Some Statistical Issues Regarding Inter-comparison and Validation of GPM Rain Rate Estimates

We consider two approaches to inter-comparison of satellite and/or ground-based estimates of rain rate: (i) a regression analysis of two data sets, and (ii) examination of suitably defined metrics that quantify the statistical difference between them. For the first approach we demonstrate that a regression of nearly collocated observations necessarily contains a spurious bias caused by the space-time mismatch that is present even if the measurements were perfect and propose a method of reducing this bias. In the context of the second method we show that for perfect measurements some recently considered metrics, such as the normalized bias B(r) and r.m.s. difference E(r) considered as function of the rain rate, can be theoretically modeled if the joint distribution of rain rate at two different times is empirically known. We discuss application of these approaches in the context of the problem of inter-comparison and validation of GPM rain rate estimates.