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Recent developments of the local ensemble transform Kalman filter (LETKF) at JMA

2007/3/19 MRI, Tsukuba. Recent developments of the local ensemble transform Kalman filter (LETKF) at JMA. Takemasa Miyoshi (NPD/JMA) Collaborators: Shozo Yamane (CIS and FRCGC) Yoshiaki Sato (NPD/JMA) Kohei Aranami (NPD/JMA) Takeshi Enomoto (ESC). Outline. 1. What is LETKF?

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Recent developments of the local ensemble transform Kalman filter (LETKF) at JMA

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  1. 2007/3/19 MRI, Tsukuba Recent developmentsof the local ensemble transform Kalman filter (LETKF) at JMA Takemasa Miyoshi (NPD/JMA) Collaborators: Shozo Yamane (CIS and FRCGC) Yoshiaki Sato (NPD/JMA) Kohei Aranami (NPD/JMA) Takeshi Enomoto (ESC)

  2. Outline 1. What is LETKF? 2. LETKF developments at JMA with three models: • AFES (AGCM for the Earth Simulator) • Collaborative workamong the Forecast Department/JMA, JAMSTEC, and Chiba Institute of Science • NHM (JMA Nonhydrostatic Regional Model) • GSM (JMA Global Model)

  3. A schematic of EnKF Obs. Analysis Ens. mean P FCST Ens. mean Generate ensemble members best representing the analysis errors An initial condition with errors T=t0 T=t1 T=t2 EnKF = ensemble fcst. + ensemble update

  4. EnKF • EnKF considers flow-dependent error structures, or the “errors of the day” • “advanced” data assimilation method • 4D-Var is also an “advanced” method. How different? • EnKF analyzes the analysis errors in addition to analysis itself • “ideal” ensemble perturbations

  5. EnKF vs. 4D-Var

  6. What is LETKF? • Two categories of the EnKF (Ensemble Kalman Filter) • LETKF (Local Ensemble Transform Kalman Filter) • is a kind of ensemble square root filter (SRF) • is efficient with the parallel architecture

  7. AFES-LETKF (Miyoshi, Yamane, and Enomoto) AFES: AGCM for the Earth Simulator Resolution: T159/L48 – 480x240x48 grid points 40 ensemble members Assimilate observations except satellite radiances 1.5-year cycle from May 2005 till Nov 2006:ALERA (AFES-LETKF Experimental Reanalysis) This is the collaborative work among the Forecast Department/JMA, JAMSTEC, and Chiba Institute of Science. We used the Earth Simulator under support of JAMSTEC.

  8. AFES-LETKF tested in Aug 2004 Sea-level pressureAugust 16, 2004 00UTC LETKF JMA DIFFERENCE SPREAD

  9. Flow of analysis errors 500hPaHeight Analysis (usually available by reanalysis) Analysis ensemble spread (analysis error field) (available by EnKF)

  10. Forecast verifications in Aug 2004 Adapted from Miyoshi and Yamane (2006)

  11. Summary of the test • Test exp. have shown very good performance of the AFES-LETKF system • Miyoshi and Yamane, 2007: Mon. Wea. Rev., in press.

  12. ALERA (AFES-LETKF Experimental ReAnalysis) 500Z RMS diff (1-day running mean) ALERA - NCEP REANAL Very stable! Apply vertical localization of Ps

  13. Summary • ALERA (AFES-LETKF Experimental ReAnalysis) • Miyoshi, Yamane and Enomoto, 2007: SOLA, in press. • Stable performance over 1.5 years • The product of every 6-hour analysis of 40 ensemble members is useful for further studies • “Ensemble reforecasting” • Further verifications and analyses of the products are in progress

  14. LETKF without local patches SLP analysis ensemble spread after the first analysis step The discontinuities caused by the local patches disappear.

  15. NHM-LETKF (Miyoshi and Aranami) NHM: JMA nonhydrostatic model (in operations) Perfect model experiment in a small region Miyoshi and Aranami, 2006: SOLA, 128-131. 5-km grid spacing, 10 members Experiment with real obs in July 2004 20-km grid spacing, 20 members

  16. Perfect model experiment

  17. Precipitation NO DA w/o rain obs w/ rain obs TRUTH TIME

  18. Exp. with real observations • Experimental settings

  19. 6-hr fcst initiated at 00Z July 4, 2004 Operational hydrostatic MSM as of July 2004 LETKFensemble mean

  20. Ensemble spreads

  21. Summary • Perfect model experiment indicates the LETKF works appropriately. • With real obs, LETKF reproduces similar analysis as the JMA operational MSM. • Growing modes appear inside the region; the effects of boundaries are limited near the boundaries • NOTE: Growing modes with longer wavelengths are artificially damped due to the fixed boundary. • NHM-LETKF is a useful tool for future studies in mesoscale NWP

  22. GSM-LETKF (Miyoshi and Sato) GSM: JMA global model (in operations) Resolution: TL159/L48 – 320x160x48 grid points 20 and 50 ensemble members Real obs including satellite radiances Miyoshi and Sato, 2007: SOLA, 37-40.

  23. Assimilation of satellite radiances AMSU-A Vertical localization is required. • Normalized sensitivity function is used as the localization weights. • Canadian operational EnKF uses the Guassian function in the same manner as the conventional obs. SSM/I

  24. Spaghetti diagrams w/o satellite radiances w/ satellite radiances w/o vertical localization Too small spread Caused by spurious covariance due to sampling errors w/ satellite radiances w/ vertical localization Larger spread due to damping sampling errors

  25. Residuals against JMA analysis Too large RMSE Too small SPREAD 20members BIAS SLP [hPa] Red: w/ vertical local. Blue: w/o vertical local. Green: w/o satellite assim. RMSE (solid) SPREAD(dashed) SLP [hPa]

  26. Effects by satellite radiances Reduced negative bias of Z and T Reduced RMSE of Z in mid-upper troposphere (500-100hPa), especially in the SH and Tropics RMSE and bias against radiosondes Blue: w/o satellite radiances Red: w/ satellite radiances 20members

  27. Ensemble size 20  50 RMSE and bias against radiosondes Blue: Operational 4D-Var Red: 20-member LETKF Green: 50-member LETKF 50 members > 20 members Generally 4D-Var > LETKF Exception: mid-upper tropospheric temperature in the SH w/ satellite radiances

  28. Z500 global forecast anomaly score Anomaly Correlations (against own analyses) Blue: Operational 4D-Var Red: 20-member LETKF Green: 50-member LETKF

  29. Tuning parameters…in progress Red: LETKF Blue: 4D-Var

  30. Summary • LETKF has been successfully applied to the three models: • AFES (AGCM for the Earth Simulator) • NHM (JMA nonhydrostatic regional model) • GSM (JMA global model) • GSM-LETKF with 50 members indicates identical performance to the operational 4D-Var system in the NH. • Ideas for further improvements • Further retuning • 50 members  100 members • TL159  TL319 • Adaptive bias correction for satellite radiances • Incremental method (high-resolution first guess) The ALERA dataset will be available to researchers for free!

  31. Thank you for your attention!

  32. ALERA system description

  33. SLP analyses on May 2, 2006

  34. KF and EnKF Forecast equations Ensemble forecasts Approximated by Kalman gain [pxp] matrix inverse Analysis equations Solve for the ensemble mean Ensemble perturbations

  35. LETKF algorithm In the space spanned by Eigenvalue decomposition: Analysis equations LETKF analysis Ensemble analysis increments

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