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.
| Original language | English |
|---|---|
| Pages (from-to) | 8999-9018 |
| Number of pages | 20 |
| Journal | Water Resources Research |
| Volume | 53 |
| Issue number | 11 |
| Early online date | 16 Oct 2017 |
| DOIs | |
| Publication status | Published - 1 Nov 2017 |
Funding
This work was carried out in the framework of the Marie Skłodowska Curie Initial Training Network QUICS. The QUICS project has received funding from the European Union’s Seventh Framework Programme for research, technological development, and demonstration under grant 607000. M. A. Rico-Ramirez also acknowledges the support of the Engineering and Physical Sciences Research Council (EPSRC) via grant EP/ I012222/1. The authors would like to thank the UK Met Office and the Environment Agency (environment- agency.gov.uk), which provided the radar rainfall data and the rain gauge data to develop this study. The rain gauge data can be requested at national.requests@environment- agency.gov.uk and the radar data can be downloaded through the British Atmospheric Data Centre (badc.nerc. ac.uk; Met Office, 2003). We are also thankful to Andreas Scheidegger and Jo€rg Rieckermann, from EAWAG, and Antonio M. Moreno Rodenás and Henry Badger, from TU Delft, for providing technical and scientific feedback. We also thank the reviewers for providing insightful comments that helped to improve the manuscript.
Keywords
- Box-Cox
- Gaussian transformations
- kriging with external drift
- normal score transformation
- radar-rain gauge merging
- singularity analysis
ASJC Scopus subject areas
- Water Science and Technology