Spatio-Temporal Modeling of Rain Rates

Abstract

Modeling episodes of heavy rain is an important component of hydrological studies. Based on the analysis of ship-borne radar data over the tropical ocean, we propose a new class of probability densities that capture the frequency of heavy rain occurrences. This density is constructed by inverting the characteristic function constructed from the moments computed at both integral and fractional orders, for all spatial scales. We demonstrate an improvement over the conventional log-normal distribution at explaining the behavior of intense rain events, and successfully explain the multiscaling characteristics of the rain field. An important assumption in the analysis of space-time characteristics of rain fields is isotropy and homogeneity. We test the equality of spectral densities at multiple locations in a non-parametric setting using the data periodograms. The efficacy of our methodology is demonstrated through simulation, and the theoretical properties of the proposed test statistic are examined. We establish the fact that the test asymptotically maintains the desired level of significance and is consistent at any alternative, and apply our methodology to real life rain rate data set taken from a network of rain gauges in Melbourne, South Florida. This research was supported by a NASA grant under the Precipitations Measurement Missions (PMM) program.