1. Improved ensemble-mean forecast skills of ENSO events by a zero-mean stochastic model-error model of an intermediate coupled model Jiang Zhu and Fei Zheng Institute of Atmospheric Physics Chinese Academy of Sciences Beijing, China

2. Outlines The ENSO model: what it has and what it misses Sampling the model errors Building the model-error model stochastically Improvement of ensemble-mean forecast skills Ensemble-mean dynamics Summary

3. The ENSO model: what it has and what it misses An intermediate coupled model (Keenlyside and Kleeman, 2002; Zhang et al., 2005) is used for this study: Dynamical ocean model Response of ocean currents and waves from wind forcing SSTA budget model Horizontal and vertical transport/diffusion effects on SST, simple heat flux Subsurface temperature anomaly model A regression from sea level anomaly Wind model A regression from SST gradient

4. The model can describe the main/classic ENSO mechanism: Bjerknes’ positive feedback: positive correlation between SST zonal gradient and westerly wind anomaly; Delayed negative feedback: a westerly anomaly can trigger Rossby and Kalvin waves that will be bounced back later from the west and east boundaries and reduce the SST zonal gradient.

5. The model misses the following processes: explicit air-sea heat interactions, stochastic atmospheric forcing/MJO, extra-tropical cooling and warming, Indian Ocean Dipole mode, the feedback of cloud and the salinity effect, etc. However the net effect of these missing processes on ENSO is less studied.

6. Sampling the model errors A EnKF data assimilation scheme is developed (a coupled assimilation scheme, see Zheng and Zhu poster in this workshop); The SST data is assimilated into model (1963-1996); Lunch a 12-month forecast every month (1963-1996); Compare forecasted SST (ensemble mean) to SST observations (f-o); Obtain 408 f-o samples for each lead time (1-month,..12-month); Perform EOF analysis for each set of 408 samples (12 sets). By this method, we assume that the forecast errors are all due to model errors, or in another word, the initial errors are zero.

8. Results from model error sampling Over the multi-decade period, the model errors are of random, zero-mean (or model is not biased over multi-decade period) The random model errors have spatial patterns The random model errors have time correlations (scale: several months) (or the model is biased over interannual time scale)

9. Building the model-error model stochastically A first-order Markov stochastic model is used to modelling the mode error; The model error model is only acting on the time coefficients of EOF modes; 10 Modes are used; The model error model has only one variable: SST anomaly. Original SSTa model SSTa error EOF modeWhite noise i : mode index; j : lead time index

10. Correlation RMSE ( o C) Lead time Persistence Exp1: Deterministic forecast no initial perturbation no model error Exp2: Ensemble forecast with initial perturbation no model error Exp3: Ensemble forecast no initial perturbation with model error Exp4: Ensemble forecast with initial perturbation with model error Nino 3.4 index of deterministic and ensemble-mean forecast skills with SST&SLA assimilation Improvement of ensemble-mean forecast skills

11. Ensemble-mean dynamics How does a zero-mean stochastic model-error interact with the nonlinear ENSO model and improve the ensemble-mean forecast? Nino 3.4 index

12. Ensemble mean departure caused by 1st mode zero-mean perturbations: Nonlinear term contributions

13. T’ (+) - + Wind < 0 Linear terms (zero-mean) Nonlinear terms Horizontal pattern induced by a 1 st -mode positive perturbation

14. Wind Linear terms (zero-mean)Nonlinear terms + - < 0 Horizontal pattern induced by a 1st- mode negative negative perturbation T’(-)

15. Forecast case starting at 1997.01 The difference between the ensemble-mean and deterministic forecasts

16. Summary A stochastic model is developed for modeling the model errors of an intermediate coupled model for ENSO prediction; The stochastic model-error perturbations have significant impacts on improving the ensemble-mean prediction skills; The nonlinear heating mechanism in the tropic air-sea couple system can sum a series of weather time scale random perturbations up to a positive “heating source” over a period of longer time scale; The nonlinear terms in the model can form a positive ensemble- mean from a series of zero-mean perturbations, which resembles the real world to some extend.

17. END THANKS

19. 18-year averaged difference (Ensemble Mean – Deterministic)

20. Prediction skills of ensemble mean forecast for Nino 3.4 index (1993-2007)