The Window Probability Matching Method for Rainfall Measurements with Radar

Abstract

A simplified probability matching method is introduced that relies on matching the unconditional probabilities of R and Ze, using data from a C-band radar and raingage network near Darwin, Australia. This is achieved by matching raingage intensifies to radar reflectivities taken only from small ?windows? centered about the gauges in time and space. The windows must be small enough for the gauge to represent the rainfall depth within the radar window yet large enough to encompass the tinting and geometrical errors inherent to such coincident observations. The calculation of the Ze ? R relation with the window probability marching method (WPMM) is quite straightforward, whereby the unconditional cumulative probabilities of Ze, and R, which are obtained from all of the windows, are matched. In practice Ze and R, having the same cumulative percentile, are related to each other. A relatively small sample size (about 600 mm for all gauges combined) is required to achieve a stable Ze ? R relation with a standard deviation of 15% of R for a given Ze. The obtained Ze ? R relations are curved lines in log-log space and therefore may better represent the transformation of Ze into R than any straight-line power law. The WPMM also performs significantly better for rainfall integrations than power law. The standard deviation of the WPMM rainfall integration, after correction for systematic bias errors, is only two-thirds that of the standard deviation obtained when using a power law based on disdrometer measured drop size distribution. Additional improvement in the accuracy of the WPMM is provided upon its application to data that has been objectively clarified into different rain regimes, which is the topic of another related study in this journal.