Hybrid 4D EnVar for the NCEP GFS

1. 12th JCSDA Workshop – May 2014 Hybrid 4D EnVar for the NCEP GFS Daryl Kleist1,3, Jeff Whitaker2, Kayo Ide3, and John Derber1 Lili Lei2,4, Rahul Mahajan1,5, Catherine Thomas1,3,5 1NOAA/NWS/NCEP/EMC 2NOAA/OAR/ESRL/PSD 3University of Maryland 4CIRES 5IMSG With acknowledgements to Dave Parrish (EMC), Ricardo Todling (NASA/GMAO), Xuguang Wang (OU), Ting Lei (OU) and many others

2. Ensemble-Var methods: nomenclature En-4DVar: Propagate ensemble Pbfrom one assimilation window to the next (updated using EnKF for example), replace static Pb with ensemble estimate of Pb at start of 4DVar window, Pbpropagated with tangent linear model within window. 4D-EnVar: Pbat every time in the assim. window comes from ensemble estimate (TLM no longer used). As above, with hybrid in name: Pbis a linear combination of static and ensemble components. 3D-EnVar: same as 4D ensemble Var, but Pbis assumed to be constant through the assim. window (current NCEP implementation).

3. Dual-Res Coupled Hybrid Var/EnKF Cycling Generate new ensemble perturbations given the latest set of observations and first-guess ensemble member 1 forecast member 1 analysis T254L64 EnKF member update member 2 forecast member 2 analysis recenter analysis ensemble member 3 analysis member 3 forecast Ensemble contribution to background error covariance Replace the EnKF ensemble mean analysis and inflate GSI Hybrid Ens/Var high res forecast high res analysis T574L64 ** Implemented into GDAS/GFS in May 2012 Previous Cycle Current Update Cycle

4. 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 (to replace 4DVAR later this year), UKMO (potentially replace En4DVar)

5. Hybrid 4D-Ensemble-Var[H-4DENSV] Extension of 3D hybrid to 4D straightforward 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. No TLM or ADJ.

6. Single Observation (-3h) Examplefor 4D Variants ENSONLY 4DVAR TLMADJ 4DENSV H-4DVAR_AD bf-1=0.25 H-4DENSV bf-1=0.25 TLMADJ ENSONLY

7. Time Evolution of Increment TLMADJ ENSONLY 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 t=-3h t=0h t=+3h H-4DENSV H-4DVAR_AD

8. 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

9. 3D to 4D hybrid • 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

10. 500 hPa AC (against EC NR)

11. Constraint Options • Tangent Linear Normal Mode Constraint (Kleist et al. 2009) • Based on past experience and tests with 3D hybrid, default configuration includes TLNMC over all time levels (quite expensive) • Weak Constraint “Digital Filter” • Construct filtered/initialized state as weighted sum of 4D states • Combination of the two • Apply TLNMC to center of assimilation window only in combination with JcDFI (Cost effective alternative?)

12. 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

13. Low Resolution GFS/GDASExperiments with real observations • 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

14. 500 hPa Die Off Curves Southern Hemisphere Northern Hemisphere 4DHYB ---- 3DHYB ---- 3DVAR ---- 4DHYB ---- 3DHYB ---- 3DVAR ---- 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.

16. (Preliminary) Results and Comments • 4D extension has positive impact in OSSE and real observation (low resolution) framework • 4D EnVar does have slower convergence (not shown) • 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 • Lots of time spent in I/O, optimization will be necessary prior to implementation.

17. (4D) Incremental Analysis Update • 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

18. EnKF-IAU and EnKF-DFI EnKF-IAU noticeably better Courtesy: Lili Lei

19. 2014 GFS/GDAS Implementation • T1534 Semi-Lagrangian GFS (~13km), no change in vertical resolution • High resolution SST • Physics Changes • Full resolution to 10 Days • 80 Member T574 SL GFS EnKF-based hybrid • Significantly reduce additive inflation with more appropriate treatment of system uncertainty • Analysis on the ensemble grid and not T1534 grid • Observation improvements yielding significant gains in SH

20. Accounting for under-represented source of uncertainty • 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

21. Better spread behavior (2014042400) 3HR 6HR 9HR • Current operations • Spread too large • Spread decays and recovers • Stochastic Physics • Spread decreased overall (consistent with error estimates) • Spread grows through assimilation window

22. Next Steps/Future Development • 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 (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 EnVartentatively scheduled to be part of GDAS/GFS upgrade in 2015

23. Beyond Initial Implementation • Unification of DA (EnKF and GSI Hybrid) codes • EVIL – Auligne/NCAR • Mean-Pert – Lorenc/Met Office (ensemble of EnVars) • Can EnKF replace Var? • VarBC for satellite assimilation • Physical space localization • Hybridization • Ease of implementation of noise control and balance equations • Improve static B within 4D EnVar hybrid • Add temporal information without TLM/ADJ? • Role of 4D hybrid on cloudy assimilation • Designing effective noise-control and balancing mechanisms • How to improve ensemble? • Resolution • Ensemble size • Does stochastic physics provide enough spread in cloud, for example, or effective assimilation?

24. Backup Slides

25. Hybrid ensemble-4DVAR[H-4DVAR_AD] Incremental 4DVAR: bin observations throughout window and solve for increment at beginning of window (x0’). Requires linear (M) and adjoint (MT) models ADJ TLM Can be expanded to include hybrid just as in the 3DHYB case ADJ TLM With a static and ensemble contribution to the increment at the beginning of the window

26. 4D-Ensemble-Var[4DEnVar] 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.

27. 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)