfall data in the central United States. The sampling errors considered include all combinations of 3, 6, 12, or 24 h sampling of rainfall over 32, 64, 128, 256, or 512 km square domains, and 1, 5, or 30 day rainfall accumulations. Results of this study reveal that the sampling error distribution depends strongly on the rain rate; hence the conditional distribution of sampling error is more informative than its marginal distribution. The distribution of sampling error conditional on rain rate is strongly affected by the sampling interval. At sampling intervals of 3 or 6 h, the logistic distribution appears to fit the conditional sampling error quite well, while the shifted-gamma, shifted-weibull, shifted-lognormal, and normal distributions fit poorly. At sampling intervals of 12 or 24 h, the shifted-gamma, shifted-weibull, or shifted-lognormal distribution fit the conditional sampling error better than the logistics or normal distribution. These results are vital to understanding the accuracy of satellite rainfall products, for performing validation assessment of these products, and for analyzing the effects of rainfall-related errors in hydrological models.