Jeffrey Anderson, NCAR Data Assimilation Research Section

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Presentation transcript:

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

Observation Error Time Series Example: Correlated Error AR1 with Variance 1. Single Step Cov 0.999. Fixed for all cases. EGU, 20 Apr., 2016

Observation Error Time Series Example: Correlated Error AR1 with Variance 1. Single Step Cov 0.999. Fixed for all cases. Vary uncorrelated error variance, 0.01 EGU, 20 Apr., 2016

Observation Error Time Series Example: Correlated Error AR1 with Variance 1. Single Step Cov 0.999. Fixed for all cases. Vary uncorrelated error variance, 0.1 EGU, 20 Apr., 2016

Observation Error Time Series Example: Correlated Error AR1 with Variance 1. Single Step Cov 0.999. Fixed for all cases. Vary uncorrelated error variance, 1.0 EGU, 20 Apr., 2016

Observation Error Time Series Example: Correlated Error AR1 with Variance 1. Single Step Cov 0.999. Fixed for all cases. Vary uncorrelated error variance, 10.0 EGU, 20 Apr., 2016

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

Assimilating Correlated Observations EGU, 20 Apr., 2016

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

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

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

Unlinked Difference Observations EGU, 20 Apr., 2016

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

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

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

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

Linked Difference Observations EGU, 20 Apr., 2016

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

Linked Difference Observations EGU, 20 Apr., 2016

Linked Difference Observations EGU, 20 Apr., 2016

Linked Difference Observations EGU, 20 Apr., 2016

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

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

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

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

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

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

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

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

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

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

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

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

Low-Order Dry Dynamical Core Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core: Grid Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core: Observations Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core: Observations Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core: PS Results Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

Low-Order Dry Dynamical Core: T Results Slide 7: GPS occultation forward operators Non-local refractivity : (Sokolovskiy et al., MWR 133, 2200-2212) 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

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, 2200-2212) 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

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, 2200-2212) 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

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, 2200-2212) 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

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, 2200-2212) 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

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, 2200-2212) 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

Learn more about DART at: www.image.ucar.edu/DAReS/DART 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: 10.1175/2009BAMS2618.1 EGU, 20 Apr., 2016