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Comparison of different combinations of ensemble-based and variational data assimilation approaches for deterministic NWP Mark Buehner Data Assimilation.

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Presentation on theme: "Comparison of different combinations of ensemble-based and variational data assimilation approaches for deterministic NWP Mark Buehner Data Assimilation."— Presentation transcript:

1 Comparison of different combinations of ensemble-based and variational data assimilation approaches for deterministic NWP Mark Buehner Data Assimilation and Satellite Meteorology Meteorological Research Division September 15, 2009 Third THORPEX International Science Symposium Co-authors: Peter Houtekamer, Cecilien Charette, Herschel Mitchell, and Bin He

2 Introduction Goal: compare 4D-Var, EnKF, and combination approaches in the context global deterministic NWP 4D-Var and EnKF: both operational at CMC since 2005 both use GEM forecast model both assimilate similar set of observations using mostly the same observation operators and observation error covariances 4D-Var is used to initialize medium range global deterministic forecasts EnKF (96 members) is used to initialize global Ensemble Prediction System (20 members)

3 Contents Configurations used for the intercomparison
Idealized experiments: effect of covariance localization effect of covariance evolution Full analysis-forecast experiments February 2007 July 2008 (preliminary results) Conclusions

4 Experimental Systems Modifications to configurations operational during summer 2008
4D-Var incremental approach: ~35km/150km grid spacing, 58 levels, 10hPa top  Increased horizontal resolution of inner loop to 100km to match EnKF EnKF 96 ensemble members: ~100km grid spacing, 28 levels, 10hPa top  Increased number of levels to 58 to match 4D-Var Same observations assimilated in all experiments: radiosondes, aircraft observations, AMVs, US wind profilers, QuikSCAT, AMSU-A/B, surface observations eliminated AIRS, SSM/I, GOES radiances from 4D-Var quality control decisions and bias corrections extracted from an independent 4D-Var experiment

5 Experimental Configurations
Variational data assimilation system: 3D-FGAT and 4D-Var with B matrix nearly like operational system: NMC method 3D-FGAT and 4D-Var with flow-dependent B matrix from EnKF at middle or beginning of assimilation window (same localization parameters as in EnKF) Ensemble-4D-Var (En-4D-Var): use 4D ensemble covariances to produce 4D analysis increment without TL/AD models (most similar to EnKF approach) EnKF: Deterministic forecasts initialized with EnKF ensemble mean analysis (requires interpolation from ~100km to ~35km grid)

6 Experimental Configurations Differences between EnKF and 4D-Var with EnKF covariances
Differences in spatial localization (most evident with radiance obs): 4D-Var: K = (ρ◦P)HT ( H(ρ◦P)HT + R )-1 (also En-4D-Var) EnKF: K = ρ◦(P HT) ( ρ◦(HPHT) + R )-1 Differences in temporal propagation of error covariances: 4D-Var: implicitly done with TL/AD model (with NLM from beginning to middle of assimilation window) EnKF: explicitly done with NLM in subspace of background ensemble (also En-4D-Var approach)

7 Single observation experiments Difference in vertical localization between 3D-FGAT and EnKF
AMSU-A ch9 peak sensitivity near 70hPa with same B, increment slightly larger & less local with 3D-FGAT than EnKF without localization increments nearly identical 10 - 10 - 3 3 10 - 10 - 3

8 Single observation experiments Difference in vertical localization between 3D-FGAT and EnKF
10 - assimilate all AMSU-A channels (4-10) with same B, largest differences near model top assimilate entire temperature profile of nearby raob with same B, variational and EnKF analysis nearly identical same general shape as with AMSU-A in layer 150hPa-700hPa 3 3 10 - 3 3

9 4D error covariances Temporal covariance evolution (explicit vs
4D error covariances Temporal covariance evolution (explicit vs. implicit evolution) 3D-FGAT-Benkf: 96 NLM integrations EnKF (and En-4D-Var): 96 NLM integrations 4D-Var-Benkf: 96 NLM integrations 55 TL/AD integrations, 2 outer loop iterations -3h 0h +3h

10 Single observation experiments Difference in temporal covariance evolution (obs at +3h)
radiosonde temperature observation at 500hPa contours are 500hPa GZ background state at 0h (ci=10m) + + contour plots at 500 hPa + +

11 Analysis and Forecast Verification Results – February 2007
EnKF (ensemble mean) vs. 4D-Var-Bnmc and 4D-Var-Benkf vs. 4D-Var-Bnmc

