Comparing the satellite rainfall estimates with rain gauge data: Optimal stategies suggested by a spectral model

Abstract

The statistical problem of comparing rain gauge measurements to satellite rain-rate estimates over an area surrounding the gauge(s) is examined using a model of rainfall variability developed for studies of sampling error in averages of satellite data. The model is able to capture a number of important aspects of the space-time spectrum of rain-rate variability, including the interdependence of time and space scales of variability. Four parameters must be specified in the model. Sets of parameters have been obtained that fit the statistics of radar-derived rain rates over the eastern tropical Atlantic (from GATE) and the western tropical Pacific (from TOGA COARE). The model predicts that there is an optimal averaging time for gauge data when gauge averages are compared to average satellite rain-rates for a specified area around the gauge. The optimal averaging time ranges from minutes to days as the diameter of the area around the gauge is extended from 2 km to 200 km. The optimal averaging time shrinks as more gauges are added to the area viewed by the satellite, but the model suggests that even over fairly dense gauge networks it is necessary to compare averages of several hundred satellite overflights in order to bring the comparison error down to the 10% level. The possibility that comparisons of gauge data with satellite averages might be improved by weighting the gauge data differently depending on how close the gauge data are in time to the satellite overflights is investigated, and it is found that in some cases the variance of the comparison error can be reduced by a factor of two by using optimal time-dependent weighting.