Estimating Rainfall Intensities from Weather Radar Data: The Scale-Dependency Problem

Abstract

Meteorological radar is a remote sensing system that provides rainfall estimations at high spatial and temporal resolutions. The radar-based rainfall intensities (R) are calculated from the observed radar reflectivities (Z). Often, rain gauge rainfall observations are used in combination with the radar data to find the optimal parameters in the Z?R transformation equation. The scale dependency of the power-law Z?R parameters when estimated from radar reflectivity and rain gauge intensity data is explored herein. The multiplicative (a) and exponent (b) parameters are said to be ?scale dependent? if applying the observed and calculated rainfall intensities to objective function at different scale results in different ?optimal? parameters. Radar and gauge data were analyzed from convective storms over a midsize, semiarid, and well-equipped watershed. Using the root-mean-square difference (rmsd) objective function, a significant scale dependency was observed. Increased time- and space scales resulted in a considerable increase of the a parameter and decrease of the b parameter. Two sources of uncertainties related to scale dependency were examined: 1) observational uncertainties, which were studied both experimentally and with simplified models that allow representation of observation errors; and 2) model uncertainties. It was found that observational errors are mainly (but not only) associated with positive bias of the b parameter that is reduced with integration, at least for small scales. Model errors also result in scale dependency, but the trend is less systematic, as in the case of observational errors. It is concluded that identification of optimal scale for Z?R relationship determination requires further knowledge of reflectivity and rain-intensity error structure.