NCEP Global Ensemble: recentNCEP Global Ensemble: recentdevelopments and plans developments and plans

Mozheng Wei*, Zoltan Toth,Mozheng Wei*, Zoltan Toth,Dick Wobus*, Yuejian Zhu, Dingchen Hou* and Bo Cui*Dick Wobus*, Yuejian Zhu, Dingchen Hou* and Bo Cui*

NOAA/NCEP/EMC, USANOAA/NCEP/EMC, USA

*SAIC at NOAA/NCEP/EMC *SAIC at NOAA/NCEP/EMC

7 April 20057 April 2005 2 2ndnd SRNWP Workshop on Short Range Ensemble SRNWP Workshop on Short Range Ensemble

Bologna, Italy 7-8 April, 2005Bologna, Italy 7-8 April, 2005

OUTLINEOUTLINE

NCEP GLOBAL ENSEMBLE SYSTEM

A SUMMARY OF VARIOUS SCHEMES

EXPERIMENTAL RESULTS

DISCUSSION, NCEP 2005 PLAN AND OTHER RESEARCH ACTIVITIES

NCEP GLOBAL ENSEMBLE FORECAST SYSTEMNCEP GLOBAL ENSEMBLE FORECAST SYSTEMTHE BREEDING METHOD THE 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 errorsExtension of linear concept of Lyapunov Vectors into nonlinear environment

Fastest growing nonlinear perturbations

Not optimized for future growth –

(Toth et. al 2004)

NCEP GLOBAL ENSEMBLE FORECAST SYSTEM(Toth et. al 2004)

FORMER SYSTEM

NEW CONFIGURATIONMARCH 2004

RECENT UPGRADE (April 2003)

10/50/60% reductionin initial perturbation size over NH/TR/SH

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.

)( aP

DA EPSfP

Best analysis error variances

Accurate forecast error covariance

POSSIBLE SOLUTIONS

CONSISTENCY can 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

EXISTING/PROPOSED APPROACHES• FIRST GENERATION INITIAL PERTURBATION GENERATION

TECHNIQUES

PERTURBED OBSERVATIONS

(MSC, Canada)

BREEDING with Regional Rescaling

(NCEP, USA)

SINGULAR VECTORS with Total Energy

(ECMWF)

ESTIMATION Realistic through sample, case dependent patterns & amplitudes

Fastest growing subspace, case dependent patterns

No explicit estimate, not flow dependent

SAMPLING Random for all errors, incl. non-growing, potentially hurting short-range performance

Nonlinear LVs, subspace of fastest growing errors; Some dependence among perts.

Directed, dynamically fastest growing in future, quite orthogonal.

CONSISTENCY BETWEEN ENS & DA SYSTEMS

Good; quality of DA lagging behind 3DVAR?

Not consistent, time-constant variance due to use of fixed mask

Not consistent, potentially hurting short-range performance

EXISTING/PROPOSED APPROACHES - 2

• SECOND GENERATION INITIAL PERTURBATION GENERATOIN TECHNIQUES

ETKF, perts influenced by fcsts and observed data

ET/BREEDING with Analysis Error Variance Estimate from DA

Hessian Singular Vectors

ESTIMATION Fast growing subspace, case dependent patterns & amplitudes

Fastest growing subspace, case dependent patterns & amplitudes

Case dependent variance

SAMPLING Orthogonal in subspace of observations

Orthogonal in analysis covariance

norm

Directed, dynamically fastest growing in future

CONSISTENCY BETWEEN ENS & DA SYSTEMS

Very good; quality of DA lagging 4D-VAR.

Good; DA=>ens; Ens=>DA

Climatologically consistent

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

DESCRIPTION OF 4 METHODS TESTED

BREEDING with regional rescaling (Toth & Kalnay, 1993; 1997)Simple scheme to dynamically recycle perturbationsVariance 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 spaceVariance constrained by distribution & error variance of observationsConstraint does not work well with only 10 ensemble membersIssue of pert inflation is challenging for large variation of obsComputationally expensiveBuilt 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.

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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

Initial energy spread, Rescaling factor distribution

ET

ETKF

Breeding

ET+rescaling

Amp Factor

Effective Dim Correlation

PECA

Variance

AC

RMS error

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

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 EPS Good DA

NCEP GLOBAL ENSEMBLE PLAN 2005(Wei et. al 2005)

00z 06z 12z 18z

time

00z

80-perts, ET,ST

01-20, ST16-day fcsts

21-40, ST16-day fcsts

41-60, ST16-day fcsts

61-80, ST16-day fcsts

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.

80-perts, ET,ST 80-perts, ET,ST 80-perts, ET,ST 80-perts,ET,ST

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)

(a) 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.