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Recent developments in data assimilation for global deterministic NWP: EnVar vs. 3D-Var and 4D-Var

Recent developments in data assimilation for global deterministic NWP: EnVar vs. 3D-Var and 4D-Var. Mark Buehner 1 , Josée Morneau 2 and Cecilien Charette 1 1 Data Assimilation and Satellite Meteorology Research Section 2 Data Assimilation and Quality Control Development Section

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Recent developments in data assimilation for global deterministic NWP: EnVar vs. 3D-Var and 4D-Var

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  1. Recent developments in data assimilation for global deterministic NWP: EnVar vs. 3D-Var and 4D-Var Mark Buehner1, Josée Morneau2 and Cecilien Charette1 1Data Assimilation and Satellite Meteorology Research Section 2Data Assimilation and Quality Control Development Section February, 2013

  2. Contents • Background • The ensemble-variational (EnVar) data assimilation approach • Recent results from using EnVar compared with standard 3D-Var and 4D-Var (but NO comparisons with 4D-Var-Bens or EnKF) • Conclusions and next steps

  3. Background • Environment Canada currently has 2 relatively independent state-of-the-art global data assimilation systems • 4D-Var (Gauthier et al 2007) and EnKF (Houtekamer et al 2009): • both operational since 2005 • both use GEM forecast model and assimilate similar set of observations • current effort towards unifying code of the two systems • 4D-Var is used to initialize medium range global deterministic forecasts (GDPS) • EnKF is used to initialize global ensemble forecasts (GEPS) • Intercomparison of approaches and various hybrid configurations was performed in carefully controlled context: similar medium-range forecast quality from EnKF and 4D-Var analyses, 4D-Var-Ben best • Results presented at WMO workshop on intercomparison of 4D-Var and EnKF, Buenos Aires, 2008 (Buehner et al 2010, MWR)

  4. Ensemble-Variational assimilation: EnVar • EnVar approach is currently being tested in the context of replacing 4D-Var in the operational Global Deterministic Prediction System • EnVar uses a variational assimilation approach in combination with the already available 4D ensemble covariances from the EnKF • By making use of the 4D ensembles, EnVar performs a 4D analysis without the need of the tangent-linear and adjoint of forecast model • Consequently, it is more computationally efficient and easier to maintain/adapt than 4D-Var • Hybrid covariances can be used in EnVar by averaging the ensemble covariances with the static NMC-method covariances • Like 4D-Var, EnVar uses an incremental approach with: • analysis increment at the horizontal/temporal resolution of EnKF ensembles • background state and analysis at the horizontal/temporal resolution of the higher-resolution deterministic forecast model

  5. EnVar formulation • In 4D-Var the 3D analysis increment is evolved in time using the TL/AD forecast model (here included in H4D): • In EnVar the background-error covariances and analysed state are explicitly 4-dimensional, resulting in cost function: • Computations involving ensemble-based B4D can be more expensive than with Bnmc depending on ensemble size and spatial/ temporal resolution, but significant parallelization is possible

  6. 4D error covariancesTemporal covariance evolution (explicit vs. implicit evolution) EnKF and EnVar (4D B matrix): 192 NLM integrations provide 4D background-error covariances 4D-Var: TL/AD inner loop integrations, 2 outer loop iterations, then 3h NLM forecast -3h 0h +3h “analysis time”

  7. EnVar: a possible replacement of 4D-Var Overall, EnVar analysis ~6X faster than 4D-Var on half as many cpus, even though higher resolution increments Wall-clock time of 4D-Var already close to allowable time limit; increasing number of processors has negligible impact To progress with 4D-Var, significant work would be required to improve scalability of TL/AD versions of forecast model at resolutions and grid configuration used in 4D-Var Current focus for model is on development of higher-resolution global Yin-Yang configuration that scales well Decision made to try to replace 4D-Var with more efficient EnVar if EnVar is at least as good as current 4D-Var

  8. Dependencies between global systems • Current system (1-way dependence): • GEPS relies on GDPS to perform quality control (background check) for all observations and bias correction for satellite radiance observations xa xb xb xb, obs GDPS: Bgcheck+BC 4D-Var GEM (9h fcst) obs xb xa xb GEPS: EnKF GEM (9h fcst)

