Radar rainfall estimation as an optimal prediction problem

A formulation of the radar rainfall estimation problem as optimal statistical prediction of area-averaged rainfall accumulations based on the radar measured reflectivity is presented. Questions of the estimation and validation of such optimal prediction procedures based on large samples of synchronous radar and raingage measurement are analyzed. Our approach accepts the truth that radar cannot mimic the near-point raingage sampling and that proper quantification of the area-point difference is necessary. The questions and consequences which originate from our formulation of the radar rainfall estimation/validation problem are formalized statistically and investigated using both statistical modeling and data analysis.;A general definition of the error of the radar rainfall predictions in terms of bivariate probability distributions of the radar and true rainfalls is discussed. The raingage representativeness error structure is analyzed based on the available data. An analytically tractable statistical model of the radar-raingage comparisons is developed. It shows the large impact of the estimation method on the resulting reflectivity-rainrate conversion and the incompleteness of the system due to the radar and raingage errors. These effects prove the need of additional data on the raingage area-point difference structure. Next, an Error Separation Method for the error variance estimation of the radar rainfall predictions is developed. This method is based on additional data on the rainfield small scale correlation structure. Finally, a global optimization approach to the multiparameter radar rainfall prediction is developed. The prediction algorithm is designed to minimize the error variance of the final radar rainfall product. The general radar rainfall estimation/validation methodologies developed here can also be applied to other remote sensing rainfall estimation problems. The work is concluded with a summary discussion of the obtained results and of the research directions that might stem from those results.