Ensemble Prediction Systems Global Regional and Convective Yuejian

Ensemble Prediction Systems - Global, Regional and Convective Yuejian Zhu Ensemble Team Leader EMC/NCEP/NWS/NOAA Acknowledgements: EMC ensemble team members Presents for NWP Forecast Training Class March 30, Fuzhou, Fujian, China

Responsibilities of Ensemble Development (NCEP) - Assess, model, communicate uncertainty in numerical forecasts • Present uncertainty in numerical forecasting – Tasks • Design, implement, maintain, and continuously improve ensemble systems – Sciences • Initial value related uncertainty • Model related forecast uncertainty – Ensemble systems • • • Global – GEFS / NAEFS / NUOPC Regional – SREF / HREF / NARRE-TL / HWAF ensemble Climate – Contributions to future coupling CFS configuration NAEFS/GEFS downscaled Ocean wave ensemble (MMA/EMC) • Statistical correction of ensemble forecasts – Current tasks • Correct for systematic errors on model grid, correct ensemble spread. • Downscale information to fine resolution grid (NDFD) • Combine all forecast info into single ensemble/probabilistic guidance • Probabilistic product generation / user applications – Contribute to design of probabilistic products – Support use of ensembles by • Internal users (NCEP Service Center, WFOs, OHD/RFC forecasters and et al. ) 2 • External users (research, development, and applications)

Challenge Issues? • Initial uncertainties – Observations, data assimilation – Growing mode? • Model uncertainties – Single model with stochastic physics – Multi-physics • Multi-model ensembles – Multi-system, multi-model ensemble • Spatial resolutions – Changes with lead time, or uniform resolution? • Ensemble sizes – What is more comfortable ensemble members? • Coupling system – Coupling with land, ocean, ice and others – Perturbations (or uncertainties) of land, ocean and ice 3

Uncertainties & disagreements Ensemble forecast is widely used in daily weather forecast

December 2012 was 20 anniversary of both NCEP and ECMWF global ensemble operational implementation

Description of the ECMWF, MSC and NCEP systems Each ensemble member evolution is given by integrating the following equation Initial problem Model problem where ej(0) is the initial condition, Pj(ej, t) represents the model tendency component due to parameterized physical processes (model uncertainty), d. Pj(ej, t) represents random model errors (e. g. due to parameterized physical processes or sub-grid scale processes – stochastic perturbation) and Aj(ej, t) is the remaining tendency component (different physical parameterization or multi-model). Operation: ECMWF-1992; NCEP-1992; MSC-1998 Reference: Buizza, R. , P. L. Houtekamer, Z. Toth, G. Pellerin, M. Wei, Y. Zhu, 2005: "A Comparison of the ECMWF, MSC, and NCEP Global Ensemble Prediction Systems“ Monthly Weather Review, Vol. 133, 1076 -1097

Evolution of NCEP GEFS configuration (versions) Version Implem entation Initial uncertainty TS relocation Model uncertainty Resolution Forecast length Ensemble members Daily frequency V 1. 0 1992. 12 BV None T 62 L 18 12 2 00 UTC V 2. 0 1994. 3 T 62 L 18 16 10(00 UTC) 4(12 UTC) 00, 12 UTC V 3. 0 2000. 6 T 126 L 28(0 -2. 5) T 62 L 28(2. 5 -16) V 4. 0 2001. 1 T 126(0 -3. 5) T 62 L 28(3. 5 -16) V 5. 0 2004. 3 T 126 L 28(0 -7. 5) T 62 L 28(7. 5 -16) V 6. 0 2005. 8 V 7. 0 2006. 5 V 8. 0 2007. 3 V 9. 0 2010. 2 V 10. 0 2012. 2 V 11. 0 2015. 04 TSR 10 00, 06, 12, 18 UTC T 126 L 28 BV- ETR 14 20 STTP T 190 L 28 T 254 L 42 (0 -8) T 190 L 42 (8 -16) En. KF (f 06) TL 574 L 64 (0 -8) TL 382 L 64 (8 -16)

Estimating and Sampling Initial Errors: The Breeding Method - 1992 • DATA ASSIM: Growing errors due to cycling through NWP forecasts • BREEDING: - Simulate effect of obs by rescaling nonlinear perturbations – Sample subspace of most rapidly growing analysis errors • Extension of linear concept of Lyapunov Vectors into nonlinear environment • Fastest growing nonlinear perturbations References • Not optimized for future growth – – Norm independent 1. Toth and Kalnay: 1993 BAMS 2. Tracton and Kalnay: 1993 WAF – Is non-modal behavior important? 3. Toth and Kalnay: 1997 MWR Courtesy of Zoltan Toth

