Data Transformation and Uncertainty in Geostatistical Combination of Radar and Rain Gauges

Abstract

eostatistics provides a popular framework for deriving high-resolution quantitative precipitation estimates (QPE) by combining radar and rain gauge data. However, the skewed and heteroscedastic nature of precipitation is in contradiction to assumptions of classical geostatistics. This study examines the potential of trans-Gaussian kriging to overcome this contradiction. Combination experiments are undertaken with kriging with external drift (KED) using several settings of the Box?Cox transformation. Hourly precipitation data in Switzerland for the year 2008 serve as test bed to compare KED with and without transformation. The impact of transformation is examined with regard to compliance with model assumptions, accuracy of the point estimate, and reliability of the probabilistic estimate. Data transformation improves the compliance with model assumptions, but some level of contradiction remains in situations with many dry gauges. Very similar point estimates are found for KED with untransformed and appropriately transformed data. However, care is needed to avoid excessive transformation (close to log) because this can introduce a positive bias. Strong benefits from transformation are found for the probabilistic estimate, which is rendered positively skewed, sensitive to precipitation amount, and quantitatively more reliable. Without transformation, 44% of all precipitation observations larger than 5 mm h?1 are considered as extremely unlikely by the probabilistic estimate in the test application. Transformation reduces this rate to 4%. Although transformation cannot fully remedy the complications for geostatistics in radar?gauge combination, it seems a useful procedure if realistic and reliable estimation uncertainties are desired, such as for the stochastic simulation of QPE ensembles.