Hybrid 4D EnVar for the NCEP GFS(with comments on initialization)

Daryl Kleist1,3, Jeff Whitaker2, Kayo Ide3, and John Derber1

Lili Lei2,4, Rahul Mahajan1,5, Catherine Thomas1,3,5

1NOAA/NWS/NCEP/EMC2NOAA/OAR/ESRL/PSD

3University of Maryland4CIRES5IMSG

With acknowledgements to Dave Parrish (EMC), Ricardo Todling (NASA/GMAO), Xuguang Wang (OU), Ting Lei (OU) and many others

16th EnKF Workshop

Ensemble-Var methods: nomenclature

• En-4DVar: Propagate ensemble Pb from one assimilation window to the next (updated using EnKF for example), replace static Pb with ensemble estimate of Pb at start of 4DVar window, Pb propagated with tangent linear model within window.

• 4D-EnVar: Pb at every time in the assim. window comes from ensemble estimate (TLM no longer used).

• As above, with hybrid in name: Pb is a linear combination of static and ensemble components.

• 3D-EnVar: same as 4D ensemble Var, but Pb is assumed to be constant through the assim. window (current NCEP implementation).

2

3

EnKFmember update

member 2 analysis

high resforecast

GSIHybrid Ens/Var

high resanalysis

member 1 analysis

member 2 forecast

member 1 forecast

recenter analysis ensemble

Dual-Res Coupled HybridVar/EnKF Cycling

member 3 forecast

member 3 analysis

T254

L64

T574

L64

Generate new ensemble perturbations given the

latest set of observations and first-guess ensemble

Ensemble contribution to background error

covarianceReplace the EnKF

ensemble mean analysisand inflate

Previous Cycle Current Update Cycle

4D EnVar: The Way Forward ?

• Natural extension to operational 3D EnVar– Uses variational approach with already available 4D ensemble perts

• No need for development of maintenance of TLM and ADJ models– Makes use of 4D ensemble to perform 4D analysis – Modular, usable across a wide variety of models

• Highly scalable– Aligns with technological/computing advances

• Computationally inexpensive relative to 4DVAR (with TL/AD)– Estimates of improved efficiency by 10x or more, e.g. at Env. Canada (6x

faster than 4DVAR on half as many cpus)• Compromises to gain best aspects of (4D) variational and ensemble

DA algorithms• Other centers exploring similar path forward for deterministic NWP

– Canada (potentially replace 4DVAR), UKMO (potentially replace En4DVar)

Single Observation (-3h) Examplefor 4D Variants

5

4DVAR

H-4DVAR_ADf-1=0.25

H-4DENSVf-1=0.25

4DENSVTLMADJ

TLMADJ

ENSONLY

ENSONLY

6

Observing System SimulationExperiments (OSSE)

• Joint OSSE– International, collaborative effort between ECMWF, NASA/GMAO, NOAA

(NCEP/EMC, NESDIS, JCSDA), NOAA/ESRL, others– ECMWF-generated nature run (c31r1)

• T511L91, 13 month free run, prescribed SST, snow, ice• Observations from (operational) 2005/2006 observing system

developed– NCEP: ‘conventional’, sbuv ozone retrievals, GOES sounder radiances– NASA/GMAO: all other radiances (AMSUA/B, HIRS, AIRS, MSU)

• Older version of the CRTM• Simulated observation errors developed by Ron Errico

(GMAO/UMBC)– Horizontally correlated errors for radiances– Vertically correlated errors for conventional soundings

• Synthetic observations used in this study were calibrated by Nikki Prive (GMAO)

– Attempt to match impact of various observation types with results from data denial experiments

3D to 4D hybrid

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• Model/Assimilation• NCEP Global Forecast System

(GFS) (T382L64; post May 2011 version – v9.0.1)

• 80 member EnKF, 25% static hybrid, additive/mult. inflation

• Test Period• 01 July 2005-31 August 2005 (3

weeks ignored for spin-up)

