Empirical Distribution of Conditional Errors in Radar Rainfall Products

Abstract

Efficient quantification of conditional errors in radar rainfall (RR) products requires a realistic model of random error distribution. Nonparametric estimate of the probability density function (pdf) of standardized RR errors is obtained using a large data sample. The standardization is based on a second-order separation of systematic and random effects. The estimated empirical distribution is skewed and has exponential shapes of its tails with two different scales. It cannot be modeled with the Gaussian law that was used in several previous studies. A good representation of the tails of the empirical distribution of RR errors is obtained with a three-parameter modified Laplace model with a shift and unequal slopes of its two sides. Plain Language Summary Reliable measurement of rainfall is important for hydrology, water management, agriculture, and other users. It is a challenging task because rainfall is highly variable and networks of rain gauges are too sparse to capture this variability. Thus, rainfall estimates based on weather radars are becoming indispensable because they provide continuous coverage of the area up to about 100 km around the radars. However, they are ridden by many uncertainties that must be known in order to avoid dangerous mistakes in all applications of the estimates. In this paper, we contribute an important new piece to this knowledge-the empirically based information about the frequency of occurrence of different magnitudes of the errors that is called the error probability distribution. It allows to evaluate their impact on different applications of radar rainfall. It also enables more reliable comparisons of different rainfall estimation methods in order to monitor progress in this area. The new information was obtained by applying a new mathematical modeling method to a large sample of radar rainfall estimates combined with rain gauge measurements of true rainfall. Many previous applications assumed that radar rainfall errors were distributed according to the commonly used bell curve called normal distribution. Our results show that the actual error distribution differs considerably from normality and that using the normal model leads to misrepresentation of the uncertainties. We now have the strongly supported mathematical tool to treat them in a much more realistic way.