the recent developments of wrfda (wrf-var) hans huang, ncar wrfda: wrf data assimilation wrf-var:...
TRANSCRIPT
The recent developments of WRFDA(WRF-Var)
Hans Huang, NCAR
WRFDA: WRF Data AssimilationWRF-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).
2004082600 ~ 2004092812
Threshold = 5.0mm
TIME
3 6 9 12 15 18 21 240.0
0.2
0.4
0.6
0.8
1.0
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Th
reat
Sco
re
Bias
KMA Pre-operational Verification:
(with/without radar)
WRF-Var Radiance Assimilation StatusLiu 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
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
DMSP(SSMI/S)
Aqua (AMSU, AIRS)
NOAA (HIRS, AMSU)
The first WRF-Var tutorial
• July 21-22, 2008
• 9 hours lectures and 4 hours hands on
• 53+ participants, US and international
WRF-Var tutorial agenda
http://www.mmm.ucar.edu/events/tutorial_708/agenda/agenda.php
WRF-Var tutorial presentations
http://www.mmm.ucar.edu/wrf/users/tutorial/tutorial_presentation.htm
WRF-Var online tutorial and user guide
http://www.mmm.ucar.edu/wrf/users/docs/user_guide_V3/users_guide_chap6.htm
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
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
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
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
BIASBIAS RMSERMSECONVCONV AIRSAIRS
UU VV
TT QQ
UU VV
TT QQ
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 2007. (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-Var
3D-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)
2007.08Number 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
J =12
x−xb( )TB−1 x−xb( ) +
12
y−H x( )( )TR−1 y−H x( )( )
J =12
x−xg + xg −xb( )TB−1 x−xg + xg −xb( ) +
12
y−H xg( ) + H xg( )−H x( )( )TR−1 y−H xg( ) + H xg( )−H x( )( )
d =y−H xg( ) H x( )−H xg( ) ≈Hδx
J =12
δx+ xg −xb( )TB−1 δx+ xg −xb( ) +
12
d−Hδx( )T R−1 d−Hδx( )
δx = x − xg
J =12δxTB−1δx+
12
d−Hδx( )T R−1 d−Hδx( )
3D-Var (4D-Var replace H by HM)
The incremental formulation (in the general form, !)xg ≠xb
The first outer-loop: xg = xb
Outer-loop:
d (and QC, etc) … nonlinear!
Inner-loop: minimization
update xg
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≥ntmaxor
|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 1Outer-loop 2
ptop 1000 900 800 600 400 300 250 200 150 100 50 0obs type var pbot 1200 999.9 899.9 799 599.9 399.9 299.9 249.9 199.9 149.9 99.9 2000--------- ------- ------- --------- ------ ------- ------- ------- ------- ------- ------- ------- -------- ------ ---------sound U used 19 50 40 45 79 40 38 37 42 65 96 551
rej 4 12 11 5 0 0 0 0 0 0 0 32sound V used 21 42 39 46 79 40 38 37 42 65 96 545
rej 2 20 12 4 0 0 0 0 0 0 0 38sound T used 35 96 112 380 494 181 78 67 96 164 273 1976
rej 0 0 0 1 0 0 0 0 0 0 6 7
WRF-Var data utilization statistics for outer iteration 1
Outer-loop 1Outer-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
< MA,B >=< A,MTB >
F =<δxf ,δxf >=< Mδxa,δxf >=<δxa,M Tδxf >=< Kd,M Tδxf >=< d,K TM Tδxf >
′J = 0δxa = BHT HBHT + R( )-1
d = Kd
∂F
∂y=
∂F
∂d= KTMTδx f
Simply Math:
Linear assumption:
Analysis:
Forecast error:
Forecast error sensitivity to initial state:
Forecast error sensitivity to observations:
∂F
∂xa=
∂F
∂δxa= MTδx f
δx f = Mδxa
Observation(y) WRF-VAR
Data Assimilation
WRF-ARWForecast
Model
Forecast(xf)
DeriveForecastAccuracy
Background(xb)
Analysis(xa)
Adjoint of WRF-ARW
ForecastTL Model
(WRF+)
ObservationSensitivity
(F/ y)
BackgroundSensitivity(F/ xb)
AnalysisSensitivity(F/ xa)
Observation Impact<y-H(xb)> (F/ y)
Adjoint of WRF-VAR
Data Assimilation
Obs Error Sensitivity(F/ ob)
Adjoint sensitivity (Thomas Auligne)
Gradient of F
(F/ xf)
DefineForecastAccuracy
ForecastAccuracy
(F)
Bias CorrectionSensitivity(F/ k)
Adjoint of WRF-VAR DA: Introduction
• Analysis incrementsδx = xa - xb = K.[y-H(xb)] = K.d
• Adjoint of analysisF/y = KT.F/xa
• 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 packageSolve variational problem with Lanczos algorithm:
• Minimize Cost Function
• Estimate Analysis Error
• EXACT adjoint of analysis gain KT
• Link with current Conjugate GradientDue 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 (Jb) per observation
Adjoint of WRF-VAR DA: Observation Impact
Impact (Jb) per observation type
SOUND
SYNOPPILOT
SATEM
GEO AMV
AIREP
GPSRF
METARSHIP
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)
Summary1. 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