fast opt
DESCRIPTION
Non-Linear Parameter Optimisation of a Terrestrial Biosphere Model Using Atmospheric CO 2 Observation - CCDAS. Marko Scholze 1 , Peter Rayner 2 , Wolfgang Knorr 1 , Thomas Kaminski 3 , Ralf Giering 3 & Heinrich Widmann 1 European Geosciences Union, Nice, 27 th April 2004. 1. 2. 3. - PowerPoint PPT PresentationTRANSCRIPT
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
Overview
• CCDAS set-up• Calculation and propagation of
uncertainties• Data fit• Global results• Summary
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)
Calibration Step
Flow of information in CCDAS. Oval boxes represent the various quantities. Rectangular boxes denote mappings between these fields.
Prognostic Step
Oval boxes represent the various quantities. Rectangular boxes denote mappings between these fields.
Methodology
Minimize cost function such as (Bayesian form):
DpMDpMpp pppJ DT
pT
)()()( 21
21 1
01
0 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
Calculation of uncertainties
• Error covariance of parameters1
2
2
ji,
p pJ
C = inverse Hessian
T
pX p)p(X
p)p(X
CC
• Covariance (uncertainties) of prognostic quantities
Figure from Tarantola, 1987
Gradient Method
1st derivative (gradient) ofJ (p) to model parameters p:
yields direction of steepest descent.
pp
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
)(
Data fit
Global Growth Rate
Calculated as:
observed growth rateoptimised modeled growth rate
Atmospheric CO2 growth rate
MLOSPOGLOB CCC 75.025.0
Parameters I• 3 PFT specific parameters (Jmax, Jmax/Vmax and )• 18 global parameters• 57 parameters in all plus 1 initial value (offset)
Param Initial Predicted 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
Parameters II
Relative Error Reduction
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)
Posterior uncertainty in net flux
Uncertainty in net carbon flux 1980-2000gC / (m2 year)
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.