1. 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 February, 2013

2. Page 2 – September 3, 2015 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. Page 3 – September 3, 2015 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. Page 4 – September 3, 2015 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. Page 5 – September 3, 2015 In 4D-Var the 3D analysis increment is evolved in time using the TL/AD forecast model (here included in H 4D ): In EnVar the background-error covariances and analysed state are explicitly 4-dimensional, resulting in cost function: Computations involving ensemble-based B 4D can be more expensive than with B nmc depending on ensemble size and spatial/ temporal resolution, but significant parallelization is possible EnVar formulation

6. Page 6 – September 3, 2015 4D error covariances Temporal covariance evolution (explicit vs. implicit evolution) EnKF and EnVar (4D B matrix): 4D-Var: -3h0h+3h 192 NLM integrations provide 4D background-error covariances TL/AD inner loop integrations, 2 outer loop iterations, then 3h NLM forecast “analysis time”

7. Page 7 – September 3, 2015 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. Page 8 – September 3, 2015 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 Dependencies between global systems Bgcheck+BC4D-VarGEM (9h fcst) EnKF xbxb xbxb xbxb xbxb x b, obs obs xaxa xaxa GDPS: GEPS:

9. Page 9 – September 3, 2015 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 Dependencies between global systems Bgcheck+BC4D-VarGEM (9h fcst) EnKF xbxb xbxb xbxb xbxb x b, obs obs Bgcheck+BCEnVarGEM (9h fcst) EnKF xbxb xbxb xbxb xbxb x b, obs obs xbxb xaxa xaxa xaxa xaxa GDPS: GEPS:

10. Page 10 – September 3, 2015 Preconditioned cost function formulation at Environment Canada: In EnVar with hybrid covariances, the control vector (  ) is composed of 2 vectors: The analysis increment is computed as (e k is k’th ensemble perturbation divided by sqrt(N ens -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 EnVar formulation: Preconditioning 

11. Page 11 – September 3, 2015 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. Page 12 – September 3, 2015 EnVar uses Hybrid Covariance Matrix Model 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) Bens scale factor Bnmc scale factor scale factor pressure 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

13. Page 13 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Radiosonde verification scores – 6 weeks, Feb/Mar 2011 EnVar vs. 3D-Var 120h forecast North extra-tropics U|U| GZT T-T d

14. Page 14 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Radiosonde verification scores – 6 weeks, Feb/Mar 2011 EnVar vs. 3D-Var 120h forecast North extra-tropics EnVar vs. 4D-Var 120h forecast North extra-tropics U|U| GZT T-T d U|U| GZT T-T d

15. Page 15 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Radiosonde verification scores – 6 weeks, Feb/Mar 2011 EnVar vs. 3D-Var 120h forecast South extra-tropics U|U| GZT T-T d

16. Page 16 – September 3, 2015 EnVar vs. 4D-Var 120h forecast South extra-tropics Forecast Results: EnVar vs. 3D-Var and 4D-Var Radiosonde verification scores – 6 weeks, Feb/Mar 2011 EnVar vs. 3D-Var 120h forecast South extra-tropics U|U| GZT T-T d U|U| GZT T-T d

17. Page 17 – September 3, 2015 EnVar vs. 3D-Var 24h forecast Tropics Forecast Results: EnVar vs. 3D-Var and 4D-Var Radiosonde verification scores – 6 weeks, Feb/Mar 2011 U|U| GZT T-T d

18. Page 18 – September 3, 2015 EnVar vs. 3D-Var 24h forecast Tropics Forecast Results: EnVar vs. 3D-Var and 4D-Var Radiosonde verification scores – 6 weeks, Feb/Mar 2011 EnVar vs. 4D-Var 24h forecast Tropics U|U| GZT T-T d U|U| GZT T-T d

19. Page 19 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Verification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 EnVar vs. 3D-Var EnVar vs. 4D-Var 120h forecast, global domain no EnKF covariances transition zone ½ EnKF and ½ NMC covariances no EnKF covariances transition zone ½ EnKF and ½ NMC covariances U GZ RH T U GZ RH T

