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Jeffrey Anderson, NCAR Data Assimilation Research Section

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1 Jeffrey Anderson, NCAR Data Assimilation Research Section
Assimilating Observations with Spatially and Temporally Correlated Errors in a Global Atmospheric Model Jeffrey Anderson, NCAR Data Assimilation Research Section EGU, 20 Apr., 2016

2 Observation Error Time Series
Example: Correlated Error AR1 with Variance 1. Single Step Cov Fixed for all cases. EGU, 20 Apr., 2016

3 Observation Error Time Series
Example: Correlated Error AR1 with Variance 1. Single Step Cov Fixed for all cases. Vary uncorrelated error variance, 0.01 EGU, 20 Apr., 2016

4 Observation Error Time Series
Example: Correlated Error AR1 with Variance 1. Single Step Cov Fixed for all cases. Vary uncorrelated error variance, 0.1 EGU, 20 Apr., 2016

5 Observation Error Time Series
Example: Correlated Error AR1 with Variance 1. Single Step Cov Fixed for all cases. Vary uncorrelated error variance, 1.0 EGU, 20 Apr., 2016

6 Observation Error Time Series
Example: Correlated Error AR1 with Variance 1. Single Step Cov Fixed for all cases. Vary uncorrelated error variance, 10.0 EGU, 20 Apr., 2016

7 1D Linear Exponential Growth Model
True trajectory is always 0. Evolution is Perturbations grow exponentially in time. EGU, 20 Apr., 2016

8 Assimilating Correlated Observations
EGU, 20 Apr., 2016

9 1D Exponential Growth Model Results
Exact Smoother Result. Can’t do better than this. EGU, 20 Apr., 2016

10 1D Exponential Growth Model Results
EAKF Poor Unless Uncorrelated Error Dominates RMSE Spread EGU, 20 Apr., 2016

11 Two Types of Difference Observations
EGU, 20 Apr., 2016

12 Unlinked Difference Observations
EGU, 20 Apr., 2016

13 1D Exponential Growth Model Results
Exact Unlinked Difference Obs Much worse. Exact Unlinked EGU, 20 Apr., 2016

14 Uninked Difference Observations
Unlinked Diff 1 Unlinked Diff 3 Unlinked Diff 5 Obs1 Obs2 Obs3 Obs4 Obs5 Obs6 EGU, 20 Apr., 2016

15 Uninked Difference Observations
Unlinked Diff 1 Unlinked Diff 3 Unlinked Diff 5 Obs1 Obs2 Obs3 Obs4 Obs5 Obs6 EGU, 20 Apr., 2016

16 1D Exponential Growth Model Results
EAKF is nearly exact for Unlinked Difference Obs. RMSE and Spread EGU, 20 Apr., 2016

17 Linked Difference Observations
EGU, 20 Apr., 2016

18 1D Exponential Growth Model Results
Exact linked Difference Obs Nearly Identical to Analytic. Linked EGU, 20 Apr., 2016

19 Linked Difference Observations
EGU, 20 Apr., 2016

20 Linked Difference Observations
EGU, 20 Apr., 2016

21 Linked Difference Observations
EGU, 20 Apr., 2016

22 1D Exponential Growth Model Results
EAKF Linked Diff. Obs. Good when correlated error dominates. RMSE Spread EGU, 20 Apr., 2016

23 1D Exponential Growth Model Results
Comparison to Just Using Raw Observations Obs EGU, 20 Apr., 2016

24 Lorenz 63 Model Observing System 1 3 Instruments.
Each has own correlated error. EGU, 20 Apr., 2016

25 Lorenz 63 Model Observing System 2
1 Instrument measures x,y,z each time. EGU, 20 Apr., 2016

26 L63 Results, Linked Difference Obs
3 Instruments 5 ensemble members. Adaptive inflation. Observations every 6 model timesteps. EGU, 20 Apr., 2016

27 L63 Results, Linked Difference Obs
3 Instruments 1 Instrument 5 ensemble members. Adaptive inflation. Observations every 6 model timesteps. EGU, 20 Apr., 2016

28 L63 Summary Difference obs better unless uncorrelated error variance dominates. Improvement greater for single instrument. Ensembles often under-dispersive (what a surprise!). EGU, 20 Apr., 2016

29 Lorenz 96 Model, 40-variables
Observing System 1 40 Instruments. Each has own correlated error. EGU, 20 Apr., 2016

30 Lorenz 96 Model, 40-variables
Observing System 2 1 instrument measures all 40 variables each time. EGU, 20 Apr., 2016

31 L96 Results, Linked Difference Obs
40 Instruments 10 ensemble members. Adaptive inflation, 0.2 halfwidth localization. Observations every model timestep. EGU, 20 Apr., 2016

32 L96 Results, Linked Difference Obs
40 Instruments 1 Instrument 10 ensemble members. Adaptive inflation, 0.2 halfwidth localization. Observations every model timestep. EGU, 20 Apr., 2016

