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Data assimilation using an adjoint model First Test

Data assimilation using an adjoint model First Test. By S. Taguchi TransCom Paris 14 June 2005 Collaboration of AIST and FastOpt. Continuous + adjoint  annual mean flux. Formulation c: Observation vector G: Transport matrix x:Flux area, prior estimate and uncertainty

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Data assimilation using an adjoint model First Test

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  1. Data assimilation using an adjoint modelFirst Test By S. Taguchi TransCom Paris 14 June 2005 Collaboration of AIST and FastOpt

  2. 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

  3. 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 • Posteriorerror covariance

  4. 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.

  5. 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 • σcc: 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.

  6. [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

  7. [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.

  8. [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 Weather Forecast, ERA-15, Operational(p), • 1979-1999

  9. [G.1] Adjoint sensitivity;output of a transport model running 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 concentrations will be obtained at observational site. • 1979-1999

  10. [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 !

  11. Blue=CMDLRed=OriginalGreen=Trend adjusted Baseline

  12. Observation vector and Observation error

  13. Area of unknown flux Prior flux uncertainty = sum of flux at 9 grid with 1ppm/6h

  14. Solution

  15. Min=0.1

  16. Min-0.5

  17. Min=1.0

  18. Updated SourceMinObs Error=1.Init=1996.Dec.31

  19. 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

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