Bred Vector ( 2006) Ensemble Transform with Rescaling (2006 ) 2006 Rescaling ANL Rescaling P 1 forecast P 2 forecast P 1 ANL N 1 P 3 forecast t=t 0 t=t 1 t=t 2 P 4 forecast t=t 0 t=t 1 t=t 2 P#, N# are the pairs of positive and negative P 1, P 2, P 3, P 4 are orthogonal vectors P 1 and P 2 are independent vectors No pairs any more Simple scaling down (no direction change) To centralize all perturbed vectors (sum of all vectors are equal to zero) Scaling down by applying mask, P 2 The direction of vectors will be tuned by ET. ANL N 2 References: 1. 2. Wei and et al: 2006 Tellus Wei and et al: 2008 Tellus

Bred Vector ( 2006) Ensemble Transform with Rescaling (2006 ) 2006 Rescaling ANL P 1 ANL N 1 2 Dmask P 3 forecast t=t 0 Rescaling P 1 forecast P 2 forecast t=t 1 t=t 2 P 4 forecast t=t 0 t=t 1 t=t 2 P#, N# are the pairs of positive and negative P 1, P 2, P 3, P 4 are orthogonal vectors P 1 and P 2 are independent vectors No pairs any more Simple scaling down (no direction change) To centralize all perturbed vectors (sum of all vectors are equal to zero) Scaling down by applying mask, P 2 The direction of vectors will be tuned by ET. ANL N 2 References: 1. 2. Wei and et al: 2006 Tellus Wei and et al: 2008 Tellus

Latest ECMWF ensemble forecast system Initial Condition = Unperturbed Analysis + EDA-based perturbation + SV-based perturbation Unperturbed Analysis - 4 D-VAR (TL 1279 L 91) EDA-based perturbation - the difference between the perturbed (perturb all obs and sea-surface T and use SPPT to simulate random model error) and unperturbed first-guesses (TL 399 L 91) SV-based perturbation - initial singular vectors (T 42 L 62) EDA 1 + + EDA 2 mem 1 mem 2 mem 3 SV 6 SV 7 SV 8 SV 9 SV 10 …… …… …… EDA 10 SV 1 SV 2 SV 3 SV 4 SV 5 mem 50

Similar to En. KF, growing slowly, good CRPS scores Buizza R, Leutbecher M, Isaksen L, et al. 2010. Combined use of EDA- and SV-based perturbations in the EPS. Newsletter n. 123, ECMWF, Shinfield Park, Reading RG 2 -9 AX, UK, pg 22– 28.

CMC’s Multi-model EPS for the assimilation (current) # Deep convection Surface scheme Mixing length Vertical mixing parameter 1 2 3 4 5 Kain & Fritsch Oldkuo Relaxed Arakawa Schubert Kuo Symétrique Oldkuo ISBA force-restore Bougeault Blackadar Bougeault 1. 0 0. 85 1. 0 6 7 8 9 10 Kain & Fritsch Kuo Symétrique Relaxed Arakawa Schubert Kain & Fritsch Oldkuo force-restore ISBA Blackadar Bougeault 0. 85 1. 0 11 12 13 14 15 Relaxed Arakawa Schubert Kuo Symétrique Oldkuo Kain & Fritsch Kuo Symétrique force-restore ISBA Blackadar Bougeault Blackadar 1. 0 0. 85 1. 0 16 17 18 19 20 Relaxed Arakawa Schubert Kuo Symmetric Kain & Fritsch Oldkuo Relaxed Arakawa Schubert ISBA force-restore Bougeault Blackadar 0. 85 1. 0 21 22 23 24 Relaxed Arakawa Schubert Oldkuo Kain & Fritsch Kuo Symétrique ISBA force-restore ISBA Blackadar Bougeault 0. 85 1. 0 0. 85 Courtesy of Dr. P. Houtekamer, ARMA

Changes to the 16 day forecast system P. Houtekamer, ARMA/MSC, Canada • Like in the En. KF : – Use of a more recent version of the model and the model physics, – Removing an old surface scheme, – 20 minute time step, – Use of a topography filter, • No perturbation of model physics when convection is active, • No longer ramping down the stochastic physics in the tropics. • With these changes the system is a lot more robust (on occasion with the currently operational system we have to rerun an integration). • Implementation: Jan/Feb 2013

Evolution of NCEP SREF configuration IC uncertainty 2001 BV Physics uncertainty Multi-model (MM, Eta and RSM) 2003 Multi-model + Multiphysics (MMMP, add ETA_kf) 2004 MMMP (add more diverse physics schemes to Eta) 2005 MMMP (add NMM and ARW) Model resolution 48 km Forecast length 63 hr Ensemble members 10 Daily frequency 09, 21 z 15 40 km 87 hr 21 2006 03, 09, 15, 21 z 2009 BV + downscaled ETR MMMP (less Eta and more WRF, add more physics scheme to RSM) 32 km 87 hr 21 03, 09, 15, 21 Z 2012 BV + Downscaled ETR NEMS-NMMB WRF-NMM WRF-ARW 22 km 87 hrs 21 03, 09, 16, 21 Z

