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Hybrid variational - e nsemble d ata a ssimilation for the NCEP GFS

Hybrid variational - e nsemble d ata a ssimilation for the NCEP GFS. Tom Hamill, for Jeff Whitaker NOAA Earth System Research Lab, Boulder, CO, USA jeffrey.s.whitaker@noaa.gov Daryl Kleist, Dave Parrish and John Derber National Centers for Environmental Prediction, Camp Springs, MD, USA

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Hybrid variational - e nsemble d ata a ssimilation for the NCEP GFS

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  1. Hybridvariational-ensemble data assimilation for the NCEP GFS Tom Hamill, for Jeff Whitaker NOAA Earth System Research Lab, Boulder, CO, USA jeffrey.s.whitaker@noaa.gov Daryl Kleist, Dave Parrish and John Derber National Centers for Environmental Prediction, Camp Springs, MD, USA Xuguang Wang University of Oklahoma, Norman, OK, USA a NOAA-THORPEX funded project

  2. Hybrid: best of both worlds?

  3. NCEP GSI 3D-Var Hybrid • Incorporate ensemble perturbations directly into variational cost function through “extended control variable” • Lorenc (2003), Buehner (2005), Wang et. al. (2007), etc. βf& βe: weighting coefficients for fixed and ensemble covariance respectively xt: (total increment) sum of increment from fixed/static B (xf) and ensemble B αk: extended control variable; :ensemble perturbation L: correlation matrix [localization on ensemble perturbations] [more info]

  4. Single-observation increments GSI EnKF hybrid Single 850 hPa Tvobservation (1K O-F, 1K error)

  5. Single-observation increments GSI EnKF hybrid Single 850 hPa zonal wind observation (3 m/s O-F, 1m/s error) in Hurricane Ike

  6. Why use EnKF for ensemble data assimilation and ensemble forecast initialization instead of operational ETR? • ETR (Ensemble transform with rescaling) • Not designed to represent 6-h forecast error covariances- viable for hybrid paradigm? • Update of breeding method to include orthogonalization of perturbations in analysis variance norm. • Virtually no additional computational cost beyond forward integration • Perturbations based on resizing to analysis-error mask derived for 500 hPa streamfunction • Tuned for medium range forecast spread and “fast error growth” • T190L28 version of the GFS model • EnKF • Perturbations specifically designed to represent analysis and background errors (parameters tuned by running DA stand-alone) • T254L64 version of the GFS • Extra computational costs worth it for hybrid?

  7. EnKF vs. ETR perturbation magnitude comparison, surface pressure EnKF (green) versus ETR (red) spread/standard deviation for surface pressure (mb) valid 2010101312 Surface Pressure spread normalized difference (ETR has much less spread, except poleward of 70N)

  8. EnKF vs. ETR comparison, u-wind component EnKF zonal wind (m/s) ensemble standard deviation valid 2010101312 ETR zonal wind (m/s) ensemble standard deviation valid 2010101312

  9. EnKF vs. NMC B comparison, u-wind component EnKF zonal wind (m/s) ensemble standard deviation valid 2010101312 Zonal Wind standard deviation (m/s) from “NMC-method”

  10. Hybrid Var-EnKF GFS experiment • Model • GFS deterministic (T574L64; current operational version) • GFS ensemble (T254L64) • 80 ensemble members, EnKF update, GSI for observation operators • Observations • All operationally available observations (including radiances) • Includes early (GFS) and late (GDAS/cycled) cycles as in production • Dual-resolution/Coupled • High resolution control/deterministic component • Includes TC Relocation on guess (will probably drop) • Ensemble is re-centered every cycle about hybrid analysis • Discard ensemble mean analysis • Satellite bias corrections • Coefficients come from GSI/VAR (although EnKF can compute it’s own) • Parameter settings • 1/3 static B, 2/3 ensemble • Fixed localization: 2000 km & 1.5 scale heights • Additive and multiplicative inflation. • Test Period • 15 July 2010 – 15 October 2010 (first3weeks ignored for “spin-up”)

  11. The bad: RMS errors, 20100807 - 20101022 3D-Var Zonal wind (Tropics) Temperature (NH) [higher errors in stratosphere, apparently due to allowing ozone to increment state] Hybrid minus 3D-Var

  12. The ok news: 500 hPa anomaly correlation (3D-Var, Hybrid) Day 5 0.871 0.883 Day 5 0.824 0.846

  13. The good news • Precipitation over CONUS with respect to 1-degree analyses, July-Oct 2010. EnKF here, not hybrid. • EnKF+ T254 + new GFS narrows the difference between NCEP and ECMWF, especially at higher amounts. • Much of impact due to new GFS model version, however.

  14. The excellent news

  15. Conclusions and plans • Mostlyimprovement in forecasts seen in using EnKF-based ensemble covariances in GSI 3D-Var, but • EnKF analyses are somewhat noisy – post analysis balancing degrades performance. • Increments to wind/temp from stratospheric ozone obs can be quite large (unrealistic?) • Schedule (deadlines already slipping…) • Testing at NCEP and ESRL, now-August 2011 • Code frozen late Oct 2011 • Final real-time parallel testing Dec 2011-Jan 2012 • Final field evaluation late Jan 2012 • Operational implementation Feb 2012

  16. Extensions and improvements • Scale-dependent weighting of fixed and ensemble covariances? • Expand hybrid to 4D • Hybrid within‘traditional 4D-Var’(with adjoint) • Pure ensemble 4D-Var (non-adjoint) • Ensemble 4D-Var with static B supplement (non-adjoint) • EnKF improvements • Adaptive localization • Stochastic physics • Perturbed SSTs • Balance • Non-GFS applications in development • Other global models (NASA GEOS-5, NOAA FIM, GFDL) • NAM /Mesoscale Modeling • Hurricanes/HWRF • Storm-scale initialization • Rapid Refresh • NCEP strives to have single DA system to develop, maintain, and run operationally (global, mesoscale, severe weather, hurricanes, etc.) • GSI (including hybrid development) is community code supported through DTC • EnKF used for GFS-based hybrid being expanded for use with other applications

  17. Pure Ensemble 4D-Var (Xuguang Wang, Ting Lei: Univ of Oklahoma) • Extension of 3D-Var hybrid using 4D- ensemble covariances at hourly intervals in assimilation window without TLM/adjoint(similar to Buehner et al 2010). • T190L64 experiments show Improvement over 3D-Var hybrid – similar to pure EnKF. • To do: Dual resolution, 2-way coupling, addition of static B component.

  18. Computational expense • Analysis / GSI side • Minimal additional cost (mostly I/O reading ensemble) • Additional “GDAS” Ensemble (T254L64 GDAS) • EnKF ensemble update • Cost comparable to current GSI 3D-Var • Includes ensemble of GSI runs to get O-F and actual ensemble update step • 9-h forecasts, needs to be done only in time for next (not current) cycle. Already done for ETR, but with fewer vertical levels and only to 6-h.

  19. [back] Lorenc 2003 QJ

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