GMAO Hybrid Ensemble 3D-Var

Amal El Akkraoui and Ricardo TodlingGlobal Modeling and Assimilation Office

Many thanks to: D. Kleist, D. Parish, J. Whitaker, and R. Treadon.

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Outline

1 Background and motivation

2 Experiment Settings

3 Results

4 Summary and ongoing work

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Background and motivation

Background and motivation

Use flow-dependent background error information derived fromensemble techniques but still within the variational framework.The 3D-Var cost function:

J(δx) =12δxTB−1δx +

12(Hδx − y′)TR−1(Hδx − y′)

The hybrid 3D-Var cost function:

J(x′) =12x′T (βB + (1− β)Pe ◦ S)−1x′ +

12(Hx′ − y′)TR−1(Hx′ − y′)

x′ = δx +K∑

k=1

ak ◦ xek , and Pe =K∑

k=1

xek(xek)

T

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Experiment Settings

Experiment setting

Control run (Ctl):

Conventional 3D-Var;analysis at 0.5o ;forecasts at 0.5o ;close run to ops.

Ensemble:32 members at 1o ; S-EnKF;Additive inflation; Verticallyvarying localization scales;Re-centering around ctl ana.

Hyrid run (Hyb):

Dual resolution (central at 0.5o , ensemble at 1o); β = 0.5;members re-centered around the central analysis.Time frame: mid-November through end of december 2011.2-week spin up period, and hybrid starts on Dec 1st.

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Results

Results: OMF —— Hyb —— Ctl

Uwind

Temp

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Results

Results: Monthly means (Temperature)

Ctl vs. NCEP Hyb vs. NCEP

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Results

Results: Monthly means (Temperature)

Ctl vs. ECMWF Hyb vs. ECMWF

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Results

Results: Monthly means (U-winds)

Ctl vs. NCEP Hyb vs. NCEP

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Results

Results: Monthly means (U-winds)

Ctl vs. ECMWF Hyb vs. ECMWF

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Results

Results: Monthly means (U-winds at 200 mb)

vs. NCEP vs. ECMWF

Ctl

Hyb

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Results

Forecast skills: Anomaly correlations ( 500 mb height)

—— Ctl —— hyb

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Results

Forecast skills: Anomaly correlations (500 mb Uwind)

—— Ctl —— hyb

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Results

Forecast skills: Anomaly correlations (200/850 Uwind)

—— Ctl —— hyb

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Results

Forecast skills: RMS ( Temperature tropics )

—— Ctl —— hyb

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Results

Forecast skills: RMS ( Uwind tropics )

—— Ctl —— hyb

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Summary and ongoing work

Summary

Overall, the results are significantly positive : largely positive for thetropical winds around 500-200mb, and slightly positive to neutralelsewhere;Ensemble likely to be pointing to a weakness in the static B in thetropics;Still need to examine why the hybrid impact is marginal fortemperature for instance.

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Summary and ongoing work

What next?

Better understand the added value of the ensemble in a hybrid modeby exploring other hybrid configurations:− Experiment with a different values of the weighting parameter β;− Experiment with a higher resolution ensemble; 32 members at 1/2

degree. (Ongoing) ;− Experiment with a larger ensemble size (64 members at 1 degree);− Evaluate which is more beneficial, reducing the sampling error

(large ens. size) or the representiveness error (higher resolutionensemble).Examine the stratospheric levels.

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