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Hybrid Variational-Ensemble Data Assimilation at NCEP

Hybrid Variational-Ensemble Data Assimilation at NCEP. NOAA/NWS/NCEP/EMC. Daryl Kleist. with acknowledgements to Kayo Ide , Dave Parrish, Jeff Whitaker, John Derber , Russ Treadon , Wan- Shu Wu, Jacob Carley , and Mingjing Tong.

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Hybrid Variational-Ensemble Data Assimilation at NCEP

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  1. Hybrid Variational-Ensemble Data Assimilation at NCEP NOAA/NWS/NCEP/EMC Daryl Kleist with acknowledgements to Kayo Ide, Dave Parrish, Jeff Whitaker, John Derber, Russ Treadon, Wan-Shu Wu, Jacob Carley, and Mingjing Tong Workshop on Probabilistic Approaches to Data Assimilation for Earth Systems Banff, Alberta, Canada – February 2013

  2. Outline • Introduction • (Brief) background on hybrid data assimilation • Hybrid Var/Ens at NCEP • OSSE-based hybrid experiments • Future Work and Summary

  3. Hybrid Variational-Ensemble(ignoring preconditioning for simplicity) • Incorporate ensemble perturbations directly into variational cost function through extended control variable • Lorenc (2003), Buehner (2005), Wang et. al. (2007), etc. bf & be: weighting coefficients for fixed and ensemble covariance respectively xt’: (total increment) sum of increment from fixed/static B (xf’) and ensemble B ak: extended control variable; :ensemble perturbations - analogous to the weights in the LETKF formulation L: correlation matrix [effectively the localization of ensemble perturbations]

  4. Single Temperature Observation 3DVAR bf-1=0.0 bf-1=0.5

  5. Outline • Introduction • (Brief) background on hybrid data assimilation • Hybrid Var/Ens at NCEP • OSSE-based hybrid experiments • Future Work and Summary

  6. Forecast NOAA’s NWS Model Production Suite Oceans HYCOM WaveWatch III Climate CFS Coupled Hurricane GFDL HWRF MOM3 1.7B Obs/Day Satellites 99.9% Dispersion ARL/HYSPLIT Regional NAM NMM-B Global Forecast System Global Data Assimilation Severe Weather Regional Data Assimilation WRF NMM/ARW Workstation WRF Short-Range Ensemble Forecast North American Ensemble Forecast System Air Quality WRF: ARW, NMM NMM-B GFS, Canadian Global Model NAM/CMAQ *Rapid Update for Aviation NOAH Land Surface Model

  7. GDAS Hybrid: 22 May 2012 • Package 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 skill in summer (Improved by land surface bug fix) • Overall significant improvement of GFS forecasts

  8. TC Track Error Reduction HYBRID TEST GFS OPERATIONAL NHC/JTWC OFFICIAL

  9. Impact on Geopotential Height 1000 mb NH 500 mb SH 3DHYB-3DVAR

  10. 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 Vector Wind RMS error Height RMS error Ops NAM NAMB (improved physics) NAMX (improved physics + EnKF) Day 1 = Black Day 2 = Red Day 3 = Blue Thanks to Eric Rogers and Wan-Shu Wu

  11. RAP hybrid DA using global ensemble Temp Rel Hum 3dvar hybrid hybrid 3dvar Wind RAP GSI-hybrid vs. RAP GSI-3dvar upper-air verification 3dvar hybrid + 6 h forecast RMS Error 28 Nov – 3 Dec 2012

  12. Assimilation of NOAA-P3 Tail Doppler Radar (TDR) Data using GSI hybrid method for HWRF TDR data for Isaac 2012082712 • HWRF Model: 3 domains with 0.18-0.06-0.02 degree (27-9-3 km) horizontal resolutions, 43 vertical levels with model top at 50 hPa, with ocean coupling • TC environment cold start from GDAS forecast, TC vortex cycled from HWRF forecast • GSI hybrid analysis using GFS EnKF ensemble • 80% of background error covariance from ensemble B. • Horizontal localization 150 km, vertical localization 10 model levels for weak storm and 20 model levels for strong storm • Conventional data plus TDR data • Modified gross error check, re-tuned observation error and rejected data dump with very small data coverage for TDR data • 19 TDR missions for Hurricane Isaac, Leslie and Sandy

  13. Outline • Introduction • (Brief) background on hybrid data assimilation • Hybrid Var/Ens at NCEP • OSSE-based hybrid experiments • Future Work and Summary

  14. Observing System SimulationExperiments (OSSE) • Typically used to evaluate impact of future observing systems • Doppler-winds from spaced-based lidar, for example • Useful for evaluating present/proposed data assimilation techniques since ‘truth’ is known • Series of experiments are carried out to test hybrid variants • 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

  15. Availability of SimulatedObservations [00z 24 July] SURFACE/SHIP/BUOY SONDES AMSUA/MSU AIRS/HIRS AMVS AIRCRAFT PIBAL/VADWND/PROFLR SSMI SFC WIND SPD AMSUB GOES SOUNDER

  16. 3D Experimental Design • Model • NCEP Global Forecast System (GFS) model (T382L64; post May 2011 version – v9.0.1) • Test Period • 01 July 2005-31 August 2005 (3 weeks ignored for spin-up) • Observations • Calibrated synthetic observations from 2005 observing system (courtesy Ron Errico/Nikki Privi) • 3DVAR • Control experiment with standard 3DVAR configuration (time mean increment compared to real system and found to be quite similar) • 3DHYB • Ensemble (T190L64) • 80 ensemble members, EnSRF update, GSI for observation operators • Additive and multiplicative inflation • Dual-resolution, 2-way coupled • High resolution control/deterministic component • Ensemble is recentered every cycle about hybrid analysis • Discard ensemble mean analysis • Parameter settings • bf-1=0.25, be-1=0.75 [25% static B, 75% ensemble] • Level-dependent localization