SREF system upgrade (Aug. 21, 2012) • Model Change 1. Model adjustment (eliminate Eta and RSM legacy models and add new NEMS-based NMMB model) 2. Model upgrade (two existing WRF cores from v 2. 2 to version 3. 3) 3. Resolution increase (from 32 km/35 km to 16 km) 4. All models run with 35 levels in the vertical and 50 mb model top. • IC diversity improvement 1. More control ICs (NDAS -> NMMB, GDAS -> NMM, RAP blended @ edges w/GFS -> ARW) 2. More IC perturbation diversity (a mix of Breeding, ETR as well as a Blending of the two) 3. Diversity in land surface initial states (NDAS, GFS, and RAP). • Physics diversity improvement 1. More diversity of physics schemes (flavors from NAM, GFS, NCAR and RAP) 16

Member (Model) IC nmmb_ctl nmmb_n 1 List of the physics schemes IC LBC perturb. physics conv mp lw sw pbl Sfc layer stochastic model initial perturb. NDAS BV gfs gefs 1 BMJ FER GFDL MYJ no NOAH NAM no nmmb_p 1 nmmb_n 2 nmmb_p 2 nmmb_n 3 nmmb_p 3 nmm_ctl GFS Blend gefs 2 gefs 3 gefs 4 gefs 5 gefs 6 gfs SAS BMJ GFDL GFDL GFS MYJ M_Obuhov (Janjic Eta) no NOAH GFS no nmm_n 1 nmm_p 1 nmm_n 2 gefs 1 gefs 2 gefs 3 SAS GFDL MYJ NOAH gefs 4 gefs 5 GFDL MYJ no NOAH nmm_p 3 arw_ctl RAP ETR gefs 6 gfs GFDL MYJ M_obuhov (Janjic Eta) no NOAH RAP no arw_n 1 arw_p 1 arw_n 2 gefs 1 gefs 2 gefs 3 KF (new Eta) BMJ M_Ouhov (janjic Eta) M_obuhov (janjic Eta) no nmm_p 2 nmm_n 3 GFDL MYJ M_obuhov (Janjic Eta) no NOAH arw_p 2 arw_n 3 gefs 4 gefs 5 BMJ GFDL MYJ NOAH gefs 6 M_Obuhov (Janjic Eta) no arw_p 3 GFS WSM 6 FER (new Eta) FER (new Eta) FER (new eta) Land surface 17

What do we expect from ensemble forecast? What is good ensemble forecast? We could discuss more about science of ensemble development if there is time allowed 18

Which ensemble is better? NCEP/GEFS NCEP - single model CMC/GEFS CMC - multi-physics (parameterizations)

NH 1000 h. Pa height 53 =1. 06 50 57 =1. 14 50 10 -day forecast: Spring 2011 Improvement of ensemble spread Spring 2012 NH 500 h. Pa height 84 =1. 2 70 78 =1. 08 72 Spring 2011 Last implementation: Reduced RMS errors Increasing spread Spring 2012

Current three operational ensembles: NCEP, CMC and ECMWF is tuning perfect for 850 h. Pa T (EDA+SV+SPPT) ECMWF is tuning perfect for 1000 h. Pa H Don’t see any reason they need to replace SV method, except for computation cost

In general, breeding method is more conception, and SV is more practical. Since we don’t know the size of initial uncertainties, we believe that smaller initial perturbations will be better (if it grows faster and catch up forecast errors) Early study from Zoltan Toth: BAMS 1992

Two-scale Lorenz ‘ 96 model slow large-scale variables xi (i=1, 2, …I) fast small-scale variables yi, j (i=1, 2, …I; j=1, 2, …J) yi, j Let I=36 and J=10 in this study. Thus, the slow large-scale variables xi could be thought of some atmospheric quantity in 36 sectors of a latitude circle, so that each large sector covers 10 degrees of longitude, while the fast small-scale variables yi, j can represent the values of some other quantity in 36*10 sectors, so that each small sector covers 1 degree of longitude in one large sector. Courtesy of Jessie Ma 23

Results from Lorenz experiments No interaction High interaction Courtesy of Jessie Ma 24

Interactions between DA and EPS v Ideally, EPS and DA systems should be consistent for best performance of both. v DA provides best estimates of initial uncertainties, i. e. analysis error covariance, for EPS. v EPS produces accurate flow dependent forecast (background) covariance for DA. Best analysis error variances DA Accurate forecast error covariance EPS

