A parsimonious and efficient statistical method to correct large scale precipitation products: Empirical Conditional Probability (ECP)method

Satellite-based precipitation products show significant bias with respect to ground-based data which prevents their use in several geophysical applications. In this study, we developed a method, the “Empirical Conditional Probability (ECP) method”, to augment the information of remotely sensed precipitation products using ground-based observation. The method relaxes the assumption of Gaussianity typical of many statistical processors which is a strong limitation specifically for the heavily skewed and intermittent daily precipitation signal leading to problems such as extrapolation to extreme values. We proposed a non-parametric and parsimonious approach to optimally merge the satellite and ground-based data.

The performance of our developed method is investigated in different experiments using the Climate Hazards Group InfraRed Precipitation with Station data (CHIRPS) precipitation product. Rain gauges are assumed as a priori information (predictors) about the true precipitation and is used to provide its posterior probabilistic estimation by our proposed empirical conditional probability approach. We compare our method with the classical Quantile mapping (QM) correction method to evaluate the added value of our approach.

The analysis was carried out in Aosta Valley, a region located in northern Italy with a dense rain gauge network. The time series was split into two sub-periods: 2008-2021 was used for generating the posterior distribution of precipitation and 2005-2007 was used for the validation of the method. The results demonstrated that the corrected CHIRPS product by our method is superior with respect to the original CHIRPS product and the corrected one with QM during both split periods (i.e., it performs better in terms of KGE, R, NSE, and RMSE). In a second experiment, using the proposed method, the posterior probability distribution of precipitation has been obtained according to the kriged ground-based precipitation data. In this way, instead of having gridded single-value data, a range of expected values is available for each pixel.

The idea of using uncertainty assessment for the satellite data (specifically precipitation) is going toward having cubic uncertainty-conscious satellite products with a range of expected values. Furthermore, since the ECP method is based on ground data, we investigated the sensitivity of the method to the density of rain gauges.