# Presentation: 548091

## The use of  Ensemble Transform technique for generating initial ensemble perturbationsMozheng Wei*, Zoltan Toth, Yuejian Zhu,  Dick Wobus*,  Craig Bishop**  NCEP/EMC, MD*SAIC at NCEP/EMC  ** Naval Research Lab  NOAA Thorpex PI Workshop, Jan. 17, 2006

**Notes:**
Outline slide

## OUTLINE

** ****Motivation for Experiments**
** ****A Summary of Tested Schemes**
** ****Experimental Results**
** ****A Summary and Discussion**
** ****Ongoing Work and Plan**

## Links between EFS and DA

*Is there a ``best way”  to generate ensemble perturbations?  *
*Capture dynamically relevant initial growing  perturbations*
*Purely dynamically based (e.g.  breeding)*
*No added stochastic noise to initial perts*
*Initial perts are restrained by using analysis error information *
*What is the best way to combine fcst and observation data?**     (4D-VAR, or various ensemble based Kalman filters)*
*Use dynamical information (fcst error covariance) from ensemble *
*     **fcst system*
*Describe observational errors through statistical methods (independent of  ensemble fcsts)*
*Produce  accurate analysis error variance*
*    *
*     **To some extent, EFS and DA can be developed separately, but for ideal performance of both, they need to be coupled.*
*      *

## MOTIVATION FOR EXPERIMENTS

*   **EFS and DA systems must be consistent for best *
*      **performance of both.** *
*  *SSI/GSI currently* ** provides ** **best estimate of analysis, GSI will be *
*       **used to derive ** **analysis uncertainties (error variance) for EFS.    *
*  **EFS produces flow dependent forecast (background) error *
*       **covariance to be tested in GSI later.          *

- GSI

- EFS

- Best analysis error variances

- Accurate forecast error covariance

- A Hybrid DA-EFS system

## DESCRIPTION OF 4 METHODS TESTED

**ET plus rescaling **
-   As ET,  additional constraint  (regional rescaling as in breeding).
**Ensemble Transform (ET)** (Bishop & Toth 1999, initially for adaptive observation)
-       Dynamical recycling with orthogonalization (inverse analysis error variance norm)
-       Variance constrained statistically by flow-dependent analysis error estimate.
-       Constraint does not work well with only 10 ensemble members
**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 2006) – 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
- Computationally expensive for current time allocation for ensemble forecasts
- Built on ETKF DA assumptions => ***NOT consistent with 3/4DVAR***
- Issue of pert inflation is challenging for large variation of obs

## ET Formulation 

**ET Formulation**

## ET Formulation 

- Simplex transformation is to center analysis perts  around the analysis, and preserve the analysis error covariance.

**Notes:**
CIRA operational and research experience

## 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 fcsts are short 6-hour.

- 00z

- 06z

- 12z

- 18z

- time

- 00z

- 80-perts, ET,ST

- 01-20,    ST
- 16-day fcsts

- 21-40,   ST
- 16-day fcsts

- 41-60,    ST
- 16-day fcsts

- 61-80,  ST
- 16-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 fcsts are short 6-hour.

- 80-perts, ET,ST

- 80-perts, ET,ST

- 80-perts, ET,ST

- 80-perts,ET,ST

## Initial energy spread distribution   

## Ave correlation between fcst and ana perts   

## Initial energy spread     Rescaling factor distribution   

- ET(10)

- ETKF(10)

- Breeding(10)

- ET/rescaling(10)

## Spread for Temp at 500mb ET80/80

## Pert versus Error Correlation Analysis (PECA)

## Fcst variance explained by ensemble (from scatter-plots) 

- Fcst variance explained by ensemble (from scatter-plots)

## S - 20/80 ET

- Dotted: resolution
- Solid: reliability

**S - 20/80 ET**
**X -10 ET/rescaling**
**O  - my10 breeding**
**E  -10 ETKF**

## ROC: the Relative Operating Characteristic

**S - 20/80 ET**
**X -10 ET/rescaling**
**O  - my10 breeding**
**E  -10 ETKF**

## S - 20/80 ET

**S - 20/80 ET**
**X -10 ET/rescaling**
**O  - my10 breeding**
**E  -10 ETKF**

## S - 20/80 ET

**S - 20/80 ET**
**X -10 ET/rescaling**
**O  - my10 breeding**
**E  -10 ETKF**

## S - 20/80 ET

**S - 20/80 ET**
**X -10 ET/rescaling**
**O  - my 10 breeding**
**E  -10 ETKF**

## SUMMARY OF RESULTS

**The main difference between Breeding and ET/rescaling is**
**                  ****Paired strategy  vs. Simplex structure**
**Variance distribution** (geographically)
- Breeding and ET/rescaling  are similar.
**RMSE, PAC of ensemble mean forecast****  **
- Paired breeding and ET/rescaling are best, ET second, ETKF last.
**All probability scores are improved, especially in the tropics.**
**Explained variance** (scatterplots) – ET best, ET/rescaling,ETKF, breeding.
**Perts vs. Fcst error correlation** (PECA) – *Important for DA*
-  ET/rescaling best, breeding second.
-  80-90% of variances can be explained by 80 ET perts, great for DA
**Growth rate (not shown):  ****ET/rescaling is**** ****slightly higher****.**
**Effective number of degrees of freedom (***Important for DA***):**** **
-            ET is higher  due to simplex structure (not shown).
**Time consistency** of perturbations (PAC between fcst vs. analysis perts: excellent for all, ET highest (0.999, breeding “lowest”, 0.988)

## Ongoing Work and Plan

- 00z

- 06z

- 12z

- 18z

- time

- 00z

- 56-perts, ET,ST

- 01-14,    ST
- 16-day fcsts

- 15-28,   ST
- 16-day fcsts

- 29-42,    ST
- 16-day fcsts

- 43-56,  ST
- 16-day fcsts

- At every cycle, both ET and Simplex Transformation (ST) are carried out for all 56 perts. Only 14 members are used for long fcsts.  ST  is imposed on the  14 perts to ensure they are centered around the analysis. 42 fcsts are short 6-hour.
- Number of members will be increased to 20/80 configuration later when
- resources are available.

- 56-perts, ET,ST

- 56-perts, ET,ST

- 56-perts, ET,ST

- 56-perts,ET,ST

## Next Step

- Derive  flow dependent 3-D analysis error variance from GSI to restrain the initial   perturbations.
- Test the use of ensemble based forecast error     covariance to improve GSI performance.

## Ensemble Perturbations vs. “NMC” Method

- Wei and Toth (2003,  MWR)

- Ensemble perts can better explain their respective 1-day fcst errors than the NMC method:  50 EC ensembles at 1-day  lead time can explain about 80% of fcst error variance over contiental scale (middle panel);  80 ET based perts cana explain 90% forecast error variance at 6-hour lead time (right panel).