Comparing Approaches to Deal with Non-Gaussianity of Rainfall Data in Kriging-Based Radar-Gauge Rainfall Merging

Merging radar and rain gauge rainfall data is a technique used to improve the quality of spatial rainfall estimates and in particular the use of Kriging with External Drift (KED) is a very effective radar-rain gauge rainfall merging technique. However, kriging interpolations assume Gaussianity of the process. Rainfall has a strongly skewed, positive, probability distribution, characterized by a discontinuity due to intermittency. In KED rainfall residuals are used, implicitly calculated as the difference between rain gauge data and a linear function of the radar estimates. Rainfall residuals are non-Gaussian as well. The aim of this work is to evaluate the impact of applying KED to non-Gaussian rainfall residuals, and to assess the best techniques to improve Gaussianity. We compare Box-Cox transformations with λ parameters equal to 0.5, 0.25, and 0.1, Box-Cox with time-variant optimization of λ, normal score transformation, and a singularity analysis technique. The results suggest that Box-Cox with λ = 0.1 and the singularity analysis is not suitable for KED. Normal score transformation and Box-Cox with optimized λ, or λ = 0.25 produce satisfactory results in terms of Gaussianity of the residuals, probability distribution of the merged rainfall products, and rainfall estimate quality, when validated through cross-validation. However, it is observed that Box-Cox transformations are strongly dependent on the temporal and spatial variability of rainfall and on the units used for the rainfall intensity. Overall, applying transformations results in a quantitative improvement of the rainfall estimates only if the correct transformations for the specific data set are used.