Radar surface rainfall estimates using a typical shape function approach to correct for the variations in the vertical profile of reflectivity

Abstract

A new approach is presented to the problem of correcting radar estimates of surface rainfall for errors resulting from the changes in reflectivity between the surface and the height at which the radar measures reflectivity. In this approach, a set of five typical shape functions (TSF) of a sample of 89 000 vertical profiles was found. These vertical profiles were formed from volumes scan information, interpolated onto 10 levels, at 250 m spacing, with level 6 being set to the height of the top of the bright band. The TSF class for each vertical profile was determined from a limited set of observations of reflectivity aloft using Bayesian discriminant functions. Regression equations were developed for each TSF class to estimate the lowest interpolated level reflectivity (level 1) from these observations aloft. Application of the discriminant functions shows that the 62% of the dependent sample could be correctly classified into its TSF class for data at heights greater than 500 m below the bright band. In four of the five TSF classes, there was significant skill in estimating the surface reflectivity, explaining 80% of the variation of the level 1 reflectivity. The fifth class explained 49% of the level 1 variation. On average, using this approach of determining the TSF for each vertical profile rather than using a single profile for each volume scan increased the variation of the surface reflectivity explained by observations aloft from 59.5% to 77.4%. Information on the skill of estimating the surface reflectivity was also produced, using the posterior probability and the explained variance of the regression equations.