• Analysis Error Difference (August)• H-4DEnVar (With TLNMC)

minus 3D hybrid

500 hPa AC (against EC NR)

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Constraint Options

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• Tangent Linear Normal Mode Constraint– Based on past experience and tests with 3D hybrid, default configuration

includes TLNMC over all time levels (quite expensive)

N

n

n

kn

kk1

ef xxCx α

• Weak Constraint “Digital Filter”– Construct filtered/initialized state as weighted sum of 4D states

iimmmmdfi ,J xxxx

u

1

i h k

K

kmkm xx

• Combination of the two– Apply TLNMC to center of assimilation window only in combination with JcDFI

(Cost effective alternative?)

Constraint impact (single case)• Impact on tendencies

• Dashed: Total tendencies• Solid: Gravity mode tendencies• All constraints reduce

incremental tendencies

• Impact on ratio of gravity mode/total tendencies• JcDFI increases ratio of gravity

mode to total tendencies• TLNMC most effective (but

most expensive)• Combined constraint potential

(cost effective alternative)

Analysis Error (cycled OSSE)

• Time mean (August) change in analysis error (total energy) relative to 4D hybrid EnVar experiment that utilized no constraints at all

• TLNMC universally better• Combined constraint mixed• JcDFI increases analysis error

Low Resolution GFS/GDASExperiments with real observations

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• Basic configuration– T254L64 GFS, opnl obs, GFS/GDAS cycles 20120701-20121001

• PR3LOEX0– 3DVAR

• PRHLOEX1– Hybrid 3D EnVar, 80 member T126L64 ensemble with fully

coupled (two-way) EnKF update, slightly re-tuned localization and inflation for lower resolution, TLNMC on total increment, 75% ensemble & 25% static

• PRH4DEX1– Hybrid 4D EnVar, TLNMC on all time levels, only 1x150

iterations– Hourly TC relocation, O-G, binning of observations

500 hPa Die Off Curves

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Northern Hemisphere Southern Hemisphere

4DHYB-3DHYB

3DVAR-3DHYB

Move from 3D Hybrid (current operations) to Hybrid 4D-EnVar yields improvement that is about 75% in amplitude in comparison from going to 3D Hybrid from 3DVAR.

4DHYB ----3DHYB ----3DVAR ----

4DHYB ----3DHYB ----3DVAR ----

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(Preliminary) Results and Comments

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• 4D extension has positive impact in OSSE and real observation (low resolution) framework

• 4D EnVar does have slower convergence• As configured, 4D EnVar was 40% more expensive than

3D hybrid (caveats being different iteration count, low resolution and machine variability)– TLNMC (balance constraint) over all time levels quite

expensive– I/O potential issue, optimization will be necessary

prior to implementation.• Option to post-process ensemble prior to use in assimilation

in subsequent cycle

(4D) Incremental Analysis Update

16

• In addition to TLNMC, we currently utilize full-field digital filter initialization in the GFS

– Can have undesirable impacts being a full field filter

• IAU (Bloom et al.) has been used at GMAO and elsewhere as alternative to DFI– Increment is passed to model throughout the window as a forcing term– However, this has typically been done using a 3D increment (rescaled) through the

window

• 4D EnVar lends itself to a minor modification of the IAU procedure to use the 4D increment

– This also provides a mechanism for passing the 4D solution to the model– Perhaps a way to help spin up/spin down of clouds, precipitation, etc.

• Promising preliminary results in EnKF context, work underway in 4D hybrid EnVar context

EnKF-IAU and EnKF-DFIEnKF-IAU noticeably better

17Courtesy of Lili Lei

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Temperature

Compare 6-h forecasts to EC analysisEnKF-IAU forecasts closer to EC analysis, esp for winds

Uwind (Vwind is similar to Uwind)

Courtesy of Lili Lei

Next Steps/Future Development

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• Configure update and outer loop– Continue to investigate use of IAU to force 4D increment into model

• Replace all other initialization options? Get rid of TLNMC as well?

