Combining Rain Gages With Satellite Measurements for Optimal Estimates of Area‐Time Averaged Rain Rates

摘要

The problem of optimally combining data from an array of point rain gages with those from a low Earth‐orbiting satellite to obtain space‐time averaged rain rates is considered. The mean square error due to sampling gaps in space‐time can be expressed as an integral of a filter multiplied by the space‐time spectral density of the rain rate field. It is shown that for large numbers of gages or large numbers of overpasses the two estimates can be regarded as orthogonal in the sense that the optimal weighting is the same as for independent estimators, i.e., the weights are inversely proportional to the error variances that would occur in the single‐component case. The result involving point gages and satellite overpasses appears to hold under quite general conditions. The result is interesting since most other design combinations do not exhibit the orthogonality