non-linear parameter optimisation of a terrestrial biosphere model using atmospheric co 2...
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Non-Linear Parameter Optimisation of a Terrestrial
Biosphere Model Using Atmospheric CO2 Observation -
CCDAS
Marko Scholze1, Peter Rayner2, Wolfgang Knorr1, Thomas Kaminski3, Ralf Giering3 & Heinrich
Widmann1
European Geosciences Union, Nice, 27th April 2004FastOpt1 2 3
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Overview
• CCDAS set-up• Calculation and propagation of
uncertainties• Data fit• Global results• Summary
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Carbon Cycle Data Assimilation System (CCDAS) set-up
2-stage-assimilation:
1. AVHRR data(Knorr, 2000)
2. Atm. CO2 data
Background fluxes:1. Fossil emissions (Marland et al., 2001 und Andres et al., 1996)2. Ocean CO2 (Takahashi et al., 1999 und Le Quéré et al., 2000)3. Land-use (Houghton et al., 1990)
Transport Model TM2 (Heimann, 1995)
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Calibration Step
Flow of information in CCDAS. Oval boxes represent the various quantities. Rectangular boxes denote mappings between these fields.
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Prognostic Step
Oval boxes represent the various quantities. Rectangular boxes denote mappings between these fields.
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Methodology
Minimize cost function such as (Bayesian form):
DpMDpMpp pppJ D
T
pT
)()()( 2
1
2
1 10
10 0
-- C C
where- is a model mapping parameters to observable quantities- is a set of observations- error covariance matrixC
DM
p
need of (adjoint of the model)Jp
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Calculation of uncertainties
• Error covariance of parameters
1
2
2
ji,
p pJ
C = inverse Hessian
T
pX p)p(X
p)p(X
CC
• Covariance (uncertainties) of prognostic quantities
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Figure from Tarantola, 1987
Gradient Method
1st derivative (gradient) ofJ (p) to model parameters p:
yields direction of steepest descent.
p
p
ppJ
)(
cost function J (p) p
Model parameter space (p)p
2nd derivative (Hessian)of J (p):
yields curvature of J.Approximates covariance ofparameters.
p
22 ppJ
)(
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Data fit
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Global Growth Rate
Calculated as:
observed growth rate
optimised modeled growth rate
Atmospheric CO2 growth rate
MLOSPOGLOB CCC 75.025.0
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Parameters I
• 3 PFT specific parameters (Jmax, Jmax/Vmax and )
• 18 global parameters• 57 parameters in all plus 1 initial value (offset)
Param InitialPredicted
Prior unc. (%) Unc. Reduction (%)
fautleafc-costQ10 (slow)
(fast)
0.41.251.51.5
0.241.271.351.62
2.50.57075
3917278
(TrEv)(TrDec) (TmpDec) (EvCn) (DecCn) (C4Gr) (Crop)
1.01.01.01.01.01.01.0
1.440.352.480.920.731.563.36
25252525252525
7895629591901
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Parameters II
Relative Error Reduction
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Carbon Balance
latitude N*from Valentini et al. (2000) and others
Euroflux (1-26) and othereddy covariance sites*
net carbon flux 1980-2000gC / (m2 year)
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Posterior uncertainty in net flux
Uncertainty in net carbon flux 1980-2000gC / (m2 year)
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Summary
• CCDAS with 58 parameters can fit 20 years of CO2 concentration data.
• Significant reduction of uncertainty for ~15 parameters.
• A tool to test model with uncertain parameters and to deliver a posterior uncertainties on parameters and prognostics.
• Model is developed further within the system a low resolution version of the biosphere model is available (~20 times faster).
• Adjoint, tangent linear and Hessian code is derived by automatic differentiation (TAF) extremely easy update of derivative code for improved model versions.