The recent developments of WRFDA (WRF-Var) Hans Huang, NCAR WRFDA: WRF Data Assimilation WRF-Var: WRF Variational data assimilation Acknowledge: NCAR/ESSL/MMM/DAG, NCAR/RAL/JNT/DATC, AFWA, USWRP, NSF-OPP, NASA, AirDat, KMA, CWB, CAA, BMB, EUMETSAT

Outline 1.WRFDA overview 2.A few new capabilities 3.Incremental formulation and outer-loop 4.Forecast error sensitivity to observations 5.Future plan and Summary

WRF-Var (WRFDA) Data Assimilation Overview Goal: Community WRF DA system for regional/global, research/operations, and deterministic/probabilistic applications. Techniques: 3D-Var 4D-Var (regional) Ensemble DA, Hybrid Variational/Ensemble DA. Model: WRF (ARW, NMM, Global) Support: NCAR/ESSL/MMM/DAG NCAR/RAL/JNT/DATC Observations: Conv.+Sat.+Radar

The WRF-Var Program NCAR staff: 15FTE Non-NCAR collaborators: ~10FTE. Community users: ~30 (more in 6000 general WRF downloads?).

WRF-Var Observations  In-Situ: -Surface (SYNOP, METAR, SHIP, BUOY). -Upper air (TEMP, PIBAL, AIREP, ACARS).  Remotely sensed retrievals: -Atmospheric Motion Vectors (geo/polar). -Ground-based GPS Total Precipitable Water. -SSM/I oceanic surface wind speed and TPW. -Scatterometer oceanic surface winds. -Wind Profiler. -Radar radial velocities and reflectivities. -Satellite temperature/humidities. -GPS refractivity (e.g. COSMIC).  Radiative Transfer: -RTTOVS (EUMETSAT). -CRTM (JCSDA). Threat Score Bias KMA Pre-operational Verification: (with/without radar)

WRF-Var Radiance Assimilation Status Liu and Auligne BUFR 1b radiance ingest. RTM interface: RTTOV or CRTM NESDIS microwave surface emissivity model Range of monitoring diagnostics. Quality Control for HIRS, AMSU, AIRS, SSMI/S. Bias Correction (Adaptive, Variational in 2008) Variational observation error tuning Parallel: MPI Flexible design to easily add new satellite sensors DMSP(SSMI/S) Aqua (AMSU, AIRS) NOAA (HIRS, AMSU)

The first WRF-Var tutorial July 21-22, hours lectures and 4 hours hands on 53+ participants, US and international WRF-Var tutorial agenda WRF-Var tutorial presentations WRF-Var online tutorial and user guide

Outline 1.WRFDA overview 2.A few new capabilities 3.Incremental formulation and outer-loop 4.Forecast error sensitivity to observations 5.Future plan and summary

AIRS assimilation: Experiments  T8 domain  45km horizontal resolution  57 vertical levels ( up to 10hPa )  Domain-specific background error covariances ( ensemble-based )  48h forecasts at 00UTC and 12UTC  Experiments:  Conventional Data (CONV)  Conventional + AIRS (AIRS)

AIRS assimilation: Impact on forecast BIAS RMSE CONV AIRS U U V V T T Q Q U U V V T T Q Q 24h forecasts minus conventional observations over a 30-day period

WRF 4D-Var Summary 4D-Var included within WRF-Var. Linear/adjoint models based on WRF- ARW. Status: Parallel code, JcDFI, limited physics. Delivered to AFWA in 2006 and (2008) Current focus: PBL/microphysics, optimization. Advantages of 4D-Var Flow-dependent response to obs Better treatment of cloud/precip obs Forecast model as a constraint Obs at obs-times => Xin’s 4D-Var talk 4D-Var3D-Var

WRF-Var and NMM (Pattanayak and Rizvi) Analysis increments

Global WRF-Var (Rizvi and Duda) Analysis increments

Use ensemble information in QC (Yongsheng Chen) Number of rejected observations

Outline 1.WRFDA overview 2.A few new capabilities 3.Incremental formulation and outer-loop 4.Forecast error sensitivity to observations 5.Future plan and summary

3D-Var (4D-Var replace H by HM) The incremental formulation (in the general form, !) The first outer-loop: x g = x b Outer-loop: d (and QC, etc) … nonlinear! Inner-loop: minimization update x g

Investigate impact on observation rejection algorithm due to multiple “outer-loops”. Code Development –Activated analysis “outer-loop”; –Added observation rejection check to outer-loop; –Generated statistics for data utilization/rejection for each outer-loop; –Graphic tools developed to monitor data utilization/rejection. Minimization i≥ntmax or |  Jnew|< eps |  J| Update first-guess j ≥ max_ext_its No Yes No Yes Outer Inner First-guess & Observation Update first-guess & Observation rejection - Led by Rizvi Syed