  9. Dependencies between global systems • Current system (1-way dependence): • With EnVar (2-way dependence): • 2-way dependence (EnVar uses EnKF ensemble of background states) increases complexity of overall system  2 systems have to be run simultaneously xa xb xb xb, obs GDPS: Bgcheck+BC 4D-Var GEM (9h fcst) obs xb xa xb GEPS: EnKF GEM (9h fcst) xa xb xb xb, obs GDPS: Bgcheck+BC EnVar GEM (9h fcst) xb obs xb xb xa GEPS: EnKF GEM (9h fcst)

  10. EnVar formulation: Preconditioning • Preconditioned cost function formulation at Environment Canada: • In EnVar with hybrid covariances, the control vector (x) is composed of 2 vectors: • The analysis increment is computed as (ek is k’th ensemble perturbation divided by sqrt(Nens-1) ): •  • Better preconditioned than original “alpha control vector” formulation (with L-1 and 1/β in background term of J) • Most, but maybe not all, applications of the approach use the better preconditioned formulation 

  11. Experimental results:Configuration • EnVar tested in comparison with new version of forecast system recently implemented in operations: • model top at 0.1hPa, 80 levels • model has ~25km grid spacing • 4D-Var analysis increments with ~100km grid spacing • EnVar experiments use ensemble members from new configuration of EnKF: • 192 members every 60min in 6-hour window • model top at 2hPa, 75 levels • model ~66km grid spacing EnVar increments ~66km

  12. EnVar uses Hybrid Covariance MatrixModel top of EnKF is lower than GDPS Bens and Bnmc are averaged in troposphere ½ & ½, tapering to 100% Bnmc at and above 6hPa (EnKF model top at 2hPa) Therefore, EnVar not expected to be better than 3D-Var above ~10-20hPa Also tested 75% Bens and 25% Bnmc in troposphere, but results slightly worse Also did preliminary tests with a full outer loop, but degraded the results pressure Bens scale factor Bnmc scale factor scale factor

  13. Forecast Results: EnVar vs. 3D-Var and 4D-VarRadiosonde verification scores – 6 weeks, Feb/Mar 2011 U |U| GZ T EnVar vs. 3D-Var 120h forecast North extra-tropics T-Td

  14. Forecast Results: EnVar vs. 3D-Var and 4D-VarRadiosonde verification scores – 6 weeks, Feb/Mar 2011 U |U| U |U| GZ T GZ T EnVar vs. 3D-Var 120h forecast North extra-tropics EnVar vs. 4D-Var 120h forecast North extra-tropics T-Td T-Td

  15. Forecast Results: EnVar vs. 3D-Var and 4D-VarRadiosonde verification scores – 6 weeks, Feb/Mar 2011 U |U| GZ T EnVar vs. 3D-Var 120h forecast South extra-tropics T-Td

  16. Forecast Results: EnVar vs. 3D-Var and 4D-VarRadiosonde verification scores – 6 weeks, Feb/Mar 2011 U |U| U |U| GZ T GZ T EnVar vs. 3D-Var 120h forecast South extra-tropics EnVar vs. 4D-Var 120h forecast South extra-tropics T-Td T-Td

  17. Forecast Results: EnVar vs. 3D-Var and 4D-VarRadiosonde verification scores – 6 weeks, Feb/Mar 2011 U |U| GZ T EnVar vs. 3D-Var 24h forecast Tropics T-Td

  18. Forecast Results: EnVar vs. 3D-Var and 4D-VarRadiosonde verification scores – 6 weeks, Feb/Mar 2011 U |U| U |U| GZ T GZ T EnVar vs. 3D-Var 24h forecast Tropics EnVar vs. 4D-Var 24h forecast Tropics T-Td T-Td

  19. Forecast Results:EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 120h forecast, global domain EnVar vs. 3D-Var EnVar vs. 4D-Var no EnKF covariances no EnKF covariances transition zone transition zone ½ EnKF and ½ NMC covariances ½ EnKF and ½ NMC covariances U RH U RH GZ T GZ T

  20. Forecast Results:EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 North extra-tropics 500hPa GZ correlation anomaly EnVar vs. 3D-Var EnVar vs. 4D-Var

  21. Forecast Results:EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 South extra-tropics 500hPa GZ correlation anomaly EnVar vs. 3D-Var EnVar vs. 4D-Var This is the only significant degradation seen vs. 4D-Var in troposphere; Not in radiosonde scores because it originates from south of 45°S (see next slide)

  22. Forecast Results:EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 Tropics 250hPa U-wind STDDEV EnVar vs. 3D-Var EnVar vs. 4D-Var

  23. Forecast Results:EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, July-Aug 2011 North extra-tropics 500hPa GZ correlation anomaly EnVar vs. 3D-Var EnVar vs. 4D-Var

  24. Forecast Results:EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, July-Aug 2011 South extra-tropics 500hPa GZ correlation anomaly EnVar vs. 3D-Var EnVar vs. 4D-Var

  25. Forecast Results:EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, July-Aug 2011 Tropics 250hPa U-wind STDDEV EnVar vs. 3D-Var EnVar vs. 4D-Var

  26. Experimental results:4D-EnVar vs. 3D-EnVar • 3D version of EnVar also tested: only uses EnKF flow-dependent ensembles valid at the centre of the 6h assimilation window, instead of every 60 minutes throughout the window • 3D-EnVar compared with: • 4D-EnVar: impact of 4D vs 3D covariances, and • 3D-Var: impact of flow dependent vs stationary (NMC) covariances (both 3D)

  27. Forecast Results:4D-EnVar vs. 3D-EnVarVerification against ERA-Interim analyses – 4 weeks, Feb 2011 North extra-tropics 500hPa GZ correlation anomaly 4D-EnVar vs. 3D-EnVar 3D-EnVar vs. 3D-Var

  28. Forecast Results:4D-EnVar vs. 3D-EnVar Verification against ERA-Interim analyses – 4 weeks, Feb 2011 South extra-tropics 500hPa GZ correlation anomaly 4D-EnVar vs. 3D-EnVar 3D-EnVar vs. 3D-Var

  29. Forecast Results:4D-EnVar vs. 3D-En-Var Verification against ERA-Interim analyses – 4 weeks, Feb 2011 Tropics 250hPa U-wind STDDEV 4D-EnVar vs. 3D-EnVar 3D-EnVar vs. 3D-Var

  30. Conclusions • Comparison of EnVar with 3D-Var and 4D-Var: • EnVar produces similar quality forecasts as 4D-Var below ~20hPa in extra-tropics, significantly improved in tropics • above ~20hPa, scores similar to 3D-Var, worse than 4D-Var; potential benefit from raising EnKF model top to 0.1hPa • EnVar is an attractive alternative to 4D-Var: • like EnKF, uses full nonlinear model dynamics/physics to evolve covariances; no need to maintain TL/AD version of model • instead, makes use of already available 4D ensembles • more computationally efficient and easier to parallelize than 4D-Var for high spatial resolution and large data volumes • computational saving allows increase in analysis resolution and volume of assimilated observations; more computational resources for EnKF and forecasts

  31. Next Steps • Finalize testing EnVar with goal of replacing 4D-Var in operational global prediction system during 2013 in combination with other changes: • modified satellite radiance bias correction scheme that gives conventional observations more influence on correction • improved use of radiosonde and aircraft data • additional AIRS/IASI channels and modified observation error variances for all radiances • GEM global model: 25km lat-lon grid  15km Yin-Yang grid • CALDAS: new surface analysis system based on an EnKF • EnKF: increased resolution 66km  50km and ensemble size 192  256 members • Early results from using EnVar in regional prediction system as 4D-Var replacement look promising

  32. Humidity analysis • After combining EnVar with new bias correction and improved treatment of radiosonde/aircraft data, compared with 4D-Var: • humidity analysis significantly changed: both fit to humidity sensitive radiances and mean humidity • mass and wind medium-range (day 4 and after) forecast error std dev significantly degraded

