1. Gridding Daily Climate Variables for use in ENSEMBLES Malcolm Haylock, Climatic Research Unit Nynke Hofstra, Mark New, Phil Jones

2. Overview Applications → Scale Stochastic or Deterministic Methods Determining the best method Data preprocessing Uncertainty

3. Applications Daily P, Tmin, Tmax, SLP, Snow -Precipitation only for now Validation of RCMs -What is the true scale of RCMs? -Need to create gridded observations that are area average Analysis of past changes

4. Stochastic or Deterministic Stochastic -obs(x) = z(x) + ε(x) -assume that observed station data are only one of many possible “realisations” that could have occurred. -Interpolate using inter-station covariance. spatial and temporal -generally don’t reproduce observations (inexact interpolation). Deterministic -obs(x) = z(x) -assume that observed station data are the only possible realisation. -exact interpolation

5. Why Stochastic? Variation at the local scale can not be determined using available station network Variogram =E(z(x)-z(x 1 )] (normalised)

6. Methods Kriging Thin plate splines (Reduced Space) Optimum Interpolation Angular Distance Weighting Conditional Interpolation

7. Kriging Highly developed stochastic method used extensively in the geosciences. obs(x) = z(x) + ε(x), z(x) is an autocorrelated random field calculated as a linear weighted average of surrounding stations. Weights determined by statistically modeling the regional variation by fitting an appropriate function to the variogram. Variations to handle anisotropy (spatial covariance dependent on orientation), large scale trends and other common problems. Statistical model may be different for each day.

8. Anisotropy

9. Thin Plate Splines Stochastic method that fits a surface to the data using smooth functions of the station separation distance Can be considered as a special case of Kriging with a particular class of covariance functions, however these functions are rarely used in Kriging. Contains a smoothing parameter which is usually set by cross validation. Implicit error estimation by cross validation.

10. Optimum Interpolation Stochastic model developed for data assimilation Accounts for both spatial and temporal autocorrelation -unlike traditional Kriging and Splines which only use spatial. -is temporal autocorrelation appropriate for precip.? Assumes Gaussian covariance error distribution -one of several models possible in Kriging. Reduced Space version uses EOFs to greatly speed calculation and limit dependence on small scale variation. -appropriate for daily precip?

11. Angular Distance Weighting Interpolation of anomalies Weight based on distance and angle Stations closest to grid points have greater weight Stations with biggest mean angle have greater weight Elevation not included E.g. New et al. 2000, CRU dataset j k l θ Grid point Station dist

12. Conditional Interpolation So far only interpolation of precipitation Interpolation is conditional on synoptic state Synoptic state defined with Self Organising Maps Interpolation in two steps -Wet or dry target location -If wet: interpolation of magnitude Weights regard distance, radial distribution and synoptic state Calculation of area mean Hewitson and Crane 2005

13. Selecting the best method(s) Cross validation -for all stations, remove the station then calculate predicted value and evaluate appropriate error statistic (e.g. RMS). -Assumes predicted value is a point value, but stochastic methods give the expected value and so hopefully the smallest average error. Can test models using a region with high station density by omitting stations and comparing with true are average.

14. Data Preprocessing Stochastic methods require Gaussian- distributed data Obtain consistency across region by interpolating anomaly from monthly mean (T, SLP) or % of monthly total (P). Interpolated results can be applied to previously gridded monthly data that utilise many more stations.

15. Rainfall Skewness daily/month dry days removed

16. Uncertainty Measurement error Homogeneity error Interpolation error -method use many methods or best method -statistical model within method choose best model but still a generalisation -station network cross validation