Flexible spatial interpolation and uncertainty quantification : with applications in radar rainfall estimation.

In quantitative precipitation estimation, prediction and uncertainty quantification are difficult due to the errors in the available data sources. Weather radars are used to predict precipitation with high spatial and temporal resolution, but do not measure ground level rainfall intensity, which is the quantity of interest. To account for the error resulting from the use of a proxy variable, predictions are calibrated to ground level measurements of the rainfall intensity rate with spatial prediction methods. For prediction at a specific location, kriging is a simple and popular spatial prediction method, but suffers from several shortcomings. In particular, prediction is quite unstable and fails when sample sizes are small and the error normality assumption necessary for uncertainty quantification with kriging predictors may not hold in real data sets. In this dissertation, we propose two fexible and efficient deterministic spatial predictors, with several advantages over kriging. We then further propose a robust data fusion uncertainty quantification scheme to produce gridded prediction output with stochastic errors. These methods are illustrated with radar rainfall data.