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

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

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

EnKF vs. 4D-Var EnKF 4D-Var “advanced” method? Y Simple to code? N (e.g., Minimizer) Adjoint model? N Observation operator Only forward (e.g., TC center) Adjoint required Asynchronous obs? Y (4D-EnKF) Y (intrinsic) Initialization after analysis? Analysis errors? Y (ensemble ptb) Limitation ensemble size Assim. window EnKF with infinite ensemble size and 4D-Var with infinite window are equivalent.

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 Perturbed observation (PO) method Square root filter (SRF) Classical Relatively new Already in operations (Canadian EPS) Not in operations yet Additional sampling errors by PO No such additional sampling errors

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.

AFES-LETKF tested in Aug 2004 Sea-level pressure　August 16, 2004 00UTC LETKF JMA SPREAD DIFFERENCE

Flow of analysis errors 500hPa Height Analysis (usually available by reanalysis) Analysis ensemble spread (analysis error field) (available by EnKF)

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

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.

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

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

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

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

Perfect model experiment

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

Exp. with real observations Experimental settings Experiment period 2004/6/25-7/15 Grid spacing 20 km Region (# of grid points) JMA operational (181x145x50) Ensemble size 20 Gaussian localization length Horizontal: 5-grid Vertical: 3-grid Local patch size 21x21x13 Covariance inflation 10% multiplicative spared inflation Boundary condition Fixed for all ensemble members

6-hr fcst initiated at 00Z July 4, 2004 Operational hydrostatic MSM as of July 2004 LETKF ensemble mean

Ensemble spreads

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

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.

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

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

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

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

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

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

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

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!

Thank you for your attention!

ALERA system description Ensemble size 40 Localization parameters 21x21x13 local patch 6-grid horizontal 3-grid vertical Gaussian localization Covariance inflation parameter 10% multiplicative spread inflation (21% cov inflation) Experimental period May 1, 2005 towards present (now computing… June, 2006) Assimilated observations Operationally used observations in JMA global cycle analysis except satellite radiances

SLP analyses on May 2, 2006

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

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