12 Forecast Results: EnKF (ens mean) vs. 4D-Var-Bnmc
north tropics south Difference in stddev relative to radiosondes: Positive  EnKF better Negative  4D-Var-Bnmc better zonal wind temp. height

13 Forecast Results: EnKF (ens mean) vs. 4D-Var-Bnmc
north tropics south Significance level of difference in stddev relative to radiosondes: Positive  EnKF better Negative  4D-Var-Bnmc better zonal wind temp. Computed using bootstrap resampling of the individual scores for 48-hour non-overlapping periods. height Shading for 90% and 95% confidence levels

14 Forecast Results: 4D-Var-Benkf vs. 4D-Var-Bnmc
north tropics south Difference in stddev relative to radiosondes: Positive  4D-Var-Benkf better Negative  4D-Var-Bnmc better zonal wind temp. height

15 Forecast Results: 4D-Var-Benkf vs. 4D-Var-Bnmc
north tropics south Significance level of difference in stddev relative to radiosondes: Positive  4D-Var-Benkf better Negative  4D-Var-Bnmc better zonal wind temp. Computed using bootstrap resampling of the individual scores for 48-hour non-overlapping periods. Shading for 90% and 95% confidence levels height

16 Results – 500hPa GZ anomaly correlation
Verifying analyses from 4D-Var with Bnmc Northern extra-tropics Southern extra-tropics 4D-Var Bnmc 4D-Var Benkf EnKF (ens mean) 4D-Var Bnmc 4D-Var Benkf EnKF (ens mean)

17 Equitable Threat Score (ETS) for Tropics
Forecast Results – Precipitation 24-hour accumulation verified against GPCP analyses Equitable Threat Score (ETS) for Tropics EnKF (ens mean) 4D-Var-Bnmc 4D-Var-Benkf day day day 3 threshold (mm)

18 Forecast Results – Precipitation
Evolution of mean 3-hour accumulated precipitation

19 Analysis and Forecast Verification Results – February 2007
Differences in covariance evolution: En-4D-Var vs. 3D-FGAT-Benkf and En-4D-Var vs. 4D-Var-Benkf

20 Forecast Results: En-4D-Var vs. 3D-FGAT-Benkf
north tropics south Difference in stddev relative to radiosondes: Positive  En-4D-Var better Negative  3D-FGAT-Benkf better zonal wind temp. height

21 Forecast Results: En-4D-Var vs. 4D-Var-Benkf
north tropics south Difference in stddev relative to radiosondes: Positive  En-4D-Var better Negative  4D-Var-Benkf better zonal wind temp. height

22 Results – 500hPa GZ anomaly correlation
Verifying analyses from 4D-Var with Bnmc Northern hemisphere Southern hemisphere 3D-FGAT Benkf En-4D-Var 4D-Var Benkf 3D-FGAT Benkf En-4D-Var 4D-Var Benkf

23 EnKF (ensemble mean) vs. 4D-Var-Bnmc and 4D-Var-Benkf vs. 4D-Var-Bnmc
Analysis and Forecast Verification Results – Preliminary Results for July 2008 EnKF (ensemble mean) vs. 4D-Var-Bnmc and 4D-Var-Benkf vs. 4D-Var-Bnmc

24 Forecast Results: July 2008 EnKF (ens mean) vs. 4D-Var-Bnmc
north tropics south Difference in stddev relative to radiosondes: Positive  EnKF better Negative  4D-Var-Bnmc better zonal wind temp. height

25 Forecast Results: July 2008 4D-Var-Benkf vs. 4D-Var-Bnmc
north tropics south Difference in stddev relative to radiosondes: Positive  4D-Var-Benkf better Negative  4D-Var-Bnmc better zonal wind temp. height

26 Results – 500hPa GZ anomaly correlation
Verifying analyses from 4D-Var with Bnmc: July 2008 Northern extra-tropics Southern extra-tropics 4D-Var Bnmc 4D-Var Benkf EnKF (ens mean) 4D-Var Bnmc 4D-Var Benkf EnKF (ens mean)

27 Conclusions Based on 1-month experiments February 2007
Deterministic forecasts initialized with 4D-Var with operational B and EnKF ensemble mean analyses have comparable quality: 4D-Var better in extra-tropics at short-range, EnKF better in the medium range and tropics Largest impact (~9h gain at day 5) in southern extra-tropics for 4D-Var with flow-dependent EnKF B vs. 4D-Var with operational B and also better in tropics – smaller improvement in July 2008 Use of 4D ensemble B in variational system (i.e. En-4D-Var): improves on 3D-FGAT, but inferior to 4D-Var (both with 3D ensemble B), least sensitive to covariance evolution in tropics comparable with EnKF