  33. Humidity analysis • Just replacing EnVar humidity analysis with 4D-Var humidity analysis improves medium-range forecast error std dev, but introduces increased temperature bias at ~200hPa • Now trying to modify EnVar B matrix and bias correction scheme to obtain more similar humidity analysis as 4D-Var

  34. Some extra slides follow

  35. Model Dynamics: New approaches for global grids

  36. Proposed Upgrades and Improvements to the MSC Data Processing for Radiosonde and Aircraft Data • Increased volume of data: selection of observations according to model levels • Revised observation error statistics • Revised rejection criteria for radiosonde data based on those used at ECMWF • Horizontal drift of radiosonde balloon taken into account in both data assimilation and verification systems • Bias correction scheme for aircraft temperature reports wind speed temperature proposed for both radiosonde & aircraft operational 12h • Impact of proposed changes • General short-range forecast improvements above 500 hPa in both wind and temperature fields • The temperature forecast biases are significantly improved due to the bias correction scheme for aircraft below 200 hPa and to the new rejection criteria for radiosonde humidity data above 48h Fig: Verification scores against radiosondes over the N. Hemisphere, Jan-Feb 2009 (dash = bias; solid = stde)

  37. 2013-2017: Toward a Reorganization of the NWP Suites at Environment Canada Role of Ensembles… Perturbed members of the regional prediction system (RPS) Regional EnKF Perturbed members of the global prediction system (GPS) Background error covariances Global EnKF Control member of the regional prediction system (RPS) Regional En-Var ? Background error covariances High-resolution deterministic prediction system (HRDPS) Control member of the global prediction system (GPS) High-res En-Var Global En-Var regional system global system

  38. Forecast Results:EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 48h forecast, global domain EnVar vs. 3D-Var no EnKF covariances transition zone ½ EnKF and ½ NMC covariances U RH GZ T

  39. Forecast Results:EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 48h forecast, global domain EnVar vs. 3D-Var EnVar vs. 4D-Var no EnKF covariances no EnKF covariances transition zone transition zone ½ EnKF and ½ NMC covariances ½ EnKF and ½ NMC covariances U RH U RH GZ T GZ T

  40. Forecast Results:EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 120h forecast, global domain EnVar vs. 3D-Var no EnKF covariances transition zone ½ EnKF and ½ NMC covariances U RH GZ T

  41. Forecast Results:EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 120h forecast, global domain EnVar vs. 3D-Var EnVar vs. 4D-Var no EnKF covariances no EnKF covariances transition zone transition zone ½ EnKF and ½ NMC covariances ½ EnKF and ½ NMC covariances U RH U RH GZ T GZ T

  42. radiosonde temperature observation at 500hPa observation at beginning of assimilation window (-3h) with same B, increments very similar from 4D-Var, EnKF contours are 500hPa GZ background state at 0h (ci=10m) Single observation experimentsDifference in temporal covariance evolution EnVar + + contour plots at 500 hPa + +

  43. radiosonde temperature observation at 500hPa observation at middle of assimilation window (+0h) with same B, increments very similar from 4D-Var, EnKF contours are 500hPa GZ background state at 0h (ci=10m) Single observation experimentsDifference in temporal covariance evolution EnVar + + contour plots at 500 hPa + +

  44. radiosonde temperature observation at 500hPa observation at end of assimilation window (+3h) with same B, increments very similar from 4D-Var, EnKF contours are 500hPa GZ background state at 0h (ci=10m) Single observation experimentsDifference in temporal covariance evolution EnVar + + contour plots at 500 hPa + +

  45. Dependencies between global systems • Current system (1-way dependence): • With EnVar (2-way dependence): • Another possibility with EnVar (1-way dependence): xa xb xb xb, obs GDPS: Bgcheck+BC 4D-Var GEM (9h fcst) obs xb xa xb GEPS: EnKF GEM (9h fcst) xa xb xb xb, obs GDPS: Bgcheck+BC EnVar GEM (9h fcst) xb obs xb xb xa GEPS: EnKF GEM (9h fcst) xa xb xb xb, obs GDPS: Bgcheck+BC EnVar GEM (9h fcst) xb xb xb xa GEPS: Bgcheck+BC EnKF GEM (9h fcst) xb, obs

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