data assimilation using an adjoint model first test by s. taguchi transcom paris 14 june 2005...
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Data assimilation using an adjoint model
First Test
By S. Taguchi
TransCom Paris
14 June 2005
Collaboration of AIST and FastOpt
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Continuous + adjoint annual mean flux
• Formulation
• c: Observation vector
• G: Transport matrix
• x:Flux area, prior estimate and uncertainty
• Results(Data error, 0.1,0.5,1.0)
• Future
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Question; Not to be answered
• Relationship between the definition of adjoint and the current adjoint sensitivity
• How to derive the adjoint sensitivity used in this study
• Posterior error covariance
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Questions; to be answered
• How the problem is set up
• How we compensate the limitations in the current adjoint sensitivity (forget trend)
• Sensitivity of the solution to the specifications in observation errors.
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continuous + adjoint annual flux
• c=Gx• c: observation vector CMDL – Base Run• G: Transport Matrix Adjoint sensitivity + Prior• x: Unknown source 3x3 grids Annual mean• σc c: Obsrvation Uncertainty• σx Prior flux ucertainty f – z
• JBLS=(c-Gx)t X(c-Gx) + (f-z)t W(f-z)
• No off-diagonal elements in X and W.
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[c.1]Observation vector
• c= Observations – baseline, 1997 one year• Annual Mean; adjusted• Point barrow/CMDL from CD-ROM/WDCGG• 1 hour observations• Mean and standard deviation; 6h• Mean Fitting• Standard deviation Error (Min=1,0.5,0.1ppm)• Missing period Base run
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[c.2] Three steps in making Baseline
• NIRE-CTM-96 ECMWF 90-97
• Initial 350ppm , 90-97 year ECMWF
• (1) Fossil90+CASA+Takahashi02
• (2) CASA’ = Trend Adjusted CASA
• (3) Annual mean adjusted,
Last time series are baseline.
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[c.3]Forward model forBase run and adjoint sensitivity
• NIRE-CTM-96 one used for TransCom 2.• 2.5x2.5x15 (144x73x15~1.6 x 10 5)• 6 hour• Semi-lag, non-local PBL, Mass fixer• European Centre for Medium Range Weathe
r Forecast, ERA-15, Operational(p),• 1979-1999
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[G.1] Adjoint sensitivity;output of a transport model runni
ng in reverse time direction• 3D (144x73x15)• Max 31 days, 6hour time resolution• Specify; periods(=<31d),and point in 3D• If 1 ppm/6h is given continuously at a specified period at a point, how much c
oncentrations will be obtained at observational site.
• 1979-1999
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[G.2]1460 fixed period adjoint sensitivity
• number terminal time start time• 1. 6UTC,1st,Dec,1996 0UTC,1st,Jan,1997• 2. 12UTC,1st,Dec,1996 6UTC,1st,Jan,1997• 3.• ..• ..• 1460, 0UTC,31st,Dec,1997 18UTC,31st,Dec,1997• Ignore all information prior to 31 days !
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Blue=CMDLRed=OriginalGreen=Trend
adjusted Baseline
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Observation vector and
Observation error
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Area of unknown flux Prior flux uncertainty = sum of flux at 9 grid with 1ppm/6h
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Solution
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Min=0.1
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Min-0.5
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Min=1.0
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Updated SourceMinObs Error=1.Init=1996.Dec.31
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Future
• Extend Integration time Consistent annual 3x3grids.
• By 9 years time series 9 years mean , grid
• By 9 Stations annual mean, grid• By 12 Stations monthly mean, 3x3 grid• ( Minami-torishima, Izana, Samoa, etc.)• Column integrated concentrations