# Presentation: 865275

## An Analysis of the Impact of Observational Data on ETKF-based Ensemble Perturbations Mozheng Wei*, Zoltan Toth, Dick Wobus**, Yuejian Zhu, Craig Bishop*** and Xuguang Wang****NCEP/EMC, MD*UCAR at NCEP/EMC;    **SAIC at NCEP/EMC***UCAR at NRL, CA;    **** Penn State Uni. PA Jan. 12, 2004

**Notes:**
Outline slide

## Motivation

- Currently breeding technique (Toth & Kalnay 1993,1997) used for generating initial ensemble perturbation.
-              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 distribution
-    of observational data.
-  Multiple breeding cycles run independently, perturbations somewhat dependent.
-    make initiail perturbations orthogonal.
-    ETKF should produce optimal analysis  perturbations based on ensemble
-    forecasts from previous cycle and observations.  (if only 1 pert in ETKF,
-    it will be similar to bred vector under certain condition)

## Ensemble-based Kalman Filters

-   Perturbed observation method (Houtekamer and
-    Mictchell 1998;   Burgers et al. 1998).
-   Ensemble Transform Kalman Filter (ETKF)
-    (Bishop et al. 2001, Wang and Bishop 2002).
-   Ensemble Adjustment Kalman Filter (EAKF)
-     (Anderson 2001).
-   Ensemble Square-root Filter (Whitaker and Hamil 2001).
-   Local Ensemble Kalman Filter (Ott et al. 2003, Szunyogh
-    2004)

## ETKF Formulation (Bishop et al 2001)

**Notes:**
CIRA operational and research experience

## Slide 5

## Slide 6

## Total number of obs distribution  

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

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

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

## 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) 

## Ratio of ana/fcst variance by time in normalizedobs space (from 0115-0215/03)

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

## Ratio of Ana/Fcst Spread (ave over 0115-0215/03) Breeding                                                ETKF  

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

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

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

## Summary   

-   All the conventional data (rawinsonde and aircraft data etc) plus some retrieval  products
-      from satellite at all levels were included,   more satellite data will be in  future.
-      Only T, U  and  V were considered,   we plan to extend this to include  more  variables,
-      such as surface pressure, humidity and precipitation.
-    The error variances  along different  analysis perturbations  based on ETKF are  more  evenly
-      distributed  compared  with current  breeding method. The analysis perturbations are orthogonal
-      in  observational space.
-   In 3-D grid point space, both analysis and fcst perturbations based on ETKF span higher
-      dimensional subspaces than  those based on breeding method.
-   The impact of obs is clearly picked up by ETKF.
-   Orthogonalization of 40 members
-    Tuning global/hemispheric perturbation variances.
-    Optimization of code.
-    Potential  application to data assimilation..