2007/10/8 Research activities of the local ensemble transform Kalman filter (LETKF) at JMA Takemasa Miyoshi Numerical Prediction Division, JMA.
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2007/10/8 Research activities of the local ensemble transform Kalman filter (LETKF) at JMA Takemasa Miyoshi Numerical Prediction Division, JMA Role of data assimilation Major Methodologies in Atmos & Oceanic Sciences Observing studies Modeling studies ©Vaisala Data Assimilation Initialize model predictions; essential in NWP Observing scientists get Synergy between twoModeling majorscientists fieldsget dynamically consistent information of real nature helps scientific advancement 4-D analysis Data assimilation in NWP Numerical Weather Prediction FCST Model Simulation ANL FCST ANL OBS ANL True state (unknown) OBS FCST-ANALYSIS Cycle accumulates past observations time Data Assimilation = Analysis FCST ANL ANL Error OBS Error OBS FCST FCST Error True state (unknown) The error in the initial condition (ANL) grows in a chaotic system Probabilistic view ANL w/ errors OBS w/ errors Problem： d.o.f. of the system: ~O(106) d.o.f. of the error: even Gaussian distribution has d.o.f. of the covariance ~O(1012) P ANL w/ errors T=t0 FCST w/ errors T=t1 Too large to express explicitly A schematic of EnKF Obs. Analysis Ens. mean An initial condition with errors T=t0 Generate ensemble members best representing P the analysis errors FCST Ens. mean T=t1 T=t2 EnKF = ensemble fcst. + ensemble update EnKF - summary • 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 Research activities MISSION STATEMENT Develop a next-generation data assimilation system to improve operational NWP at JMA Path to operations 1. Develop and test LETKF (Hunt 2005; Hunt et al. 2007; Ott et al. 2004, Hunt et al. 2004) with the Earth Simulator 2. Develop LETKF with the JMA nonhydrostatic model 3. Develop LETKF with the JMA global model 4. Assess LETKF under the quasi-operational setup Researches using the Earth Simulator LETKF system • Experimental 1.5-yr reanalysis (ALERA) • Collaborative work with observing scientists • LETKF with the Earth Simulator coupled atmos-ocean GCM Outline • Developments of LETKF toward operations – Recent improvements – Quasi-operational comparison with 4D-Var – Probabilistic forecast skills • Research projects with the Earth Simulator – Experimental Ensemble Reanalysis: ALERA – Collaboration with observing scientists Developments toward operations LETKF • Two categories of the EnKF (Ensemble Kalman Filter) Perturbed observation (PO) method Square root filter (SRF) Classical Relatively new Already in operations (Canadian EPS) Additional sampling errors by PO Not in operations yet No such additional sampling errors • LETKF (Local Ensemble Transform Kalman Filter) – is a kind of ensemble square root filter (SRF) – is efficient with the parallel architecture LETKF developments at JMA • LETKF (Local Ensemble Transform Kalman Filter) has been applied to 3 models – AFES (AGCM for the Earth Simulator) Miyoshi and Yamane, 2007: Mon. Wea. Rev., in press. Miyoshi, Yamane, and Enomoto, 2007: SOLA, 45-48. – NHM (JMA nonhydrostatic model) Miyoshi and Aranami, 2006: SOLA, 128-131. – GSM (JMA global spectral model) Miyoshi and Sato, 2007: SOLA, 37-40. Quasi-operational Experimental System 4D-Var Deterministic forecast 9hr TL319/L40 LETKF QC Ensemble forecast 9hr TL159/L40 4D-Var QC Recent improvements • Assimilation of satellite radiances – greatly improves the analysis accuracy Miyoshi and Sato, 2007: SOLA, 37-40. • Removing local patches – solves the discontinuity problem near the Poles Miyoshi et al., 2007: SOLA, 89-92. • Efficient MPI parallel implementation – solves the load imbalance problem – accelerates by a factor of 3 about 30% faster than operational 4D-Var with similar settings • Adaptive satellite bias correction – a new idea analogous to the variational bias correction – showing great positive impact Impact by satellite radiances RMSE and bias against radiosondes Blue: w/o satellite radiances Red: w/ satellite radiances Reduced negative bias of Z and T Reduced RMSE of Z in midupper troposphere (500100hPa), especially in the SH and Tropics 20 members Typhoon track ensemble prediction Typhoon #13, 2004 Bred Vectors w/ 4D-Var (Currently in operations) Typhoon track ensemble prediction Typhoon #13, 2004 SV w/ 4D-Var (Next operational system) Typhoon track ensemble prediction Typhoon #13, 2004 LETKF (Developing) This was a very difficult typhoon case Best track Operational Systems as of Aug 2004 LETKF Statistical typhoon track errors Typhoons in August 2004 Satellite radiance bias correction