Probabilistic Approaches to Gridding Phil Jones CRU, UEA, Norwich, UK

Summary Brief summary of ensemble concept with HadCRUT4 Issues with the application to E-OBS Differences between temperatures and precipitation Will users be able to deal with multiple realizations? Producing regional series from the E-OBS grid Thanks to Richard Cornes (now at KNMI) for discussions

HadCRUT4 and CRUTEM4/HadSST3 Traditional way of assessing accuracy of estimates – more stations reduces errors; stations have decay distance If extrapolation goes too far, the variance in the grid reduces Infilling can’t put in extreme values, so it also reduces variance (impacts those looking at changes in extremes) Errors come from homogeneity adjustments, missing data and numbers of stations per region Separated in HadCRUT4 as measurement and grid-box sampling errors, but differently expressed in the land and marine components Land stations are fixed, so error components simpler to follow (Brohan et al., 2006; Morice et al., 2012) Marine observations have spatial and temporal structure (e.g. good/poor ships sailing the seas, Kennedy 2014) The different aspects of the error are best dealt with by creating multiple realizations, sampling possible values of the various components HadCRUT4 has 100 realizations for each grid box and also each NH or SH average. If you just want one you get, the 50th percentile. The weighted average of the 50th percentile grid box values doesn’t equal the median NH or SH A structure is there to calculate a regional average and also its error Reanalyses have different simulations (the 56 members of 20CR, or the 10 for ERA-20C)

Comparison of CRUTEM4 with papers by Callendar (1938, 1961) Includes the error estimate ranges for CRUTEM4 developed by Morice et al (2012) Hawkins, E. and Jones, P.D., 2013: On increasing global temperatures: 75 years after Callendar. Q. J. Royal Meteorol. Soc., 139, 1961-1963, DOI:10.1002/qj.2178. Callendar additionally discussed his assessment of early CO2 measurements – shown to be right by later ice cores

Robustness of the global temperature record Removal of all stations in the contiguous United States Based on CRUTEM4

Global Temperature series wrt 1951-80. US plot in °F! Jones, P.D., 2016: The Reliability of Global and Hemispheric Surface Temperature Records. Advances in Atmospheric Sciences 33, 269-282, doi:10.1007/s00376-015-5194-4.

Aim with E-OBS (Temperature) Apply consistently to temperature (Tx, Tn and Tave) Errors consistent between timescales, so smaller errors for monthly as opposed to daily data E-OBS creates monthly grids (with errors) using anomalies from a climatology (splines) If a monthly grid has a small error, due to many stations, the daily errors also need to be small Potential to use more widely available monthly stations in some parts of Europe. More monthly data as opposed to daily in decades before the 1950s, if an extension to E-OBS is considered Error structure in temperature is simpler to follow Temperature interpolation (splines) is simply undertaken as anomalies (for monthly) and as anomalies from the monthly average (for daily using kriging) Tave needs to be defined as (Tx+Tn)/2, as some countries calculate Tave based on fixed hours/formulae As monthly interpolation is in anomalies, it is possible to use different methods of calculating Tave. This assumes the anomalies of Tave are not impacted by how they are calculated Currently E-OBS grids Tx, Tn and Tave separately, but it could also interpolate DTR. Doing this would stop negative DTR values being created in winter in Northern Europe, but would omit a small number of Tx/Tn values when the other is missing Daily gridding uses anomalies of the day from its monthly mean. Decision required for # missing

Aim with E-OBS (Precipitation) Errors consistent between timescales, so smaller errors for monthly as opposed to daily data E-OBS creates monthly grids (with errors using splines as % of climatology) Daily errors developed from monthly (using kriging). Ideally these ought to add up? Does daily gridding maintain the station rain-day count? Potential to use more widely available monthly stations in some parts of Europe Precipitation error structure leads to a number of issues Precipitation interpolation is currently undertaken as percent anomalies (for monthly) and as percents of the month for daily. Percent anomalies for months emphasizes heavy precipitation months Precipitation interpolation for months appears better undertaken with a transformation (gamma distribution). Errors need to follow through in their transformed state With daily precipitation totals, should errors only be considered for the days with precipitation? If all the stations in a region have zero precipitation on a day, the grid-box average ought to be zero, with zero error?

Interpolation Error versus other errors The earlier plot comparing with Callendar (1938, 1961) indicates that for land, the error bars expand due to sparser coverage earlier in time Urban biases are relatively unimportant at the monthly timescale. Might be large at the daily timescale, but this depends on the circulation type, so difficult to deal with Homogeneity adjustments are undertaken for a few E-OBS stations, but the assumption is made that NMS data are good At the daily timescale, coverage issues will become more important Amelioration can come from improvements at the monthly scale In some regions, even with the 0.5° by 0.5° grid, some stations in dense regions are barely used. Alternate grids can be created by different choices of how many nearest gauges to use Estimates of errors can also be made using a subset of the network and then extrapolating to the infinitely sampled box E-OBS grids are not point estimates, but the 0.5° by 0.5° (and 0.25° by 0.25°) boxes are derived from the 0.1° by 0.1° grids within the larger box Multiple realizations are one of the bet ways of dealing with the various error components

Uncertainty can come from different interpolation approaches At present E-OBS uses one approach, but others could be used These could contribute to the uncertainty, as in less dense areas greater differences will be seen Will users be able to deal with multiple realizations? Simple answer is not without detailed instructions, but many datasets are going this way The approach provides a way of coping with the uncertainty Different approaches for different variables Different uncertainties with different variables Reanalysis groups know how to use an ensemble Need to make the individual ensemble members available, but most will use the 50th percentile as the average/mean

Producing regional averages from the grids As with the Callendar plot, a regional average can be produced from a multiple realization dataset Ensembles enable users to calculate series for their regions and error ranges Error ranges reduce as the domain increases in size Users might download the 0.25° grid and the 0.5° grid and calculate the same regional average. Ideally this ought to produce the same answer and the same error range?

Conclusions Introduced concept of dealing with uncertainty Ensemble approach is the most straight forward approach for dealing with this Statisticians might say that the errors should be derived analytically, but the different timescales and gamma transformations for precipitation make this difficult