Rejected Observation locations and number b) Investigate impact on observation rejection algorithm due to multiple “outer-loops”. Number of rejected sondes Outer-loop 1 Outer-loop 2 Outer-loop 1 Outer-loop 2 The obs. rejection can be monitored either in tabular form & graphical form. Analysis difference between the first and second outerloop at the 10th Eta level

Outline 1.WRFDA overview 2.A few new capabilities 3.Incremental formulation and outer-loop 4.Forecast error sensitivity to observations 5.Future plan and summary

Simply Math: Linear assumption: Analysis: Forecast error: Forecast error sensitivity to initial state: Forecast error sensitivity to observations:

Observation (y) WRF-VAR Data Assimilation WRF-ARW Forecast Model Forecast (x f ) Derive Forecast Accuracy Background (x b ) Analysis (x a ) Adjoint of WRF-ARW Forecast TL Model (WRF+) Observation Sensitivity (  F/  y) Background Sensitivity (  F/  x b ) Analysis Sensitivity (  F/  x a ) Observation Impact (  F/  y) Adjoint of WRF-VAR Data Assimilation Obs Error Sensitivity (  F/  ob ) Adjoint sensitivity (Thomas Auligne) Gradient of F (  F/  x f ) Define Forecast Accuracy Forecast Accuracy (F) Bias Correction Sensitivity (  F/  k )

Adjoint of WRF-VAR DA: Introduction Analysis increments  x = x a - x b = K.[y-H(x b )] = K.d Adjoint of analysis  F/  y = K T.  F/  x a Various methods –Ensemble Transform Kalman Filter (ETKF, Bishop et al. 2001) –Dual approach (PSAS, Baker and Daley 2000) –Exact calculation of adjoint of DA (Zhu and Gelaro, 2007) –Leading eigenvectors of Hessian (Fisher and Courtier 1995) –Lanczos algorithm (Fisher 1997, Tremolet 2008)

Adjoint of WRF-VAR DA: Lanczos Algorithm New minimisation package Solve variational problem with Lanczos algorithm: Minimize Cost Function Estimate Analysis Error EXACT adjoint of analysis gain K T Link with current Conjugate Gradient Due to theoretical similarities b/w the two approaches, the convergence and solutions are IDENTICAL Computer issues –Adjoint of analysis is calculated during minimization with no overhead –Extra storage is required during minimization –New orthonormalization of gradients results in faster convergence Products –Observation Sensitivity & Impact ! –Estimation of condition number of DA system !! –Efficient preconditioner for multiple outer loops & ensemble DA !!! –Estimation of Analysis Error covariance matrix !!!!

200 hPa 500 hPa Impact (J b ) per observation

Adjoint of WRF-VAR DA: Observation Impact Impact (J b ) per observation type SOUND SYNOP PILOT SATEM GEO AMV AIREP GPSRF METAR SHIP PROFILER BUOY SONDE`_SFC N15 AMSUA N16 AMSUA N15 AMSUB N16 AMSUB N17 AMSUB METOP AMSUA SSMIS

Outline 1.WRFDA overview 2.A few new capabilities 3.Incremental formulation and outer-loop 4.Forecast error sensitivity to observations 5.Future plan and summary

Future Plans General Goals: Unified, multi-technique WRF DA system. Retain flexibility for research, multi-applications. Leverage international WRF community efforts. WRF-Var Development (MMM Division): 4D-Var (additional physics, optimization). Sensitivities tools (adjoint, ensemble, etc.). EnKF within WRF-Var -> WRFDA. Instrument-specific radiance QC, bias correction, etc. Data Assimilation Testbed Center (DATC): Technique intercomparison: 3/4D-Var, EnKF, Hybrid Obs. impact: AIRS, TMI, SSMI/S, METOP. New Regional testbeds: US, India, Arctic, Tropics. Applications: Hurricanes/Typhoons OSEs and OSSEs Reanalysis (Arctic System Reanalysis)

Summary 1.WRFDA overview Unified system: 3D-Var, 4D-Var, ETKF, Hybrid Observations: conventional, satellite, radar Community support 2.A few new capabilities AIRS Optimization of 4D-Var (Xin’s talk) WRF-NMM interface global ARW interface Ensemble QC 3.Incremental formulation and outer-loop Background and guess(es) Handling of nonlinear aspects: QC, M and H Resolution changes between inner- and outer-loops 4.Forecast error sensitivity to observations Sensitivity to initial state: adjoint of forecast model Sensitivity to observations: need adjoint of analysis