28 EXTRA SLIDES FOLLOW

29 Experimental Configurations Differences between EnKF and 4D-Var with EnKF covariances
Differences in spatial localization (most evident with radiance obs): 4D-Var: K = (ρ◦P)HT ( H(ρ◦P)HT + R )-1 (also En-4D-Var, 3D-FGAT) EnKF: K = ρ◦(P HT) ( ρ◦(HPHT) + R )-1 Differences in temporal propagation of error covariances: 4D-Var: implicitly done with TL/AD model (with NLM from beginning to middle of assimilation window) EnKF: explicitly done with NLM in subspace of background ensemble (also En-4D-Var approach) Differences in solution technique: 4D-Var: limited convergence towards global solution (30+25 iterations) EnKF: sequential-in-obs-batches explicit solution (not equivalent to global solution) Differences in time interpolation to obs in assimilation window: 4D-Var: 45min timestep, nearest neighbour (NN) interpolation in time EnKF: 90min timestep, linear interpolation in time En-4D-Var: 45min, NN for innovation, 90min, linear interp. for increment

30 Single observation experiments Difference in temporal covariance evolution (obs at -3h)
radiosonde temperature observation at 500hPa contours are 500hPa GZ background state at 0h (ci=10m) + + contour plots at 500 hPa + +

31 Single observation experiments Difference in temporal covariance evolution
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) + + contour plots at 500 hPa + +

32 Analysis Results (O-A) – global
EnKF mean analysis vs. 4D-Var-Bnmc 4D-Var-Benkf vs. 4D-Var-Bnmc U |U| U |U| GZ T GZ T stddev & bias relative to radiosondes stddev & bias relative to radiosondes T-Td T-Td

33 En-4D-Var vs. 3D-FGAT-Benkf and En-4D-Var vs. 4D-Var-Benkf
Analysis and Forecast Verification Results – Differences in covariance evolution En-4D-Var vs. 3D-FGAT-Benkf and En-4D-Var vs. 4D-Var-Benkf

34 Forecast Results: En-4D-Var vs. 3D-FGAT-Benkf
north tropics south Difference in stddev relative to radiosondes: Positive  En-4D-Var better Negative  3D-FGAT-Benkf better zonal wind temp. height

35 Forecast Results: En-4D-Var vs. 3D-FGAT-Benkf
north tropics south Significance level of difference in stddev relative to radiosondes: Positive  En-4D-Var better Negative  3D-FGAT-Benkf better zonal wind temp. Computed using bootstrap resampling of the individual scores for 48-hour non-overlapping periods. Shading for 90% and 95% confidence levels height

36 Forecast Results: En-4D-Var vs. 4D-Var-Benkf
north tropics south Difference in stddev relative to radiosondes: Positive  En-4D-Var better Negative  4D-Var-Benkf better zonal wind temp. height

37 Forecast Results: En-4D-Var vs. 4D-Var-Benkf
north tropics south Significance level of difference in stddev relative to radiosondes: Positive  En-4D-Var better Negative  4D-Var-Benkf better zonal wind temp. Computed using bootstrap resampling of the individual scores for 48-hour non-overlapping periods. Shading for 90% and 95% confidence levels height

38 En-4D-Var vs. 4D-Var-Bnmc
Analysis and Forecast Verification Results – En-4D-Var vs. standard approaches En-4D-Var vs. EnKF and En-4D-Var vs. 4D-Var-Bnmc

39 Forecast Results: En-4D-Var vs. EnKF
north tropics south Difference in stddev relative to radiosondes: Positive  En-4D-Var better Negative  EnKF better zonal wind temp. height

40 Forecast Results: En-4D-Var vs. EnKF
north tropics south Significance level of difference in stddev relative to radiosondes: Positive  En-4D-Var better Negative  EnKF better zonal wind temp. Computed using bootstrap resampling of the individual scores for 48-hour non-overlapping periods. Shading for 90% and 95% confidence levels height

41 Forecast Results: En-4D-Var vs. 4D-Var-Bnmc
north tropics south Difference in stddev relative to radiosondes: Positive  En-4D-Var better Negative  4D-Var-Bnmc better zonal wind temp. height

42 Forecast Results: En-4D-Var vs. 4D-Var-Bnmc
north tropics south Significance level of difference in stddev relative to radiosondes: Positive  En-4D-Var better Negative  4D-Var-Bnmc better zonal wind temp. Computed using bootstrap resampling of the individual scores for 48-hour non-overlapping periods. Shading for 90% and 95% confidence levels height

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