33 L96 Results, Linked Difference Obs
Difference obs better unless uncorrelated error variance dominates. Improvement much greater for single instrument. Ensembles often over-dispersive. Dealing with time correlation harder than space correlation. EGU, 20 Apr., 2016

34 Low-Order Dry Dynamical Core
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Evolution of surface pressure field every 12 hours. Has baroclinic instability: storms move east in midlatitudes. EGU, 20 Apr., 2016

35 Low-Order Dry Dynamical Core
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Evolution of surface pressure field every 12 hours. Has baroclinic instability: storms move east in midlatitudes. EGU, 20 Apr., 2016

36 Low-Order Dry Dynamical Core
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Evolution of surface pressure field every 12 hours. Has baroclinic instability: storms move east in midlatitudes. EGU, 20 Apr., 2016

37 Low-Order Dry Dynamical Core
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Evolution of surface pressure field every 12 hours. Has baroclinic instability: storms move east in midlatitudes. EGU, 20 Apr., 2016

38 Low-Order Dry Dynamical Core
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Evolution of surface pressure field every 12 hours. Has baroclinic instability: storms move east in midlatitudes. EGU, 20 Apr., 2016

39 Low-Order Dry Dynamical Core
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Evolution of surface pressure field every 12 hours. Has baroclinic instability: storms move east in midlatitudes. EGU, 20 Apr., 2016

40 Low-Order Dry Dynamical Core
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Evolution of surface pressure field every 12 hours. Has baroclinic instability: storms move east in midlatitudes. EGU, 20 Apr., 2016

41 Low-Order Dry Dynamical Core
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Evolution of surface pressure field every 12 hours. Has baroclinic instability: storms move east in midlatitudes. EGU, 20 Apr., 2016

42 Low-Order Dry Dynamical Core
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Evolution of surface pressure field every 12 hours. Has baroclinic instability: storms move east in midlatitudes. EGU, 20 Apr., 2016

43 Low-Order Dry Dynamical Core
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Evolution of surface pressure field every 12 hours. Has baroclinic instability: storms move east in midlatitudes. EGU, 20 Apr., 2016

44 Low-Order Dry Dynamical Core: Grid
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles 30x60 horizontal grid, 5 levels. Surface pressure, temperature, wind components. 28,800 variables. EGU, 20 Apr., 2016

45 Low-Order Dry Dynamical Core: Observations
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Assimilate once per day. 0.2 radian localization. Observe each surface pressure grid point. Uncorrelated obs error variance 100 Pa. EGU, 20 Apr., 2016

46 Low-Order Dry Dynamical Core: Observations
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Uncorrelated obs error variance 100 Pa. Correlated obs error along ‘simulated polar orbiter track’. Vary ratio of correlated to uncorrelated obs error variance. EGU, 20 Apr., 2016

47 Low-Order Dry Dynamical Core: PS Results
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Linked difference better for large correlated error. Standard better for small correlated error. EGU, 20 Apr., 2016

48 Low-Order Dry Dynamical Core: T Results
Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Linked difference better for large correlated error. Standard better for small correlated error. EGU, 20 Apr., 2016

49 PS RMSE Structure: Large Uncorrelated Error, Ratio 4
Base errors largest in storm tracks. Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Linked difference errors largest in broad tropical band. EGU, 20 Apr., 2016

50 PS RMSE Structure: Moderate Uncorrelated Error, Ratio 1
Base errors largest in storm tracks. Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Linked difference errors largest in broad tropical band. EGU, 20 Apr., 2016

51 PS RMSE Structure: Small Uncorrelated Error, Ratio 1/4
Base errors largest in storm tracks. Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Linked difference errors largest in broad tropical band. EGU, 20 Apr., 2016

52 T RMSE Structure: Small Uncorrelated Error, Ratio 1/4
Base errors largest in tropics. Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles Linked difference errors have similar pattern. EGU, 20 Apr., 2016

53 Low-Order Dry Dynamical Core Summary
Linked difference obs better for large correlated error. Linked difference not sensitive to correlated error size. Adaptive inflation struggles with large correlated error. Could use base approach for uncorrelated obs, difference for correlated error obs. For example, base for sondes, difference for radiances. Difference obs allows assimilating before knowing correlated error characteristics. Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, ) NEED DETAILS OF ALGORITHM step size??? upper limits grid pictures for different latitudes Three pictures exist: ~jla/talks_and_meetings/2009/ams/cam_gps_talk/gps_lat* Expect minor differences with coarse grid, larger near poles EGU, 20 Apr., 2016

54 Learn more about DART at:
Anderson, J., Hoar, T., Raeder, K., Liu, H., Collins, N., Torn, R., Arellano, A., 2009: The Data Assimilation Research Testbed: A community facility. BAMS, 90, 1283—1296, doi: /2009BAMS2618.1 EGU, 20 Apr., 2016

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