Comparing Approaches to Deal With Non‐Gaussianity of Rainfall Data in Kriging‐Based Radar‐Gauge Rainfall Merging

Abstract

Abstract 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.