OUTLINE

1. NCEP Global Ensemble: recentdevelopments and plans Mozheng Wei*, Zoltan Toth,Dick Wobus*, Yuejian Zhu, Dingchen Hou* and Bo Cui*NOAA/NCEP/EMC, USA *SAIC at NOAA/NCEP/EMC7 April 2005 2nd SRNWP Workshop on Short Range EnsembleBologna, Italy 7-8 April, 2005

2. OUTLINE • NCEP GLOBAL ENSEMBLE SYSTEM • A SUMMARY OF VARIOUS SCHEMES • EXPERIMENTAL RESULTS • DISCUSSION, NCEP 2005 PLAN AND OTHER RESEARCH ACTIVITIES

3. NCEP GLOBAL ENSEMBLE FORECAST SYSTEMTHE BREEDING METHOD • DATA ASSIM: Growing errors due to cycling through NWP forecasts • BREEDING: - Simulate effect of obs by rescaling nonlinear perturbations (Toth and Kalnay 1993,1997) • (Zoltan Toth and Eugenia Kalnay started work in second half of 1991; Implemented in operational • suite in December 1992; Upgraded system implemented in March 1994) • Sample subspace of most rapidly growing analysis errors • Extension of linear concept of Lyapunov Vectors into nonlinear environment • Fastest growing nonlinear perturbations • Not optimized for future growth – (Toth et. al 2004)

4. NCEP GLOBAL ENSEMBLE FORECAST SYSTEM (Toth et. al 2004) RECENT UPGRADE (April 2003) NEW CONFIGURATION MARCH 2004 10/50/60% reduction in initial perturbation size over NH/TR/SH FORMER SYSTEM

5. MOTIVATION FOR EXPERIMENTS EPS and DA systems must be consistent for best performance of both. DA provides best estimates of initial uncertainties, i.e. analysis error covariance, for EPS. EPS produces accurate flow dependent forecast (background) covariance for DA. Best analysis error variances EPS DA Accurate forecast error covariance

6. POSSIBLE SOLUTIONS CONSISTENCYcan be achieved by: (a) Development & use of ensemble-based DA system Through THORPEX project, NCEP is collaborating with 4-5 groups on this. Istvan Szunyogh (Uni. of Maryland), Jeff Anderson (NCAR), Jeff Whitaker and Tom Hamill (NOAA/CDC) and Craig Bishop (NRL) and Milija Zupanski (Colorado State Uni.) (b) Coupling existing DA (3/4DVAR) with ensemble generation scheme Goal of present study As long as ensemble-based DA cannot outperform the 3/4DVAR, modify and couple existing DA and ensemble systems Simple initial perturbation scheme driven by analysis error variance from DA, 3/4DVAR driven by flow dependent forecast error covariance from ensemble

7. EXISTING/PROPOSED APPROACHES • FIRST GENERATION INITIAL PERTURBATION GENERATION TECHNIQUES

8. EXISTING/PROPOSED APPROACHES - 2 • SECOND GENERATION INITIAL PERTURBATION GENERATOIN TECHNIQUES

9. COMPARISON OF DIFFERENT METHODS GRADUAL CONVERGENCE OF METHODS? Analysis error variance is commonly used in the 2nd generation techniques. ETKF with no observation perturbation => Breeding with orthogonalization and rescaling consistent with varying observational network COMMON CONCEPT: Perturbations cycled dynamically through use of nonlinear integrations Bred Vectors (Toth & Kalnay 1993) => Nonlinear Lyapunov Vectors (Boffetta et. al 1998) Evolved SVs constrained by analysis error covariance (Hessian SVs) => Finite-time Normal Mode (finite period) => dominant Lyapunov vectors (longer time interval). (Wei & Frederiksen 2004) COMMON CONCEPT: With realistic initial constraint, evolved SV dynamics => Lyapunov dynamics

10. DESCRIPTION OF 4 METHODS TESTED BREEDING with regional rescaling (Toth & Kalnay, 1993; 1997) Simple scheme to dynamically recycle perturbations Variance constrained statistically by fixed analysis error estimate “mask” Limitations: No orthogonalization; fixed analysis variance estimate used. ETKF (Bishop et al. 2001; Wang & Bishop 2003; Wei et. al 2004) – used as perturbation generator (not DA) Dynamical recycling with orthogonalization in obs space Variance constrained by distribution & error variance of observations Constraint does not work well with only 10 ensemble members Issue of pert inflation is challenging for large variation of obs Computationally expensive Built on ETKF DA assumptions =>NOT consistent with 3/4DVAR Ensemble Transform (ET) (Bishop & Toth 1999, Wei et. al 2005) Dynamical recycling with orthogonalization (inverse analysis error variance norm) Variance constrained statistically by fixed analysis error estimate “mask Constraint does not work well with only 10 ensemble members ET plus rescaling (Wei et al. 2005) As ET, except variance constrained statistically by analysis error estimate.

