1. Phil Jones CRU, UEA, Norwich, UK
UERRA-WP1 Improved Interpolation for Temperature and Precipitation Precipitation Interpolation with a Gamma Distribution
Phil Jones
CRU, UEA, Norwich, UK

2. One of the Rationales
Gridded datasets being used to look by a larger group of users, especially at changes in extremes
Gridded datasets affected by issues of changes in station density through time
Ideally looking at extremes shouldn’t matter whether you calculate them from a gridded dataset or from the stations – but it does!
The MS Alpine dataset provides a good test-bed for comparisons, as do some national high-resolution station datasets available from Northern Europe
With higher-resolution datasets, do all the series get used in the grids?
Is the software for say E-Obs optimal? Different gridding approaches for different variables
Calculation of extremes can be improved by taking advantage of nodes or clusters within some computer systems
Cornes, R.C. and Jones, P.D., 2013: How well does ERA-Interim reanalysis replicate trends in extremes of surface temperature across Europe? J. Geophys. Res, 118, , doi: /jgrd

5. Precipitation Summary
Using a gamma distribution for precipitation instead of the normal E-OBS approach
Gamma parameters fitted separately for each month using the period, using MLE from Wilks (1990)
These fits are left censored, so that the number but not the numerical values of trace and zero values are used
Gamma shape and scale parameters then interpolated to the required grid
Interpolation of transformed precipitation amounts
Finally, back transformation of mms using the interpolated amounts and also the interpolated shape and scale parameters using an inverse gamma transformation routine
Some examples of the shape and scale parameters
RMSE values
Comparison for January and July averages (for ) with the normal E-OBS approach. Only using available stations, so E-Obs grids will use more
Interpolation for the maps shown is all done with thin-plate splines
Wilks, Daniel S., 1990: Maximum Likelihood Estimation for the Gamma Distribution Using Data Containing Zeroes. J. Climate, 3, 1495–1501. doi:

6. Gamma Scale Parameter
Wilks, Daniel S., 1990: Maximum Likelihood Estimation for the Gamma Distribution Using Data Containing Zeros. J. Climate, 3, 1495–1501.
doi:

7. Gamma Shape Parameter
Again, missing areas do not have enough precipitation amounts in the base period
Mean precipitation approximately shape*scale

8. RMSE values
Seems to highlight stations with possible erroneous data

9. Comparisons for 1971-2000 averages for January

10. Comparisons for 1971-2000 averages for July
Individual July fields show more localised structure over mountain regions