Presenting uncertainty in sea surface temperature fields through the use of an ensemble

1. Presenting uncertainty in sea surface temperature fields through the use of an ensemble Nick Rayner and John Kennedy, ERA-CLIM workshop on observation errors, Vienna, April 19-20th 2012.

2. Sources of uncertainty in gridded SST analyses • Random measurement error, uncorrelated from measurement to measurement • Grid box sampling uncertainty, uncorrelated between grid boxes (J.J. Kennedy et al, 2011, pt1, JGR) • Macro-bias adjustment uncertainty, correlated between grid boxes and in time (J.J. Kennedy et al, 2011, pt2, JGR). More on this later. • Residual micro-biases correlated between grid boxes and in time (in the analysis, we assume these are correlated within grid boxes, but not between grid boxes) • Uncertainty in the reconstruction/analysis. More on this later.

3. Why a best estimate + error bar might not be the best approach • The mean or “best estimate” might not be a representative or physically realisable state of the system • Our solution is to representuncertainties using ensembles • Multiple versions of the data withdifferent choices made when constructing the dataset • Spread of the ensemble membersrepresents underlying uncertainty • Very easy to use

4. ? Structural uncertainty Parametric uncertainty Analysis uncertainty E.g. EOF weights. E.g. bias adjustment method. E.g. biases adjustment; number of EOFs; length scales.

5. Parametric uncertainty – twiddling the knobs • Step 2 – set the parameters required by our method • The values are uncertain – no best choice • Vary parameters to understand what range of outcomes is possible • Here, this is explored for the derivation of bias adjustments for SST measured in situ

6. Parametric uncertainty Contribution (fraction) of each measurement method (ERI = Engine Room Intake) Monthly bias corrections from 100 realisations Kennedy et al., 2011, JGR, 116

7. ? Structural uncertainty Parametric uncertainty Analysis uncertainty E.g. EOF weights. E.g. bias adjustment method. E.g. biases adjustment; number of EOFs; length scales.

8. Reconstruction uncertainty • Step 3: explore uncertainties of the HadISST2 reconstructions. EOFs • Empirical orthogonal function (EOF) based reconstruction • EOF weights have defined probability distribution conditional upon the data • EOF patterns are spatially correlated → uncertainty spatially correlated

9. HadISST2 (preliminary version): ensemble captures spatial correlations in the uncertainties SST anomaly (°C relative to 61-90)

10. HadISST2 (preliminary version): ensemble captures spatial correlations in the uncertainties SST anomaly (°C relative to 61-90)

11. HadISST2 (preliminary version): ensemble captures spatial correlations in the uncertainties SST anomaly (°C relative to 61-90)

12. HadISST2 (preliminary version): ensemble captures spatial correlations in the uncertainties SST anomaly (°C relative to 61-90)

13. HadISST2 (preliminary version): ensemble captures spatial correlations in the uncertainties SST anomaly (°C relative to 61-90)

14. HadISST2 (preliminary version): ensemble captures spatial correlations in the uncertainties SST anomaly (°C relative to 61-90)

15. HadISST2 (preliminary version): ensemble captures spatial correlations in the uncertainties SST anomaly (°C relative to 61-90)

16. HadISST2 (preliminary version): ensemble captures spatial correlations in the uncertainties SST anomaly (°C relative to 61-90)

17. HadISST2 (preliminary version): ensemble captures spatial correlations in the uncertainties SST anomaly (°C relative to 61-90)

18. HadISST2 (preliminary version): ensemble captures spatial correlations in the uncertainties SST anomaly (°C relative to 61-90)

19. Summary • Uncertainties in SST analyses have complicated correlation structure • So, it can be difficult to communicate them in a simple, usable way • Ensembles provide a way to try to do this

20. Questions and answers