Implementation plans of Hybrid 4D EnVar for the NCEP GFS

Rahul Mahajan1,4, Daryl Kleist1,3, Jeff Whitaker2, and John Derber1

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

3University of Maryland4IMSG

With contributions from Lili Lei (CIRES), Misha Rancic (EMC), Catherine Thomas (IMSG) and many others

WWOSC 2014, Montreal

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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).

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EnKFmember update

member 2 analysis

high resforecast

GSI 3DHybrid Ens/Var

high resanalysis

member 1 analysis

member 2 forecast

member 1 forecast

recenter analysis ensemble

CURRENT 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 perturbations

• 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

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4DVAR

H-4DVAR_ADf-1=0.25

H-4DENSVf-1=0.25

4DENSVTLMADJ

TLMADJ

ENSONLY

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 ----

(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 is needed prior to

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

in subsequent cycle

(4D) Incremental Analysis Update

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• 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

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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)

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

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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

Wind

Tv

Q

Current Stoch. Phy

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EnKFmember update

member 2 analysis

high resforecast

GSI 4DHybrid Ens/Var

Low-to-high res analysis

member 1 analysis

member 2 forecast

member 1 forecast

recenter analysis ensemble

PROPOSED - Dual-Res Coupled HybridVar/EnKF Cycling

member 3 forecast

member 3 analysis

T574

L64

T153

4L64

Generate new ensemble perturbations given the

latest set of observations and first-guess ensemble

Ensemble contribution to background error

covariance

Replace the EnKF ensemble mean analysis

and inflate

Previous Cycle Current Update Cycle

Tests for FY2015 Implementation

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• Analysis on ensemble grid at T574 instead of hi-res deterministic grid T1534• Configure update and outer loop

– Quasi-outer loop (rerun of nonlinear model as in 4D Var)– Re-scale ensemble perturbations for successive outer-loops?

• Continue to investigate use of IAU to force 4D increment into model• Test role of stochastic physics as replacement for additive inflation• Relaxed binning criteria within the assimilation window• Lengthen assimilation window (backward) in catch-up cycle• 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 late 2015