20. Page 20 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Verification 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. Page 21 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Verification 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. Page 22 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Verification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 Tropics 250hPa U-wind STDDEV EnVar vs. 3D-Var EnVar vs. 4D-Var

23. Page 23 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Verification 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. Page 24 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Verification 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. Page 25 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Verification against ERA-Interim analyses – 6 weeks, July-Aug 2011 Tropics 250hPa U-wind STDDEV EnVar vs. 3D-Var EnVar vs. 4D-Var

26. Page 26 – September 3, 2015 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. Page 27 – September 3, 2015 Forecast Results: 4D-EnVar vs. 3D-EnVar Verification 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. Page 28 – September 3, 2015 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. Page 29 – September 3, 2015 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. Page 30 – September 3, 2015 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. Page 31 – September 3, 2015 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. Page 32 – September 3, 2015 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. Page 33 – September 3, 2015 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. Page 34 – September 3, 2015 Some extra slides follow

35. Page 35 – September 3, 2015 Model Dynamics: New approaches for global grids

36. Page 36 – September 3, 2015 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 operational proposed for both radiosonde & aircraft 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 wind speed temperature 12h 48h Fig: Verification scores against radiosondes over the N. Hemisphere, Jan-Feb 2009 (dash = bias; solid = stde)

37. Page 37 – September 3, 2015 Role of Ensembles… Global EnKF Perturbed members of the global prediction system (GPS) Control member of the global prediction system (GPS) Global En-Var Background error covariances 2013-2017: Toward a Reorganization of the NWP Suites at Environment Canada Regional EnKF Perturbed members of the regional prediction system (RPS) Control member of the regional prediction system (RPS) Regional En-Var ? Background error covariances High-res En-Var High-resolution deterministic prediction system (HRDPS) global system regional system

38. Page 38 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Verification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 EnVar vs. 3D-Var 48h forecast, global domain no EnKF covariances transition zone ½ EnKF and ½ NMC covariances U GZ RH T

39. Page 39 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Verification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 EnVar vs. 3D-Var EnVar vs. 4D-Var 48h forecast, global domain no EnKF covariances transition zone ½ EnKF and ½ NMC covariances no EnKF covariances transition zone ½ EnKF and ½ NMC covariances U GZ RH T U GZ RH T

40. Page 40 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Verification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 EnVar vs. 3D-Var 120h forecast, global domain no EnKF covariances transition zone ½ EnKF and ½ NMC covariances U GZ RH T

41. Page 41 – September 3, 2015 Forecast Results: EnVar vs. 3D-Var and 4D-Var Verification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011 EnVar vs. 3D-Var EnVar vs. 4D-Var 120h forecast, global domain no EnKF covariances transition zone ½ EnKF and ½ NMC covariances no EnKF covariances transition zone ½ EnKF and ½ NMC covariances U GZ RH T U GZ RH T

42. Page 42 – September 3, 2015 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 experiments Difference in temporal covariance evolution contour plots at 500 hPa + + + + EnVar

43. Page 43 – September 3, 2015 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 experiments Difference in temporal covariance evolution contour plots at 500 hPa + + + + EnVar

44. Page 44 – September 3, 2015 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 experiments Difference in temporal covariance evolution contour plots at 500 hPa + + + + EnVar

45. Page 45 – September 3, 2015 Current system (1-way dependence): With EnVar (2-way dependence): Another possibility with EnVar (1-way dependence): Dependencies between global systems Bgcheck+BC4D-VarGEM (9h fcst) EnKF xbxb xbxb xbxb xbxb x b, obs obs Bgcheck+BCEnVarGEM (9h fcst) EnKF xbxb xbxb xbxb xbxb x b, obs obs xbxb Bgcheck+BCEnVarGEM (9h fcst) EnKF xbxb xbxb xbxb xbxb x b, obs xbxb Bgcheck+BC x b, obs xaxa xaxa xaxa xaxa xaxa xaxa GDPS: GEPS: