Real data experiments show that, for large areas, the area average rain rate and the fraction of the area covered by rain rate above a fixed threshold are highly correlated. For the right choice of the threshold level the correlation can easily exceed 95% and may even reach 99%. This remarkable fact observed in nature is the basis for the so-called threshold method for measuring rainfall from space via satellite. The method depends critically on the threshold level, showing significant improvement in performance for optimal and nearly optimal thresholds. Under the assumption that the continuous part of the distribution of rain rate is lognormal, two theoretically derived optimal levels agree closely with the best level obtained empirically from a well-known data set of rain rate.
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Kedem et al. (1991) studied this question.
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