Hybrid Variational-Ensemble Data Assimilation at NCEP Daryl Kleist NOAA/NWS/NCEP/EMC with acnowledgements to Kayo Ide, Dave Parrish, Jeff Whitaer, John Derber, Russ Treadon, Wan-Shu Wu, Jacob Carley, and Mingjing Tong The 4th Annual PSU-UMD DA Worshop 3 December 202
Outline Introduction (Brief) bacground on hybrid data assimilation Hybrid Var/Ens at NCEP: Present and Future Research Developments (toward improving global hybrid) 4DEnsVar (and hybridization) Scale-dependent weights 2
Kalman Filter in Variational Setting Forecast Step Analysis K T B = MA M + Q KF a A = b t + = KF b = + K M KF ( a ) ( o b y H ) ( T ) R+ HB T = BKFH KFH ( I KH) B KF t Etended Kalman Filter Analysis step in variational framewor (cost function) J KF 2 ( ) ( ) T ( ) ( ) T = B + H y R ( H y ) B KF : Time evolving bacground error covariance A KF KF = B KF + 2 H T R H 3
b f & b e : weighting coefficients for fied and ensemble covariance respectively t : (total increment) sum of increment from fied/static B ( f ) and ensemble B a : etended control variable; :ensemble perturbations - analogous to the weights in the LETKF formulation L: correlation matri [effectively the localization of ensemble perturbations] 4 Hybrid Variational-Ensemble (ignoring preconditioning for simplicity) Incorporate ensemble perturbations directly into variational cost function through etended control variable Lorenc (2003), Buehner (2005), Wang et. al. (2007), etc. e ( ) ( ) ( ) ( ) ( ) ( ) ( ) y H R y H L B + + = = t T t T e f f T f f f 2 2 2 N n n n β β, J α α α ( ) = + = N n n n e f t α
Single Temperature Observation 3DVAR b f - =0.0 b f - =0.5 5
Outline Introduction (Brief) bacground on hybrid data assimilation Hybrid Var/Ens at NCEP: Present and Future Research Developments (toward improving global hybrid) 4DEnsVar (and hybridization) Scale-dependent weights 6
NOAA s NWS Model Production Suite Climate CFS MOM3 Hurricane GFDL HWRF Coupled Oceans HYCOM WaveWatch III.7B Obs/Day Satellites 99.9% Global Data Assimilation Regional Data Assimilation Global Forecast System North American Ensemble Forecast System GFS, Canadian Global Model NOAH Land Surface Model Regional NAM NMM-B Short-Range Ensemble Forecast WRF: ARW, NMM NMM-B Dispersion ARL/HYSPLIT Severe Weather WRF NMM/ARW Worstation WRF Air Quality NAM/CMAQ *Rapid Update for Aviation For eca st 7
GDAS Hybrid: 22 May 202 Pacage included other changes NPP ATMS (MW): 7 months after launch!! This is by far the fastest we have ever begun assimilating data from a new satellite sensor after launch GPS RO Bending Angle replaced Refractivity Summary of pre-implementation retrospective testing Improved Tropical winds Improved mid-latitude forecasts Fewer Dropouts Improved fits to observations of forecasts Some improvement in NA precip. in winter Increased bias in NA precip. decreased rain/no rain sill in summer (Improved by land surface bug fi) Overall significant improvement of GFS forecasts 8
TC Trac Error Reduction HYBRID TEST GFS OPERATIONAL NHC/JTWC OFFICIAL 9
500 hpa AC Northern Hemisphere Southern Hemisphere 0
NAM vs NAM parallels upper air stats vs raobs Ops NAM = Solid ; NAMB (with Physics changes) = Dashed ; NAMX (with physics changes and using global EnKF in GSI) = Dash-Dot Height RMS error Vector Wind RMS error Ops NAM NAMB (improved physics) NAMX (improved physics + EnKF) Thans to Eric Rogers and Wan-Shu Wu Day = Blac Day 2 = Red Day 3 = Blue
RAP hybrid DA using global ensemble 3dvar hybrid Temp Rel Hum hybrid 3dvar RAP GSI-hybrid vs. RAP GSI-3dvar upper-air verification + 6 h forecast RMS Error 28 Nov 3 Dec 202 Wind 3dvar hybrid
Assimilation of NOAA-P3 Tail Doppler Radar (TDR) Data using GSI hybrid method for HWRF HWRF Model: 3 domains with 0.8-0.06-0.02 degree (27-9-3 m) horizontal resolutions, 43 vertical levels with model top at 50 hpa, with ocean coupling TC environment cold start from GDAS forecast, TC vorte cycled from HWRF forecast GSI hybrid analysis using GFS EnKF ensemble Ø 80% of bacground error covariance from ensemble B. Ø Horizontal localization 50 m, vertical localization 0 model levels for wea storm and 20 model levels for strong storm Conventional data plus TDR data Modified gross error chec, re-tuned observation error and rejected data dump with very small data coverage for TDR data 9 TDR missions for Hurricane Isaac, Leslie and Sandy TDR data for Isaac 20208272
