Nonlinear Modeling of Radar-Rainfall Errors at Different Time Scales

There are large uncertainties associated with operational precipitation estimates produced by U.S. national network of WSR-88D radars. These errors are due to the measurement, sampling, and estimation aspects of the observational process. A quantitative description of radar-rainfall errors need to be empirically based and have the flexibility to account for different spatio-temporal scales, synoptic conditions and radar range effects. To describe the relation between true rainfall (RA) and radar-rainfall (RR), the authors developed a model characterized by two elements: a deterministic distortion function and a random component, which represents all the sources of uncertainty. The former can be modeled by a power law function, while the standard deviation of the latter by a hyperbolic function. For the temporal and spatial correlation of the random component, the authors have used a three-parameter exponential function. The fitting of these nonlinear expressions has been accomplished using a two-step methodology. First, a global grid search of the parameter space is performed. Then, the results are used as initial values for the Levenberg-Marquardt algorithm. In this study, the authors considered different time scales and investigated if any of the model components present scale-invariance properties. These results are based on a six-year sample of Level II data from the Oklahoma City WSR-88D radar site (KTLX) and processed through Build 4 of the Open Radar Product Generator Precipitation Processing System (PPS) that mimics NEXRAD algorithms. Although the RA values are unknown, they have been approximated with rain gauge observations from the Oklahoma Mesonet and Agricultural Research Service Micronet. The authors provide estimates of the magnitude of this approximation based on data obtained from a super-dense rain gauge network known as Oklahoma Piconet.