Observation y has a bias b b b scan b air Air mass bias (dependent on atmospheric state) Scan bias (constant) Statistically estimated offline Coefficients of predictors p are estimated statistically b air pT Zenith angle Surface temperature Constant etc. Adaptive bias correction Coefficients would change partly due to the deterioration of sensors Allow temporal variation of the coefficients using data assimilation Variational bias correction (e.g., Dee 2003; Sato 2007) J ( x) 12 ( x x f ) B 1 ( x x f )T 12 ( y Hx f ) R 1 ( y Hx f )T J ( x, ) 12 ( x x f ) B 1 ( x x f )T T f 1 T f 1 ( 2 f T 12 ( y p Hx ) R ( y p Hx ) 1 ) B ( f )T Find the minimizer of the cost function J through the variational procedure Adaptive bias correction with LETKF Analytical solution of the variational problem: minimizer (x, ) x ( Bx1 H T R 1H ) 1 H T R 1 (d pT ) (B1 pR1 pT )1 pR1 (d Hx) Adaptive bias correction with LETKF 1. Solve the LETKF data assimilation problem first x Bx H T (HBx H T R)1 d (Bx1 H T R1H )1 H T R1d pT difference 2. Solve the equation for explicitly (B1 pR1 pT )1 pR1 (d Hx) This coincides with the variational BC Time series of bias coefficients AMSU-A 4ch (sensitive to middle-lower troposphere) indicates significant drift from those estimated by 4D-Var AMSU-A 6ch (sensitive to upper troposhere) and other sensors/channels indicate no significant drift Impact by adaptive bias correction NH 24hr temperature forecast error improvements relative to 4D-Var Tropics RED: LETKF is better BLUE: 4D-Var is better Apply Adaptive BC SH Bias reduction Global T850 forecast bias against initial condition NH Red: LETKF Blue: 4D-Var Tropics SH Apply Adaptive BC The improvements would be due to the bias reduction Look at other variables Global T Z U NH Daily variations of 24-hr forecast error improvements relative to 4D-Var Horizontal axis: Date Red: LETKF is better Blue: 4D-Var is better Almost everything in the SH Tropics SH Temperature below 800hPa Temperature above 700 hPa except SH Wind except SH With adaptive satellite bias correction Global T Z U NH Daily variations of 24-hr forecast error improvements relative to 4D-Var Horizontal axis: Date Red: LETKF is better Blue: 4D-Var is better Tropics SH Improvement (%) relative to 4D-Var Apply adaptive bias correction Improvement (%) relative to 4D-Var August 2004 December 2005 LETKF is advantageous in the summer hemisphere Comparison with 3D-Var AC NH Tropics SH Red: LETKF Blue: 3D-Var Z500 Initial conditions RMSE BIAS Radiosondes RMSE BIAS Computational time LETKF 11 min x 60 nodes 4D-Var 17 min x 60 nodes 5 min for LETKF 6 min for 9-hr ensemble forecasts TL319/L60/M50 Inner: T159/L60 Outer: TL959/L60 Estimated for a proposed next generation operational condition 6 min (measured) x 8 nodes for LETKF with TL159/L40/M50 Computation of LETKF is reasonably fast, good for the operational use. Probabilistic forecast skills High T > TCLM + 2K LETKF is advantageous up to 3-day forecasts Probabilistic forecast skills Low T < TCLM - 2K LETKF is more sensitively affected by the negative temperature model bias Economic value High T > TCLM + 2K Economic value Low T < TCLM - 2K Summary • LETKF indicated identical performance in the NH to the operational 4D-Var – However, LETKF is clearly worse than 4D-Var in the SH – Larger bias in LETKF; why? • LETKF is advantageous in Typhoon prediction • Probabilistic forecast skill is generally improved – Still bias problem Researches with the Earth Simulator Ensemble Reanalysis: ALERA T159/L48 AFES (AGCM for the ES) LETKF w/ 40 members Assimilate real observations used in the JMA operational global analysis, except for satellite radiances Reanalysis from May 2005 through February 2007 ALERA (AFES-LETKF Experimental Ensemble Reanalysis) Stable performance (compared to NCEP/NCAR) System change: vertical localization of ps obs. Very Stable! Snapshot (SLP) ALERA NNR ALERA analysis is almost identical to NNR. Zonal mean winds in JJA ALERA NNR Comparison with observations T T Radiosondes AIRS retrievals Compared with radiosondes U Z Radiosondes Radiosondes 予報スコア 48-HR FCST RMSE (against own analyses) 50 LETKF-AFES2.2 JMA-AFES2.2 NNR-AFES2.2 46.4 42.4 39.6 500Z RMSE [m] 40 28.2 30 20.6 21.9 20 16 11.6 13.2 10 0 NH (20N-90N) TR (20S-20N) SH (90S-20S) Adapted from Miyoshi and Yamane (2007) ALERA dataset ALERA (AFES-LETKF Experimental Ensemble Reanalysis) data are now available online for free!! http://www3.es.jamstec.go.jp/ Contents Ensemble reanalysis dataset for over 1.5 years since May 1, 2005 40 ensemble members ensemble mean ensemble spread Available ‘AS-IS’ for free ONLY for research purposes Any feedback is greatly