Current status of the GMAOHybrid Ensemble 3D-Var

Amal El Akkraoui and Ricardo TodlingGlobal Modeling and Assimilation Office

Contributions from: D. Kleist, D. Parish, J. Whitaker, and R. Treadon.

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Outline

1 Background and motivation

2 Some elements of the hybrid system

3 Results

4 Summary

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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(xe

k)T

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Background and motivation

GEOS DAS IAU-Based 3D-Var

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Background and motivation

GEOS DAS IAU-Based Hybrid 3D-Var

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Background and motivation

Hybrid schematic

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Some elements of the hybrid system

Current hybrid configuration:

Hybrid 3D-Var:1 32 members; S-EnKF;2 Dual resolution (central at 0.5o , ensemble at 1o);3 Covariance weights: β = 0.5 (50% Bsta / 50%Bens);4 Re-centering of the members around the central analysis;5 Blending of the members in the upper stratosphere;6 Multiplicative and additive inflation;7 Vertically varying localization scales (same for the

ensemble and the hybrid);

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Some elements of the hybrid system

Covariance Weights: T increment for one T-obs at 45N

β = 0 (full static) β = 0.5 β = 1 (full ensemble)

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Some elements of the hybrid system

Covariance Weights: Vertically varying weights

Pressurelevels

-0.5 0 0.5 1 1.5

0.01

0.1

1

10

100

1000

β_sβ_e

Cov. weights (βstat and βens)

Original transition between 5 and 1 mb.

Try deepening this layer (20 and 5 mb) to avoid the stratopause and thetransition layer for the temperaturegradients; Amsua-14 peaks at around 2mb; interactions between verticallocalization scales, covariance weights,and balance might be challenging.

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Some elements of the hybrid system

Covariance Weights: Vertical transition layer

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Some elements of the hybrid system

Ensemble post-analysis:Re-centering & additive inflation

The EnKF updates: the ensemble mean and the ensemble ofbackground perturbationsBoth products go through some "post-analysis" step before theperturbations are evolved in time to the next cycle :

Inflation (additive and/or multiplicative) for the members;Re-centering of the members around a new mean (central)⇒ the ensemble mean is modified.

post-analysis

xanai ⇐ xana

i − x̄a + xc + αεinfi

δxanai ⇐ δxana

i + δxrec + αεinfi

How large should the additive inflation be ... without compromisingthe enkf analysis?How does the dual resolution affect the size of the re-centeringincrement?

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Some elements of the hybrid system

Inflation : NMC-like additive perturbations

Mem1: Uwind analysis incr at 500mb + α x additive inflation

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Some elements of the hybrid system

Re-centering: Impact of the ensemble resolution

High/Low res Ensemble mean - Control analysis

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Some elements of the hybrid system

Re-centering: Impact of the ensemble resolution

OMF - U wind raob

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Some elements of the hybrid system

Low-res ens: inflation + re-centering

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Some elements of the hybrid system

High-res ens: inflation + re-centering

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Some elements of the hybrid system

Filter-free Hybrid 3D-Var:By-passing the EnKF: create the ensemble by "perturbing" the centralanalysis using the additive inflation perturbations

Each ensemble member is created as

{x}i = xc + α{εinf }i

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Some elements of the hybrid system

Filter-free Hybrid 3D-Var:

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Some elements of the hybrid system

Results: Showing Enkf-based hybrid results only

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

Summary

Overall3D-hybrid approach results show positive impact:noticeable reduction of model biases and improved skillscores;The filter-free scheme is also showing promising results;More configurations are currently being tested(64-member ensemble, hi-resolution ensemble)

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