Optimal perturbations and observations for decadal climate predictions Ed Hawkins, Rowan Sutton

1. Optimal perturbations and observations for decadal climate predictions Ed Hawkins, Rowan Sutton THOR annual meeting

2. Motivation – reducing uncertainty CMIP3 projections of UK decadal mean temperature after Hawkins & Sutton, 2009

3. Motivation • Decadal climate predictions are now being made (e.g. THOR CT4) • initialised from ocean state to try and predict the climate response to radiative forcings and internal variability • But, large uncertainties exist in ocean analyses • need to sample this initial condition uncertainty efficiently • need to identify regions where additional observations are most valuable for improving climate predictions • Perturbation methods developed for NWP can be exended and adapted for decadal climate predictions to address these needs

4. Example decadal predictions Atlantic sub-polar gyre heat content June 1995 Predictions from UK Met Office Decadal Prediction System (DePreSys) DePreSys hindcasts Observations June 2001 Jon Robson, Rowan Sutton, Doug Smith

5. Motivation – reliability of hindcasts 9 yr lead 1 yr lead Reliability diagrams from Smith et al. (2007) showing that for global temperature, DePreSys is slightly overconfident in it’s hindcasts, suggesting the need for greater spread in the predictions. Also found in ENSEMBLES decadal predictions.

6. reality initial uncertainty forecast uncertainty reference forecast ensemble forecasts Optimal perturbations (or ‘singular vectors’) Optimal perturbations for decadal predictions are: • perturbations which grow most rapidly, averaged over weather ‘noise’ • consistent with the observational uncertainties • useful as efficient perturbations in ensemble forecasts • suitable for identifying regions where additional observations would be most valuable to improve predictions

7. Optimal perturbations • We have been using two different methods: • Linear Inverse Modelling (LIM) e.g. Penland & Sardeshmukh 1995 • computationally cheap • initial condition independent • multi-model analysis as part of THOR • Climatic Singular Vectors (CSVs) e.g. Kleeman et al. 2003 • expensive to estimate • calculated for each initial condition separately • just HadCM3 considered so far

8. Multi-model LIM optimal perturbations Models considered so far Models planned Other models welcome! e.g. IPSL, … Only requirement is a long (>500 year) control integration Detailed analyses already published: HadCM3: Hawkins & Sutton (2009) GFDL CM2.1: Tziperman et. al. (2008)

9. LIM optimal perturbations • Linear Inverse Modelling: • fit a statistical model to the evolution of the ocean state • reduce dimensionality by representing ocean variability using leading 3d joint EOFs of temperature and salinity • using control run data, and a focus on Atlantic/Arctic domain GCM: yrepresents ocean data LIM: xrepresents leading PCs • From P, the optimal perturbations can be found

10. Multi-model amplification

11. HadCM3 decadal amplification Temperature

12. GFDL CM2.1 decadal amplification Temperature

13. Bergen CM2 decadal amplification Temperature

14. Climatic singular vectors (CSVs) HadCM3 Climatic Singular Vectors (CSVs) - are estimated for specific initial conditions rather than an average state Approximate propagator matrix (P) constructed from a series of ensemble runs from a single initial condition Optimal perturbation Computationally very expensive Predicted state 10 years later Note changed colour scales!

15. Does the CSV work? Predicted: State after 10 years Actual:

16. Demonstrated two methods for estimating optimal perturbations for decadal climate predictions In HadCM3, both methods show significant amplification largest growing perturbations located in far North Atlantic some other models show similar growth Multi-model analysis shows diverse range of variability and amplification to be explored further Plan to test these perturbations in THOR decadal predictions, and to consider other regions, e.g. Southern Ocean These approaches have potential to aid development of: efficient decadal ensemble forecasting systems optimal ocean observing systems for improving climate predictions Summary

17. Does the CSV work?

18. HadCM3 version

19. GFDL CM2.1 version