Nonlinear estimation of spatial distribution of rainfall — An indicator cokriging approach

Abstract

Indicator cokriging (Journel 1983) is examined as a tool for real-time estimation of rainfall from rain gage measurements. The approach proposed in this work obviates real-time estimation of real-time statistics of rainfall by using ensemble or climatological statistics exclusively, and reduces computational requirements attendant to indicator cokriging by employing only a few auxiliary cutoffs in estimation of conditional probabilities. Due to unavailability of suitable rain gage measurements, hourly radar rain fall data were used for both indicator covariance estimation and a comparative evaluation. Preliminary results suggest that the indicator cokriging approach is clearly superior to its ordinary kriging counterpart, whereas the indicator kriging approach is not. The improvement is most significant in estimation of light rainfall, but drops off significantly for heavy rainfall. The lack of predictability in spatial estimation of heavy rainfall is borne out in the integral scale of indicator correlation: peaking to its maximum for cutoffs near the median, indicator correlation scale becomes increasingly smaller for larger cutoffs of rainfall depth. A derived-distribution analysis, based on the assumption that radar rainfall is a linear sum of ground-truth and a random error, suggests that, at low cutoffs, indicator correlation scale of ground-truth can significantly differ from that of radar rainfall, and points toward inclusion of rainfall intermittency, for example, within the framework proposed in this work.