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

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, 10262-10272, doi:10.1002/jgrd. 50799.

Precipitation Summary Using a gamma distribution for precipitation instead of the normal E-OBS approach Gamma parameters fitted separately for each month using the 1971-2000 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 1971-2000) 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: http://dx.doi.org/10.1175/1520-0442(1990)003<1495:MLEFTG>2.0.CO;2

Gamma Scale Parameter Wilks, Daniel S., 1990: Maximum Likelihood Estimation for the Gamma Distribution Using Data Containing Zeros. J. Climate, 3, 1495–1501. doi: http://dx.doi.org/10.1175/1520-0442(1990)003<1495:MLEFTG>2.0.CO;2

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

RMSE values Seems to highlight stations with possible erroneous data

Comparisons for 1971-2000 averages for January

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