# Presentation: 665950

## Assessing/Reducing/Representing Uncertainty in Initial  Conditions and Ensemble Data Assimilation Mozheng Wei*, Zoltan Toth, Yuejian Zhu,  Dick Wobus*  NCEP/EMC, MD 3rd NCEP/NWS  Ensemble User  Workshop, Oct. 31, 2006Holiday Inn, Laurel, Maryland

**Notes:**
Outline slide

## OUTLINE

**How to Represent Initial Value related Uncertainty? **
**A Summary of ET formulation and Configuration**
**Experimental Results**
**Ongoing Work and Plan**
**Ensemble based DA and Status**

## 
                                     Estimate analysis uncertainty
Choice among sampling strategies, given an estimate
Brute force (“Monte Carlo”) sampling – “Perturbed Observations” method
Run multiple analysis cycles with perturbed observations (Canadian approach)
Both growing and non-growing error space sampled with realistic amplitude
Very poor sampling of myriad non-growing directions
Noise hurts analysis performance
Directed sampling
Singular vectors – fastest growth for pre-selected time period
Transient growth emphasized
Computationally expensive
No general solution: If transient growth is
Important - 	Need different perturbations for various lead times
Not important - 	No need for SVs
Most often norm used is uncoupled from analysis error estimates
Relevant dynamics identified via growth optimization calculations
No successful DA applications
Dynamical sampling in growing sub-space
Based on principle of breeding: Cycle growing perturbations
Capture dynamics of system responsible for error growth
Ignore noise
Successfully used in most ensemble-based DA efforts: eg, ETKF, etc

-                                      Estimate analysis uncertainty
- Choice among sampling strategies, given an estimate
- Brute force (“Monte Carlo”) sampling – “Perturbed Observations” method
- Run multiple analysis cycles with perturbed observations (Canadian approach)
- Both growing and non-growing error space sampled with realistic amplitude
- Very poor sampling of myriad non-growing directions
- Noise hurts analysis performance
- Directed sampling
- Singular vectors – fastest growth for pre-selected time period
- Transient growth emphasized
- Computationally expensive
- No general solution: If transient growth is
- Important - 	Need different perturbations for various lead times
- Not important - 	No need for SVs
- Most often norm used is uncoupled from analysis error estimates
- Relevant dynamics identified via growth optimization calculations
- No successful DA applications
- Dynamical sampling in growing sub-space
- Based on principle of breeding: Cycle growing perturbations
- Capture dynamics of system responsible for error growth
- Ignore noise
- Successfully used in most ensemble-based DA efforts: eg, ETKF, etc

**HOW TO REPRESENT INITIAL VALUE RELATED UNCERTRAINTY?**** **

## HOW TO REPRESENT INITIAL VALUE RELATED UNCERTRAINTY?

**Proposed solution:** Dynamical sampling in growing sub-space – ET / ETKF
- Link with DA
- GSI – ET
- Take error variance from GSI to specify ensemble perturbation level
- Feed back information from ensemble into background error covariance
- Ensemble-based DA – ETKF
- Same ensemble principles, except 2-way interactions tuned simultaneously
- “Ensemble Filter” or
- Variational solutions
- General applicability
- As long as transient behaviour is not dominating
- Ideal for “downstream” applications
- ET provides series of perturbed analyses consistent in time
- Important for wave, land surface, etc ensembles where
- Instantaneous error/perturbation dependent on *forcing history*
- Need for collaboration over DA & ensemble overlap
- Analysis is not complete until uncertainty estimate provided and assessed
- Consider ensemble-based DA alternative for revised product suite

## ET Formulation 

- Wei et al.  2005,   ***WMO TD No.1237****, ***WWRP  THORPEX No. 6***, *2005. p227-230.
-                  2006,   N**OAA/NCEP Office Note 453**, 33pp,  September 2006.

**Notes:**
CIRA operational and research experience

## Configuration in Operation since 05/30/2006

- 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, expected in Jan/Feb 2007.

- 56-perts, ET,ST

- 56-perts, ET,ST

- 56-perts, ET,ST

- 56-perts,ET,ST

## MOST RECENT YEAR – May 2004 – Apr. 2005Pattern Anomaly Correlation  Control (dashed) vs. Ensemble mean (solid) (Zhu and Toth, 2006)

- MOST RECENT YEAR – May 2004 – Apr. 2005Pattern Anomaly Correlation  Control (dashed) vs. Ensemble mean (solid) (Zhu and Toth, 2006)

*Performance gap between ECMWF and NCEP controls is*
*reduced when ensemble is considered*

*Ensemble mean beats control from*
*	**Day 0 for NCEP (Day 3 for hires)*
*	**Day 5 for ECMWF & MSC (hires)*

## Pert versus Error Correlation Analysis (PECA) (Buizza et al. 2005, MWR)

- Pert versus Error Correlation Analysis (PECA) (Buizza et al. 2005, MWR)

* **Period:      MJJ 2002*
*Bred vectors have highest PECA values for short lead times in NH, NA and Europe*

## S - 20/80 ET

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

*20 ET is better than 10 ET*
* *
*10 ET slightly better than 10  *
*       **breeding*

## ROC: the Relative Operating Characteristic

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

*20 ET is better than 10 ET*
* *
*10 ET slightly better than 10  *
*       **breeding*

## S - 20/80 ET

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

*20 ET is better than 10 ET*
* *
*10 ET slightly better than 10  *
*       **breeding*

## Unified EFS and DA

*   **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

- or

## Next Steps

- Parallelizing ET codes to increase computing efficiency
- Update ET codes to handle new GFS model with
-        (a)  hybrid-sigma vertical coordinate
-        (b)  grib 1 and grib 2 inputs and  outputs
- Derive  flow dependent 3-D analysis error variance from
-        GSI to restrain the initial  perturbations and rescaling
- Test the use of ensemble based forecast error covariance
-        to improve GSI performance
- Test a hybrid background covariance model like Hamill and
-        Snyder (2000)
- Build ET based perts for  (a) regional ensemble; (b) CFS
-        (Climate Forecast System)
- Test surface boundary condition perts based on ET for all
-        ensemble systems

## THORPEX LINKSENSEMBLE-BASED DATA ASSIMILATION INTERCOMPARISON PROJECT

- GOAL:
- Develop new ensemble-based DA methods and test against operational 3DVAR
- Collaborative project funded by NOAA THORPEX program
- Coordinated by Zoltan Toth

## THORPEX LINKSENSEMBLE-BASED DATA ASSIMILATION INTERCOMPARISON PROJECT

- Parallel development of two alternative paths:
- Ensemble-based DA – led by Jeff Whitaker & Tom Hamill
- Use of ensemble information within 3⁄4 DVAR – led by Mozheng Wei & D. Parrish

## Ensemble DA Flow - 2 members (from Jeff Whitaker)

## NoSat results (48-h forecasts verified against operational analysis) (from Jeff Whitaker)

**Sat results (48-h forecasts verified against operational analysis)**

**Notes:**
LETKF and LEnSRF similar, small differences attributable to tuning.