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

• Results(Data error, 0.1,0.5,1.0)

• Future

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

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.

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.

[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

[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.

[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

[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

[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 !

Blue=CMDLRed=OriginalGreen=Trend

adjusted Baseline

Observation vector and

Observation error

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

Solution

Min=0.1

Min-0.5

Min=1.0

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

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