# Presentation: 305682

## Initial Perturbations in SREF System Mozheng  Wei, Jun Du and Zoltan Toth NOAA/NCEP/EMC, USA  July 24  2007  EMC Predictability Meeting

**Notes:**
Outline slide

## Objectives 

-  Improve representation of initial uncertainty by regional  initial perturbations (breeding, ET with rescaling).
-  Regional initial conditions and integrations (control and perturbed) should be consistent with global solutions. If not consistent, the solution will be sub-optimal.
-  The regional ensemble should be able to refine the global solution, play the role of a magnifier, not to create an alternative solution?

## Ensemble  Forecast System  based on Breeding

**DATA ASSIM:** Growing errors due to cycling through NWP forecasts
**BREEDING:** - Simulate effect of obs by rescaling nonlinear perturbations  (Toth and Kalnay 1993,1997)
-  Errico *et al.* (2007) confirmed that analysis errors to first approximation look like 6-hour
-  forecast errors.  (a)  Extension of linear concept of Lyapunov Vectors into nonlinear environment.
-  (b) Fastest growing nonlinear perturbations.

- (Toth et. al 2004)

## A Summary of  Perturbations generated using ET/ST  

- The ET method resembles breeding in that they both dynamically cycle the fastest growing nonlinear perts. It can be considered as an extension of the breeding method. In the special case where there are only two ensemble members, ET and breeding will produce the same perturbations
- The ET transform is computed based on analysis error variance so that the analysis error variances can be re-constructed from the generated ensemble perts.
- The ET perts will be centered using simplex transformation (ST) to improve ensemble mean.
- The transformed perts are rescaled using the analysis error distribution to ensure perts will have right magnitudes (This ET with rescaling improves the performance).
- The simplex structure (not paired) ensures that perts  will have maximum number of  effective degrees of freedom. The variance will  be maintained in as many directions as possible  within the ensemble subspace.
- They are centered and uniformly distributed in different directions. The larger the ensemble, the closer to orthogonality they become.  They become completely orthogonal if the number of  members approaches infinity.
- The initial perts have flow dependent spatial structure since the analysis error variance is derived from operational DA system at every cycle.
- The covariance constructed from the perts is approximately consistent with the analysis covariance from the DA if the number of ensemble members is large.
- Perturbations show high consistency in time.

**Notes:**
CIRA operational and research experience

## Correlation between analysis and fcst perturbations

*Correlation in ETKF with ST is  higher than that in breeding.*
*ET with ST is expected to have similar correlation with ETKF with ST.*

**Correlation between analysis and fcst perturbations**

## SREF Configuration (from Jun Du)

-  21 members (3 Eta-bmj, 2 Eta-sat, 3 Eta_kf, 2 Eta_det,
-        3 RSM_sas, 2 RSM_ras, 3 WRF_nmm and 3 WRF_arw)
-        (8 pairs plus 5 controls)
-  32-45km
-  Four cycles per day (03, 09, 15 and 21Z)
- 3-hourly output to 87 hours for each cycle
- Three output domains: CONUS, Alaska and Pacific/Hawaii
- The boundary condition for each SREF perturbed member comes from a global ensemble member
- Perturbations for each of the 8 models are paired (SREF was designed to be consistent with the global ensemble system at that time with multi-models)

## Possible Questions

- There are 5 control runs (which are expected to be similar for short range)
-       plus 8 paired perturbed members. The effective number of degrees of freedom (EDF) may be about 8-9  in spite of  21 members in total due to the pairing strategy (8 pairs + 5 controls).
- How similar are these 5 controls?  Do we need 5 controls? One control + 4 more perturbed fcsts (same computing cost) will provide more info?
- For short-range forecast up to 2-3 days, the initial condition errors (for large scale) are generally more dominant than the model related errors.  It is important to maximize EDF in ensemble subspace.
- The boundary condition for each SREF member comes from a global ensemble member. The global ensemble perturbations have been upgraded to have ET transformed simplex structure.  It is not consistent to use paired regional perturbations based on the boundary conditions with  simplex structure. This may lead to sub-optimal solution.
- There is no contribution from DA system to describe the initial error distribution.

## 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.

- 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 for short 6-hour fcsts.

- 80-perts, ET,ST

- 80-perts, ET,ST

- 80-perts, ET,ST

- 80-perts,ET,ST

## Possible Solutions

- (A)  Build the regional ET-transformed perts with simplex structure based on the analysis error variance from regional GSI. But it may not be consistent with boundary perts which are based on global analysis error variance.
- (B)  Build perts based on the global ensemble perts (interpolated to regional grid)
-        (a)  The regional perts are obtained by adding the differences (d, in green) between global and
-               regional fcsts  to the rescaled global perts.
-        (b)  d can be measured against s (the difference between the global and regional analyses).
-              Generally d will not be out of control.
-        (c)  The regional perts could be added to global analysis or regional analysis (which is better?
-              Needs to be discussed).

- Red->global,   black->SREF,   green->difference between global and SREF

- Global analysis from GSI

- Regional  analysis from regional GSI

- d

- d

- s

## Potential Benefits of Solution B

- Greatly increase the EDF of SREF ensemble subspace due to the simplex structure of initial perturbations. This is important if ensemble info is to be used in DA system.
- SREF will be consistent with regional analysis system (if regional and global analyses are similar). It will be able to provide background error variance back to regional GSI in the future, potentially benefit  each other.
- Improve the accuracy of initial PDF represented by the initial perturbations       (Error variance is distributed in more directions in ensemble subspace). This is very important given the fact that initial condition error plays more important role in short range than in long time forecast.
- Initial states in SREF will be consistent with the initial states in global ensemble which are used as boundary conditions.   SREF perts are controlled by global boundary and regional models. It will refine the solutions of global ensemble solution.