Initial Ensemble Perturbations using the Ensemble Transform Technique
Initial Ensemble Perturbations using the Ensemble Transform Technique Mozheng Wei*, Zoltan Toth, Yuejing Zhu, Dick Wobus* and Craig Bishop** NOAA/NCEP/EMC, USA *SAIC at NOAA/NCEP/EMC ** Naval Research Lab, CA, USA IAMAS 2005, Beijing, August 9, 2005
MOTIVATION FOR EXPERIMENTS v EPS and DA systems must be consistent for best performance of both. v DA provides best estimates of initial uncertainties, i. e. analysis error covariance, for EPS. v EPS produces accurate flow dependent forecast (background) covariance for DA. Best analysis error variances DA Accurate forecast error covariance EPS
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 2005) – 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 3/4 DVAR Ensemble Transform (ET) (Bishop & Toth 1999, Wei et. al 2005 b) 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 b) As ET, except variance constrained statistically by analysis error estimate.
NCEP GLOBAL ENSEMBLE PLAN 2005 (Wei et. al 2005 b) 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. 01 -20, ST 16 -day fcsts 21 -40, ST 16 -day fcsts 41 -60, ST 16 -day fcsts 61 -80, ST 16 -day fcsts time 00 z 80 -perts, ET, ST 06 z 80 -perts, ET, ST 12 z 80 -perts, ET, ST 18 z 80 -perts, ET, ST 00 z 80 -perts, ET, ST
EXPERIMENTS • Time period – Jan 15 – Feb 15 2003 • Data Assimilation – NCEP SSI (3 D-VAR) • Model – NCEP GFS model, T 126 L 28 • Ensemble – 2 x 5 or 10 members, no model perturbations • Evaluation – 7 measures, need to add probabilistic forecast performance
Initial energy spread, Rescaling factor distribution ETKF Breeding ET+rescaling
AC RMS error
S - 20/80 ET X -10 ET/rescaling E -10 ETKF O - 10 breeding
S - 20/80 ET X -10 ET/rescaling E -10 ETKF O - 10 breeding
S - 20/80 ET X -10 ET/rescaling E -10 ETKF O - 10 breeding
S - 20/80 ET X -10 ET/rescaling E -10 ETKF O - 10 breeding
S - 20/80 ET X -10 ET/rescaling E -10 ETKF O - 10 breeding
S - 20/80 ET X -10 ET/rescaling E -10 ETKF O - 10 breeding
SUMMARY and DISCUSSION v All tests in context of 5 -10 perturbations 80 -member ET with rescaling improves the forecast Plan to experimentally exchange members with NRL (Will have total of 160 members) v 4 -dim time-dependent estimate of analysis error variance Need to develop procedure to derive from SSI (GSI) 3 DVAR v ET+Rescaling looks promising Orthogonalization appears to help breeding Cheaper than ETKF, can also be used in targeting v If ensemble-based DA can not beat 3/4 DVAR Initial ens cloud need to be repositioned to center on 3/4 DVAR analysis No need for sophisticated ens-based DA algorithm for generating initial perts? Good EPS Good DA
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