  17. Time Series of Analysis andBackground Errors • Solid (dashed) show background (analysis) errors • 3DHYB background errors generally smaller than 3DVAR analysis errors (significantly so for zonal wind) • Strong diurnal signal for temperature errors due to availability of rawinsondes 500 hPa U 850 hPa T

  18. 3DVAR and 3DHYBAnalysis Errors U T Q 3DVAR 3DHYB 3DHYB-3DVAR

  19. Zonal Wind BackgroundErrors 3DHYB 3DVAR BEN Bf

  20. 3DHYB_(Retuned Spread) U T New (RS) hybrid experiment almost uniformly better than 3DVAR Q 3DHYB_RS-3DVAR

  21. 4D-Ensemble-Var[4DENSV] 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). Note that the need for the computationally expensive linear and adjoint models in the minimization is conveniently avoided.

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

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

  24. Time Evolution of Increment 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 unfeasible for use in 4DVAR other than simple single observation testing at low resolution t=-3h t=0h t=+3h H-4DENSV H-4DVAR_AD

  25. 4D OSSE Experiments • To investigate the use of 4D ensemble perturbations, two new OSSE based experiments are carried out. • The original (not reduced) set of inflation parameters are used. • Exact configuration as was used in the 3D OSSE experiments, but with 4D features • 4DENSV • No static B contribution (bf-1=0.0) • Analogous to a dual-resolution 4D-EnKF (but solved variationally) • To be compared with 3DENSV • H-4DENSV • 4DENSV + addition of time invariant static contribution (bf-1=0.25) • This is the non-adjoint formulation • To be compared with 4DENSV

  26. Impact on Analysis Errors U T Q H-4DENSV-4DENSV 4DENSV-3DENSV

  27. OSSE-based comparison of 3DHYB andH-4DENSV (with dynamic constraints) U T Something in the 4D experiments is resulting in more moisture in the analysis, triggering more convective precipitation Q 4DHYB-3DHYB

  28. Summary of 4D Experiments • 4DENSV seems to be a cost effective alternative to 4DVAR • Inclusion of time-invariant static B to 4DENSV solution is beneficial for dual-resolution paradigm • Extension to 4D seems to have larger impact in extratropics (whereas the original introduction of the ensemble covariances had largest impact in the tropics) • Increased convection in 4D extensions remains a mystery (it is not the weak constraint on unphysical moisture as I originally hypothesized) • Original tuning parameters for inflation were utilized. Follow-on experiments with tuned parameters (reduced inflation) and/or adapative inflation should yield even more impressive results.

  29. Scale-Dependence Motivation(Courtesy: Tom Hamill)

  30. Spectrum of Dual-Resolution Increment without SD-weighting

  31. Spectrum of Dual-Resolution Increment with SD-weighting

  32. Initial scale-dependent tests inand OSSE

  33. Outline • Introduction • (Brief) background on hybrid data assimilation • Hybrid Var/Ens at NCEP • OSSE-based hybrid experiments • Future Work and Summary

  34. 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 1981-1983 periods, attempting to capture QBO transitions (a difficult problem for reduced observing system periods) • Extensions to the GDAS hybrid are ongoing, including 4DEnsVar

  35. GDAS Hybrid • EMC targeting T1148 SL GFS implementation within next year • How to configure hybrid? What can be afforded computationally on new machine? • Merging DA and EPS efforts • Currently have separate EnKF (DA) and BV-ETR (EPS) cycles/perturbations • Improving the ensemble for the hybrid • Stochastic physics (Jeff Whitaker) • TC Initialization (Yoichiro Ota) • Hybrid developments • Improved localization, flow-dependent (and/or scale-dependent) weighting • Testing and preparing 4d-ensemble-var for implementation • Helping efforts toward cloudy/precip. radiances

  36. TC relocation for EnKF(work done by Yoichiro Ota) Apply TC relocation used in deterministic analysis to each ensemble member, but allowing TC structure perturbations and some TC position spread. • Update TC center position (latitude and longitude) by the EnKF • Use updated positions as inputs to the TC relocation • Apply this procedure before the EnKF analysis and GDAS analysis The idea is to separate linear problem (TC location space) and nonlinear problem (actual relocation of fields). Blue: first guess positionRed: Updated positionGreen: TC vital position

  37. Example: spaghetti diagram Before relocation After relocation TC relocation of this method can reduce the uncertainty on the TC position, maintaining the TC structure perturbations and some of the position uncertainty. Courtesy Yoichiro Ota

  38. Comparison with GEFS TC relocation EnKF 6 hour forecast perturbation + GEFS TC relocation EnKF analysis with TC relocation GEFS operational TC relocation scheme destroyed almost all initial position uncertainty and create very small spread around TC. Courtesy Yoichiro Ota

  39. 6th WMO Symposium on DA • NCEP will be hosting the next WMO DA Symposium from 7-11 October 2013 at NCWCP • Call for papers will be out soon

  40. BACKUP SLIDES

  41. Spectral Cost Function • Assume increment cost function is in spectral space • Perform variable transforms

  42. New Control Variables andSpectral-dependent Weights • New spectral control variables then become • GSI control variables are in physical space, however, so we introduce spectral transform operator, S

  43. Extension for Dual-Resolution • The extension to dual-resolution requires a further modification to apply the scale dependence to the ensemble-based increment, and not the control variable itself

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