11. ET Formulation

12. EXPERIMENTS Time period Jan 15 – Feb 15 2003 Data Assimilation NCEP SSI (3D-VAR) Model NCEP GFS model, T126L28 Ensemble 2x5 or 10 members, no model perturbations Evaluation 7 measures, need to add probabilistic forecast performance

13. Initial energy spread, Rescaling factor distribution ET ETKF Breeding ET+rescaling

14. Amp Factor Correlation Effective Dim

15. Variance PECA

16. AC RMS error

17. SUMMARY OF RESULTS RMSE, PAC of ensemble mean forecast – Most important ET+Rescaling and Breeding are best, ET worse, ETKF worst Perts and Fcst error correlation (PECA) – Important for DA ET+Rescaling best, Breeding second Explained variance (scatterplots) – Important for DA ET best Variance distribution (climatological, geographically) Breeding, ET+Rescaling reasonable Growth rate ET+Rescaling best? (not all runs had same initial variance…) Effective degrees of freedom out of 5 members Minimal effect of orthogonalization Breeding (no orthogonalization) =4.6 ET (built-in orthogonalization) =4.7 Time consistency of perturbations (PAC between fcst vs. analysis perts) Important for hydrologic, ocean wave, etc ensemble forcing applications Excellent for all schemes, ET highest (0.999, breeding “lowest”, 0.988) New and very promising result for ET & ETKF OVERALL hits out of 7 ET+Rescaling 4 ET 3 Breeding 2

18. DISCUSSION All tests in context of 5-10 perturbations Testing with 80 members is under way Plan to experimentally exchange members with NRL (Will have total of 160 members) 4-Dim time-dependent estimate of analysis error variance Need to develop procedure to derive from SSI (GSI) 3DVAR ET+Rescaling looks promising Orthogonalization appears to help breeding Cheaper than ETKF, can also be used in targeting If ensemble-based DA can not beat 3/4DVAR Initial ens cloud need to be repositioned to center on 3/4DVAR analysis No need for sophisticated ens-based DA algorithm for generating initial perts? Good EPSGood DA

19. NCEP GLOBAL ENSEMBLE PLAN 2005 (Wei et. al 2005) At every cycle, both ET and Simplex Transformation (ST) are carried out for all 80 perts.Only 20 members are used for long fcsts. ST is imposed on the 20 perts to ensure they are centered around the analysis. 60 for short 6-hour fcsts. 41-60, ST 16-day fcsts 01-20, ST 16-day fcsts 21-40, ST 16-day fcsts 61-80, ST 16-day fcsts time 00z 00z 06z 12z 18z 80-perts, ET,ST 80-perts, ET,ST 80-perts, ET,ST 80-perts,ET,ST 80-perts, ET,ST

20. OTHER RESEARCH ACTIVITIES AT NCEP REPRESENTING MODEL RELATED UNCERTAINTIES (D. Hou) (a) Experiments with multi-model version ensembles using different Cumulus Parameterization Schemes (CPS) ( accounts for little model uncertainty). (b) Experiments with varying the horizontal diffusion coefficient suggest that relatively strong diffusion in the current system hinders the increase in ensemble spread and leads to noticeable cold bias. (c) Stochastic physics schemes, using tendency difference between high/low resolution runs, or between two ensemble members to formulate the extra forcing term, resulted in systematic reduction in bias, sufficient spread, as well as moderate improvement in some performance scores. STATISTICAL POST-PROCESSING(reducing the biases, B. Cui) Adaptive, regime dependent Bias-Correction Algorithm (Kalman Filter type), applied to NCEP Operational Ensemble. It works well for first few days. (b) Climate mean bias correction (applied to CDC GFS Reforecast Data Set) can add value, especially for wk2 prob. fcsts.