A prototype Global Carbon
Cycle Data Assimilation
System (CCDAS)
Marko Scholze1, Wolfgang Knorr2,
Peter Rayner3,Thomas Kaminski4, Ralf Giering4
1
2
3
4
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Overview
• Top-down vs. bottom-up
• Gradient method and optimisation
• Results: Optimal fluxes
• Uncertainties in parameters + results
• Uncertainties in fluxes + results
• Possible assimilation of flux data
• Conclusions and Outlook
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Top-down / Bottom-up
atm. CO2 data
inverse
atmospheric
transport
modelling
net CO2
fluxes at the
surface
process
model
climate and other driving data
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Carbon Cycle Data Assimilation
Misfit 1
Forward modelling:
Parameters –> Misfit
Misfit to
Observations
Adjoint or Tangent linear model:
Station Conc. 6,500
Atmospheric Transport
Model: TM2
 Misfit / ∂ Parameters
parameter optimization
Fluxes: 800,000
Biosphere Model:
BETHY
Parameters: 58
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Cost Function J(m)
Gradient
Method
First derivative (Gradient) of
J(m) w.r.t. m (model
parameters) :
–∂J(m)/∂m
yields direction of steepest
descent
Figure taken from
Tarantola '87
Space of m (model parameters)
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Carbon Cycle Data Assimilation
System (CCDAS)
Assimilated
veg. index
satellite +
Uncert.
CCDAS Step 1
full BETHY
Background
CO2 fluxes*
Prescribed
Assimilated
Phenology
Hydrology
CO2
+ Uncert.
CCDAS Step 2
BETHY+TM2
only Photosynthesis,
Energy&Carbon Balance
Optimized Params
+ Uncert.
Diagnostics
+ Uncert.
*
* ocean:
Takahashi et al. (1999), LeQuere et al. (2000); emissions: Marland et al. (2001), Andres et al. (1996); land use: Houghton
et al. (1990)
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BETHY
(Biosphere Energy-Transfer-Hydrology Scheme)
•
•
•
lat, lon = 2 deg
GPP:
C3 photosynthesis – Farquhar et al. (1980)
C4 photosynthesis – Collatz et al. (1992)
stomata – Knorr (1997)
Raut:
maintenance respiration = f(Nleaf, T) – Farquhar, Ryan (1991)
growth respiration ~ NPP – Ryan (1991)
Rhet:
k
fast/slow pool resp. = w Q10 T/10 C fast/slow / t fast/slow
t slow –> infin.
average NPP = b average Rhet (at each grid point)
t=1h
t=1h
t=1day
b<1: source
b>1: sink
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Optimisation
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global fluxes
Optimised
fluxes (1)
Major El Niño events
Major La Niña event
Post Pinatubo Period
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normalized CO2 flux and ENSO
lag correlation
(low-pass filtered)
Optimised
fluxes (2)
ENSO and terr. biosph. CO2:
correlation seems strong
correlation between Niño-3 SST
anomaly and net CO2 flux shows
maximum at 4 months lag, for
both El Niño and La Niña states
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Optimised
fluxes (3)
flux sites?
net CO2 flux to atm.
gC / (m2 month)
during El Niño (>+1s)
lagged correlation
at 99% significance
-0.8
-0.4
0
0.4
0.8
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Error Covariances in Parameters
J(x)
Second Derivative
(Hessian) of J(m):
∂2J(m)/∂m2
yields curvature of J,
provides estimated
uncertainty in mopt
Figure taken from
Tarantola '87
Space of m (model parameters)
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Error Covariances in Parameters
Cost function (misift):
model diagnostics
measurements
1
1
-1
-1
J(m)  [m  m0 ]Cm0 [m  m0]  [y (m)  y 0 ]Cy [y (m)  y 0 ]
2
2
assumed
model parameters
a priori covariance matrix
of
parameter + model error
a priori
parameter values
Vm(TrEv)
Vm(EvCn)
Vm(C3 Gr)
Vm(Crop)
first gues s
µm ol/m
2
optimized
s
µm ol/m
60 .0
29 .0
42 .0
11 7.0
 J
Cm   2 
mi, j 
prior unc.
2
s
%
43 .2
32 .6
18 .0
45 .4
1
2
Error covariance of parameters
after optimisation:
examples:
error covariance matrix
of measurements
opt.unc .
Vm(TrEv)
%
20 .0
20 .0
20 .0
20 .0
10 .5
16 .2
16 .9
17 .8
0.28
0.02
-0.02
0.05
= inverse Hessian
Vm(EvCn)
Vm(C3 Gr)
Vm(Crop)
erro r co va riance
0.02
-0.02
0.65
-0.10
-0.10
0.71
0.08
-0.31
0.05
0.08
-0.31
0.80
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Relative Error Reduction
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Error Covariances in Diagnostics
Error covariance of diagnostics, y,
after optimisation (e.g. CO2 fluxes):
 yi (mopt)   y i (mopt) 
Cm 

Cy (mopt)  
 m j   m j 
T
adjoint or
tangent linear
model
error covariance
of parameters
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Regional Net Carbon Balance and
Uncertainties
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Comparison shows impact of a
(pseudo) flux measurement in
the broadleaf evergreen biome
on Q10 estimated by an
inversion of SDBM:
Upper panel:
only concentration data
Lower panel:
concentration data +
pseudo flux measurement
(mean: as predicted
sigma: 10gC/m^2/year)
a priori mean/uncertainties
a posteriori mean/uncertainties
Details:
Kaminski et al., GBC, 2001
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Conclusions
• CCDAS with 58 parameters can already fit 20 years
of CO2 concentration data
• Sizeable reduction of uncertainty for ~13 parameters
• terr. biosphere response to climate fluctuations
dominated by ENSO
• System can test model with uncertain parameters,
and deliver a posteriori uncertainties on parameters,
fluxes
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Outlook
• explore more parameter configurations
• include fire as a process with uncertainties
• need more constraints, e.g. eddy fluxes –>
reduce uncertainties
• however: needs to solve scaling problem
(satellites?)
• approach can be regionalized easily
• extend approach to ocean carbon cycle
• projection of uncertainties into future
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