Download Data assimilation using an adjoint model

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
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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
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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
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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 for
Base run and adjoint sensitivity
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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
[G.1] Adjoint sensitivity;
output of a transport model
running in reverse time direction
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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
[G.2]1460 fixed period adjoint
sensitivity
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number terminal time
start time
1. 6UTC,1st,Dec,1996 0UTC,1st,Jan,1997
2. 12UTC,1st,Dec,1996 6UTC,1st,Jan,1997
3.
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1460, 0UTC,31st,Dec,1997  18UTC,31st,Dec,1997
Ignore all information prior to 31 days !
Blue=CMDL
Red=Original
Green=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 Source
MinObs 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