Quantifying the Variability of Rain Over Areas: Implications for Validation Experiments

In previous work it was found that over a small network of disdrometers, the variability of probability size distributions (PSD) expressed using the relative dispersions RD increased with the expansion of the network size. The explanation is that the network acts to integrate the Fourier transform of the spatial correlation function from the highest towards lower frequencies as the network size increases so that the contributions to the variance also increases. Consequently, RDand, hence, PSD variability grows as the size of the area increases. The limits to this growth, however, were not determined.

This finding is given fuller quantitative meaning over much larger dimensions by explicitly deriving the variance contributions at all the different drop sizes as well as for a variety of moments of the PSD by estimating the spatial radial correlation functions from transformations of temporal correlations.

The relative dispersion of the PSD is dominated by fluctuations in the occurrences of the larger drops. The RDs of the raw moments are only a few percent of the PSD. Thus, approaches attempting to estimate radial correlation functions using, say, radar measurements of moments are of limited utility, a usefulness further compromised by the distortion of the correlation function by filtering over the beam dimension. Ground-truth experiments trying to validate remote sensing observations, therefore, contain an inherent conflict because one is then trying to compare high pass filter measurements to low pass filter observations, each looking at somewhat different parts of the variance spectrum. In contrast to infinite samples, for any normal finite sample size, this is likely to lead to differences between the two mean values because of statistical fluctuations. (This is easy to understand by comparing the running average of a curve to the values of the curve itself.) Consequently, incompatibilities and inconsistencies can arise and ironically, the remote sensing measurements can become a test of the network values rather than the other way