# Presentation: 466251

## Initial Perturbations from  ETKFExperiments Mozheng Wei*, Zoltan Toth, Dick Wobus**, Yuejian Zhu Special thanks to Lacey HollandNCEP/EMC, MD*UCAR at NCEP/EMC;    **SAIC at NCEP/EMCMar. 30, 2004 Thanks also to Russ Treaton and Wan-shu Wu 

**Notes:**
Outline slide

## Motivation

- Currently breeding technique (Toth & Kalnay 1993,1997) used for generating initial ensemble perturbations.
-              Characteristics of current system
-   Nonlinearly fastest growing  perturbations,--Desirable, want to keep
-  Perturbations regionally rescaled to the same amplitude every day --
-    Not realistic, make perturbation amplitudes dependent on actual observational
-    density
-  Multiple breeding cycles run independently, perturbations somewhat dependent--
-    Make initial perturbations orthogonal.
-    ETKF produces analysis  perturbations based on ensemble forecasts from
-    previous cycle and observation locations.
-   Note:  Since initial perts are centered around 3D-Var analysis, they are still not direct
-    function of 3D-Var  analysis uncertainty.  For a fully consistent DA/Ensemble: (a)
-    implement full ETKF DA/ensmeble; (b) other alternatives based on 3D/4D-VAR.

## Ensemble-based Kalman Filters

-    Perturbed observation method (Houtekamer and
-    Mictchell 1998;   Burgers et al. 1998; stochastic solution).
-   Ensemble Transform Kalman Filter (ETKF)
-    (Bishop et al. 2001, Wang and Bishop 2002).
-    Ensemble Adjustment Kalman Filter (EAKF)
-     (Anderson 2001).
-   Ensemble Square-root Filter(EnSR) (Whitaker and
-    Hamil 2001).
-   Local Ensemble Kalman Filter (LEKF) (Ott et al. 2003,
-    Szunyogh 2004)
-    ETKF, EAKF, EnSR and LEKF are deterministic solutions of
-    ensemble Kalman filter equations

## ETKF Method

- It is based on Kalman filter theory to assimilate obs into NWP model.
- Input:     ensemble of fcst fields (K)  and observational data
- Output:   ensemble of (K) analysis perts
- Procedure:  standard Kalman filter equations
- Constraints:  fit obs into fcsts, given obs and fcst errors.
-      fcst and analysis perts are centered around ensemble
-      mean and analysis from SSI.   Only K-1 fcst and
-      analysis  perturbations are independent.
- Feature: analysis perts are orthogonal in observational space.

## Global temp obs distribution at 1500/01/03 

## Global wind obs distribution at 1500/01/03 

**Global wind obs distribution at 1500/01/03 **

## Total number of obs distribution  

- Are these fluctuations affecting quality of 3D-Var analysis?

## Local Spread of Energy Perts (ave over 0115-0215/03)                                                

## Vertical Spread Distribution of Energy Perts (ave over horizontal grid points and over 0115-0215/03)  

## Differences between the cases with and without WSR (Winter Storm Reconnaissance)  data(There are 7 days, about 20 dropsonde  observations each day)(a)   Vertical  ave rms analysis perts for Temp (K);                      (b) vertical ave rms analysis perts  for winds(m/s)  

## Mean eigenvalue distribution averaged over  0115/03-0215/03 (in normalized obs space) 

## Perts for Temp in 3-D Grid Point Space  

## Dim of Perts Subspace for Temp in 2-D Grid Point Space  

## Local Dimensions   

## Amplification Factor (6-Hour) 

## Average amplification factors of 5 optimally combined orthogonal perts from 5 original 3D Temp perts (6-hour)  

|  | GL | TR | NH | SH |
| --- | --- | --- | --- | --- |
| Breeding | 1.067 | 1.037 | 1.081 | 1.089 |
| ETKF | 1,035 | 1.033 | 1.037 | 1.032 |

## Amplification factors of  3D Temp perts  

## Summary – ETKF vs. Breeding  

-     Positive  Aspects:
-   The error variance is distributed more  evenly along different directions. The analysis perturbations are
-      orthogonal  in  observational space.  Difference in DOF is small.
-   In 3-D grid point space, both analysis and fcst perturbations based on ETKF span somewhat higher
-      dimensional subspaces than  those based on breeding method.
-   ETKF perts respond to the distributions of obs..
-    Negative  Aspects:
-  Amplification factor is lower than for bred vectors.
-  More noise in variance distributions.
-    Future work:
-   Compare PECA scores for both ETKF and breeding based systems.
-   Further study the features in 40 members.
-   Tuning global/hemispheric perturbation variances.
-   Optimization of code.
-   Potential  application to data assimilation..
-     Alternatives: (a) Orthogonalizing bred perts before applying regional rescaling.  (b) Replace constant rescaling in
-     breeding by field based info from 3D-VAR analysis