Implementation plans of Hybrid 4D EnVar for the NCEP GFS Rahul Mahajan1,4, Daryl Kleist1,3, Jeff Whitaker2, and John Derber1 1NOAA/NWS/NCEP/EMC 2NOAA/OAR/ESRL/PSD 3University of Maryland 4IMSG With contributions from Lili Lei (CIRES), Misha Rancic (EMC), Catherine Thomas (IMSG) and many others WWOSC 2014, Montreal

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).

CURRENT 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 3D Hybrid Ens/Var high res forecast high res analysis T574L64 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) Example for 4D Variants TLMADJ 4DENSV ENSONLY H-4DVAR_AD bf-1=0.25 H-4DENSV bf-1=0.25 TLMADJ

Low Resolution GFS/GDAS Experiments 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

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.

(Preliminary) Results and Comments 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 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 noticeably better EnKF-IAU and EnKF-DFI EnKF-IAU noticeably better

Compare 6-h forecasts to EC analysis EnKF-IAU forecasts closer to EC analysis, esp for winds Temperature Uwind (Vwind is similar to Uwind)

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

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

PROPOSED - 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 T574L64 EnKF member update member 2 forecast member 2 analysis recenter analysis ensemble Ensemble contribution to background error covariance member 3 analysis member 3 forecast GSI 4D Hybrid Ens/Var Replace the EnKF ensemble mean analysis and inflate high res forecast T1534L64 Low-to-high res analysis Previous Cycle Current Update Cycle

Tests for FY2015 Implementation 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