appreciated. Analyzing the analysis errors • EnKF provides not only analysis itself but also analysis errors (or uncertainties of the analysis) • What is dynamical meaning of the analysis errors? GOES-9 Image Courtesy of T. Enomoto QBO and ensemble spread Large spread at the initial stage of phase change Courtesy of T. Enomoto Stratospheric sudden warming ALERA SPREAD NCEP/NCAR Courtesy of T. Enomoto Large spread in tropical lower wind Courtesy of T. Enomoto Tropical lower wind and the spread Courtesy of T. Enomoto SPREAD Courtesy of T. Enomoto Collaboration with observing scientists There was an intensive observing project in the tropical western Pacific (a.k.a. PALAU-2005); the dropsonde obs during June 12-17, 2005 have been assimilated with the AFES-LETKF system. Satellite image and dropsonde locations Moteki et al., 2007: SOLA, accepted. Collaboration with observing scientists Impact by dropsonde observations Ensemble spreads of the ensemble analysis by LETKF NO OBS DROPSONDES Moteki et al., 2007: SOLA, accepted. Collaboration with observing scientists Propagation of observing signals Faster propagation than the advection speed, the faster speed (~12 m/s) corresponds to Rossby wave propagation Moteki et al., 2007: SOLA, accepted. Summary Development plans • Quasi-operational comparison in winter months • Try to replace SV EPS with LETKF first • Developments for high-resolution deterministic forecasts – TL959 (about 20-km resolution) global system – Incremental method (analogous to incremental 4DVar) – Improve skills in the SH (bias problem!) Research plans with the ES • ALERA-2 – 5-yr reanalysis (21st century reanalysis) – AFES-MATSIRO (SiB) (atmos-land coupled) – More diagnostics (OLR, Precipitation, land variables, etc.; any requests?) • CFES-LETKF – LETKF with coupled atmos-land-ocean model • More observing projects (e.g., PALAU-2008) Other research activities with LETKF • Collaboration with chemical-transport modeling scientists at the Meteorological Research Institute – LETKF has begun to work recently Collaborators AFES-LETKF – Prof. Shozo Yamane (Chiba Institute of Science and FRCGC/JAMSTEC, AFES) – Dr. Takeshi Enomoto (ESC/JAMSTEC, AFES) – Dr. Qoosaku Moteki (IORGC/JAMSTEC, Observing scientist) NHM-LETKF – Kohei Aranami (NPD/JMA, NHM) – Dr. Hiromu Seko (MRI/JMA, DA with NHM) GSM-LETKF – – – – Yoshiaki Sato (NPD/JMA, staying at NCEP) Takashi Kadowaki (NPD/JMA, 4D-Var) Ryouta Sakai (NPD/JMA, EPS) Munehiko Yamaguchi (NPD/JMA, Typhoon EPS) Chemical Transport – Dr. Thomas Sekiyama (MRI/JMA, Chemical model) Related publications AFES-LETKF Miyoshi and Yamane, 2007: MWR, in press. (AFES-LETKF system) Miyoshi et al., 2007: SOLA, 3, 89-92. (LETKF without local patches) Miyoshi et al., 2007: SOLA, 3, 45-48. (ALERA) Moteki et al., 2007: SOLA, accepted. (Observing project) NHM-LETKF Miyoshi and Aranami, 2006: SOLA, 2, 128-131. (perfect model experiments) GSM-LETKF Miyoshi and Sato, 2007: SOLA, 3, 37-40. (satellite radiance assimilation) Thank you for your attention! A core concept of EnKF Complementary relationship between data assimilation and ensemble forecasting Data Assimilation FCST error ANL Error Ensemble Forecasting This cycle process = EnKF Analyze w/ the flow-dependent forecast error, ensemble forecast w/ initial ensemble reflecting the analysis error Difference between EnKF and 3D-Var x a Flow-dependent errors expand in low-dimensional subspace Uniform error structure B R “Errors of the day” y o x f Analysis without flow-dependent error structure (e.g., 3D-Var) An example of EnKF analysis accuracy EnKF is advantageous to traditional data assimilation methods including 3D-Var, currently in operations at several NWP centers. Many centers (ECMWF, JMA, UK MetOffice, MeteorFrance, Canada, 30 ensemble members etc.) switched to 4D-Var 3DVAR (31m) which also considers flow-dependent error structures. LEKF (8m) Serial EnSRF (5m) EnKF vs. 4D-Var EnKF “advanced” method? Simple to code? Adjoint model? Observation operator 4D-Var Y Y N Only forward (e.g., TC center) Y (4D-EnKF) N Y N (e.g., Minimizer) Y Adjoint required Analysis errors? Y (ensemble ptb) N Limitation ensemble size Assim. window EnKF with infinite ensemble size and 4DVar with infinite window are equivalent. Asynchronous obs? Initialization after analysis? Y (intrinsic) Y 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 500 hPa height forecast verifications Red: LETKF Blue: 4D-Var Global NH Tropics SH With adaptive satellite bias correction Red: LETKF Blue: 4D-Var Global NH Tropics SH QBO (time series of tropical wind) ALERA NNR Stratospheric sudden warming ALERA NNR Stratospheric sudden warming