Modeling Radar Rainfall Estimation Uncertainties: Random Error Model

Precipitation is a major input in hydrological models. Radar rainfall data compared with rain gauge measurements provide higher spatial and temporal resolutions. However, radar data obtained form reflectivity patterns are subject to various errors such as errors in reflectivity-rainfall (Z-R) relationships, variation in vertical profile of reflectivity, and spatial and temporal sampling among others. Characterization of such uncertainties in radar data and their effects on hydrologic simulations is a challenging issue. The superposition of random error of different sources is one of the main factors in uncertainty of radar estimates. One way to express these uncertainties is to stochastically generate random error fields and impose them on radar measurements in order to obtain an ensemble of radar rainfall estimates. In the present study, radar uncertainty is included in the Z-R relationship whereby radar estimates are perturbed with two error components: purely random error and an error component that is proportional to the magnitude of rainfall rates. Parameters of the model are estimated using the maximum likelihood method in order to account for heteroscedasticity in radar rainfall error estimates. An example implementation of this approached is presented to demonstrate the model performance. The results confirm that the model performs reasonably well in generating an ensemble of radar rainfall fields with similar stochastic characteristics and correlation structure to that of unperturbed radar estimates.