A prototype Global Carbon Cycle Data Assimilation System (CCDAS)
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Transcript of A prototype Global Carbon Cycle Data Assimilation System (CCDAS)
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FastOpt
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-upatm. CO2 data
inverseatmospheric
transportmodelling
net CO2fluxes at the
surface
processmodel
climate and other driving data
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FastOpt
Carbon Cycle Data Assimilation
Biosphere Model: BETHY
Atmospheric Transport Model: TM2
Misfit to Observations
Parameters: 58
Fluxes: 800,000
Station Conc. 6,500
Misfit 1 Forward modelling:
Parameters –> Misfit
Adjoint or Tangent linear model:
Misfit / ∂ Parameters
parameter optimization
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Figure taken from Tarantola '87
Space of m (model parameters)
First derivative (Gradient) of J(m) w.r.t. m (model parameters) :
–∂J(m)/∂m yields direction of steepest
descent
Gradient Method
Cost Function J(m)
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FastOpt
Carbon Cycle Data Assimilation System (CCDAS)
CCDAS Step 2BETHY+TM2
only Photosynthesis, Energy&Carbon Balance
CO2
+ Uncert.
Optimized Params + Uncert.
Diagnostics + Uncert.
veg. indexsatellite +Uncert.
CCDAS Step 1full BETHY
PhenologyHydrology
AssimilatedPrescribedAssimilated
BackgroundCO2 fluxes*
* * 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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FastOpt
BETHY(Biosphere Energy-Transfer-Hydrology Scheme)
• 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:
fast/slow pool resp. = wQ10 T/10 C fast/slow / fast/slow
slow –> infin.
average NPP = average Rhet (at each grid point)
<1: source>1: sink
t=1h
t=1h
t=1day
lat, lon = 2 deg
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Optimisation
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Optimised fluxes (1)
global fluxes
Major El Niño events
Major La Niña event
Post Pinatubo Period
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Optimised fluxes (2)normalized CO2 flux and ENSO
ENSO and terr. biosph. CO2:correlation seems strong
lag correlation(low-pass filtered)
correlation between Niño-3 SST anomaly and net CO2 flux shows maximum at 4 months lag, forboth El Niño and La Niña states
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net CO2 flux to atm.gC / (m2 month)
during El Niño (>+1)
Optimised fluxes (3)
lagged correlationat 99% significance
-0.8 -0.4 0 0.4 0.8
flux sites?
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Figure taken from Tarantola '87
J(x)
Second Derivative (Hessian) of J(m):
∂2J(m)/∂m2 yields curvature of J,provides estimateduncertainty in m
opt
Error Covariances in Parameters
Space of m (model parameters)
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Error Covariances in Parameters
first guess optimized prior unc. opt.unc. Vm(TrEv) Vm(EvCn) Vm(C3Gr) Vm(Crop)
µmol/m2s µmol/m2s % %Vm(TrEv) 60.0 43.2 20.0 10.5 0.28 0.02 -0.02 0.05Vm(EvCn) 29.0 32.6 20.0 16.2 0.02 0.65 -0.10 0.08Vm(C3Gr) 42.0 18.0 20.0 16.9 -0.02 -0.10 0.71 -0.31Vm(Crop) 117.0 45.4 20.0 17.8 0.05 0.08 -0.31 0.80
error covarianceexamples:
Cost function (misift):
J(
m ) 1
2[m
m 0]Cm0-1 [
m
m 0] 1
2[y (
m )
y 0]Cy-1 [
y (
m )
y 0 ]
model diagnostics
error covariance matrixof measurements
measurements
assumedmodel parameters
a priori covariance matrixof parameter + model errora priori
parameter values
Error covariance of parametersafter optimisation:
Cm 2J
mi, j2
1
= inverse Hessian
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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):
Cy(m opt)
yi(m opt)
m j
Cm
y i(m opt)
m j
T
error covarianceof parameters
adjoint ortangent linear
model
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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)
Details:Kaminski et al., GBC, 2001
a posteriori mean/uncertaintiesa priori mean/uncertainties
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FastOpt
• 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
Conclusions
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• 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
Outlook