NH 500 h. Pa height RMS error (solid). vs. Spread (dash) One year statistics of three ensembles: NCEP, CMC and ECMWF

Summer 2014 Spring 2014 NCEP GEFS current status Winter 13 -14 Fall 2013

Snap shot of NCEP GEFS changes Changes in 4 -year Fall 2009 Fall 2013 Stochastic Total Tendency Perturbation (STTP) was implemented in Feb. 2010

Stochastic Total Tendency Perturbation (Hou, Toth and Zhu, 2006) NCEP operation – Feb. 2010 Formulation: Simplification: Use finite difference form for the stochastic term Modify the model state every 6 hours: Where w is an evolving combination matrix, and g is a rescaling factor. Reference: 1. Hou and et al: 2008 AMS conference extended paper 2. Hou and et al: 2010 in review of Tellus

STTP Scheme Application Generation of Stochastic Combination Coefficients: • • Matrix Notation (N forecasts at M points) S (t) = P(t) W(t) Mx. N Nx. N As P is quasi orthogonal, an orthonormal matrix W ensures orthogonality for S. Generation of W matrix: (Methodology and software provided by James Purser). – a) Start with a random but orthonormalized matrix W(t=0); – b) W(t)=W(t-1) R 0 R 1(t) R 0, R(t) represent random but slight rotation in N-Dimensional space wij(t) for i=14, and j=1, 14 Random walk (R 1) superimposed on a periodic Function (R 0)

Experiments for 2010 Operational Implementation T 126 L 28 vs. T 190 L 28 resolution, Nov. 2007 Cases STTP works with both resolutions CRPSS ROC --- T 126 L 28 + SP --- T 190 L 28 + SP

Changes of Ensemble Spread Then Now Courtesy of Dr. Alcott Trevor

Other stochastic schemes • Stochastic Kinetic Energy Backscatter (SKEB) – Represents process absent from model – Stream function is randomly perturbed to represent upscale kinetic energy transfer (Berner et al. , 2009) • Stochastic Perturbed Physics Tendencies (SPPT) – ECWMF tech memo 598 – Designed to represent the structural uncertainty (or random errors) of parameterized physics – Multiplicative noise used to perturb the total parameterized tendencies (Palmer et al. , 2009) – Biggest impact for tropic • Stochastically-perturbed boundary layer HUMidity (SHUM) – The same formula as SPPT – Designed to represent influence of sub-grid scale humidity variability on the triggering of convection (Tompkins and Berner 2008) • Vorticity confinement (VC) – Represent influence of unresolved or highly damped scales on resolved scales. – Can be deterministic and/or stochastic (Sanchez et al 2012).

Stochastic parameterization • Idealized model equations Resolved scales = “dynamics” Local tendency Horizontal diffusion Unresolved scales = “physics” (cloud microphysics, …) X = prognostic variable (e. g. u, v, T, q, …) Stochastic perturbations

An Effect Configurations of Ensemble Size and Horizontal Resolution for NCEP GEFS Juhui Ma, Yuejian Zhu, Panxin Wang and Richard Wobus AAS 2012 Ensemble size test from 5 to 80 members Comparing T 126 L 28 with 80 members to T 190 L 28 with 20 members

Northern Hemisphere 500 h. Pa Geopotential Height CRPSS PAC RMSE/SPREAD Significant test for RMSE

Northern Hemisphere 500 h. Pa Geopotential Height RMSE/SPREAD AC CRPSS RMSE 20 T 190 1 -5 d 80 T 126 12 -16 d AC CRPSS 3 -5 d 13 -16 d 11 -16 d

WMO CBS Expert Team on Ensemble Prediction System (ET-EPS) Last meeting on 14 -18 November 2011 in Geneva, Switzerland Full documentation: http: //www. wmo. int/pages/prog/www/CBS-Reports/documents/Final-Report-ET-EPS-Geneva 2011. pdf • Review each operational ensemble systems. • Present development plan of each operational center • Multi-model ensembles, such as NAEFS, GIFSTIGGE. • Stochastic perturbations • Post process and products. • Connect to WMO’s demonstration project.

WMO CBS Expert Team on Operational Weather Forecasting Support and Process (ET-OWFSP) Last meeting on 22 -24 October 2014 in Geneva, Switzerland Full documentation: http: //www. wmo. int/pages/prog/www/DPFS/Meetings/ET-OWFPS_Geneva 2014/Doc_Plan_000. html • Review each operational NWP systems from each operational center • Present development plan of each operational center • Provide operational NWP products verification (upper air and surface; deterministic and ensemble). • New project supporting: such as high resolution ensemble system. Transportation and aviation study. • Post process and products. • Connect to WMO’s demonstration project.