Hybrid Ensemble-3DVar Radar Data Assimilation Forecast Hourly Maimum Updraft Helicity (Kain et al. 20) Over hr Forecast Period Valid April 22 0-02 UTC 2007 GSI + NMMB (currently operational NAM code,.33 m grid spacing) Assimilate both dbz and velocity over a hour period at 5 min. intervals Followed by hr forecast Eperiments: 3DVar Single, deterministic simulation Hybrid ensemble-3dvar (32 ensemble members) 3 configurations 25%, 50%, 75% static B contribution (Hyb B25, Hyb B50, Hyb B75) Control (CTL) No data assimilation Single, deterministic forecast CTL Ensemble probability of UH >= 00 m 2 s -2 Hyb B75 Hyb B50 3DVar Hyb B25
Outline Introduction (Brief) bacground on hybrid data assimilation Hybrid Var/Ens at NCEP: Present and Future Research Developments (toward improving global hybrid) 4DEnsVar (and hybridization) Scale-dependent weights 5
4D-Ensemble-Var [4DENSV] As in Buehner (200), the H-4DVAR_AD cost function can be modified to solve for the ensemble control variable (without static contribution) J 2 N ( ) ( ) ( ) n T n ( ) T α = α L α + H ( ) y R H y n= 2 K = Where the 4D increment is prescribed eclusively through linear combinations of the 4D ensemble perturbations = ( N ( ) ) n n α e n= Here, the control variables (ensemble weights) are assumed to be valid throughout the assimilation window (analogous to the 4D-LETKF without temporal localization). Note that the need for the computationally epensive linear and adjoint models in the minimization is conveniently avoided. 6
7 Hybrid 4D-Ensemble-Var [H-4DENSV] The 4DENSV cost function can be easily epanded to include a static contribution Where the 4D increment is prescribed eclusively 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 eist just as in the other hybrid variants. ( ) ( ) ( ) ( ) ( ) ( ) ( ) = = + + = K N n n n, J T T e f f T f f f 2 2 2 y H R y H L B α α α β β ( ) ( ) = + = N n n n f e α
Single Observation (-3h) Eample for 4D Variants 4DVAR 4DENSV H-4DVAR_AD b f - =0.25 H-4DENSV b f - =0.25 8
Time Evolution of Increment t=-3h Solution at beginning of window same to within round-off (because observation is taen at that time, and same weighting parameters used) t=0h Evolution of increment qualitatively similar between dynamic and ensemble specification t=+3h ** Current linear and adjoint models in GSI are computationally unfeasible for use in 4DVAR other than simple single observation testing at low resolution H-4DVAR_AD H-4DENSV 9
OSSE-based comparison of 3DHYB and H-4DENSV (with dynamic constraints) U T Q 4DHYB-3DHYB Something in the 4D eperiments is resulting in more moisture in the analysis, triggering more convective precipitation 20
Scale-Dependence Motivation (Courtesy: Tom Hamill) 2
Spectrum of Dual-Resolution Increment with SD-weighting 22
Initial scale-dependent tests in and OSSE 23
Summary NCEP successfully implemented hybrid variational-ensemble algorithm into GDAS NCEP aggressively pursuing application of hybrid to other systems Mesoscale (NAM), HWRF, Rapid Refresh (and HRRR follow on), storm scale ensemble Future Reanalysis Have already run preliminary tests for 98-983 periods, attempting to capture QBO transitions (a notoriously difficult problem for reduced observing system periods) Etensions to the GDAS hybrid are ongoing, including 4DEnsVar (with a planned future implementation, much lie the UKMO and Canadians) 24
6 th WMO Symposium on DA NCEP will be hosting the net WMO DA Symposium from 7- October 203 at NCWCP Call for papers will be out in a month or two Register early, as space will be limited Will potentially be looing for volunteers to help out, especially during wee of the symposium 25