– Quasi-outer loop (rerun of nonlinear model as in 4D Var)– Lengthen assimilation window (backward) in catch-up cycle

• May require temporal localization (code in place courtesy of OU collaboration)

• Test role of stochastic physics as replacement for additive inflation in 4D EnVar context

• Improved (or at least tuned) localization• Optimize static B for 4D hybrid

– Computationally (current static B is bottleneck in code)– Add temporal information (FOTO)– Weights, including scale-dependence– Increase role of ensemble (to 100%?)

• 4D EnVar tentatively scheduled to be part of GDAS/GFS upgrade in 2015

Backup Slides

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Time Evolution of Increment

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t=-3h

t=0h

t=+3h

H-4DVAR_AD H-4DENSV

Solution at beginning of window same to within round-off (because observation is taken at that time, and same weighting parameters used)

Evolution of increment qualitatively similar between dynamic and ensemble specification

** Current linear and adjoint models in GSI are computationally impractical for use in 4DVAR other than simple single observation testing at low resolution

TLMADJ ENSONLY

Accounting for under-represented source of uncertainty

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• Current operations – Multiplicative inflation – Helps compensate for finite-sized ensemble– Additive perturbations – Helps compensate for lack of consideration of

model uncertainty

• Proposed configuration for T1534 SL (3072 x 1536) GFS– Keep multiplicative inflation– Reduce additive perturbations from 32 to 5% – Add stochastic physics in model

• SPPT -- Stochastic Physics Perturbation Tendency• SKEB – Stochastic Energy Backscatter• VC – Vorticity Confinement• SHUM – Boundary Layer Humidity perturbations

• See talk by Jeff Whitaker in Session 9

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Better spread behavior (2014042400)

• Current operations – Spread too large– Spread decays and

recovers

• Stochastic Physics– Spread decreased

overall (consistent with error estimates)

– Spread grows through assimilation window

3HR6HR9HR

Hybrid ensemble-4DVAR[H-4DVAR_AD]

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K

kkkkkkkkJ

10

1T00

1f

T00 2

1

2

1dxMHRdxMHxBxx

Incremental 4DVAR: bin observations throughout window and solve for increment at beginning of window (x0’). Requires linear (M) and adjoint (MT) models

K

kkkkkkkk

N

n

nn,J

10

1T0

1

1T

ef1

fT

fff

2

1

2

1

2

1

dxMHRdxMH

αLαxBxαx

Can be expanded to include hybrid just as in the 3DHYB case

N

n

nn

1ef0 xαTxx

With a static and ensemble contribution to the increment at the beginning of the window

ADJ

ADJ TLM

TLM

4D-Ensemble-Var[4DENSV]

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As in Buehner (2010), the H-4DVAR_AD cost function can be modified to solve for the ensemble control variable (without static contribution)

Where the 4D increment is prescribed exclusively through linear combinations of the 4D ensemble perturbations

Here, the control variables (ensemble weights) are assumed to be valid throughout the assimilation window (analogous to the 4D-LETKF without temporal localization). Need for computationally expensive linear and adjoint models in the minimization is conveniently avoided.

K

kkkkkkkk

N

n

nnJ1

1T

1

1T

2

1

2

1dxHRdxHαLαα

N

n

n

kn

k1

exαTx

Hybrid 4D-Ensemble-Var[H-4DENSV]

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The 4DENSV cost function can be easily expanded to include a static contribution

Where the 4D increment is prescribed exclusively through linear combinations of the 4D ensemble perturbations plus static contribution

Here, the static contribution is considered time-invariant (i.e. from 3DVAR-FGAT). Weighting parameters exist just as in the other hybrid variants. Again, no TLM or ADJ.

K

kkkkkkkk

N

n

nn,J

1

1T

1

1T

ef1

fT

fff

2

1

2

1

2

1

dxHRdxH

αLαxBxαx

N

n

n

kn

k1

ef xαTxx