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A Global Carbon Cycle Data Assimilation System (CCDAS) to
Infer Atmosphere-Biosphere CO2 Exchanges and
Their Uncertainties
Marko Scholze1, Peter Rayner2, Jens Kattge3, Wolfgang Knorr3, Thomas Kaminski4, Ralf Giering4 & Heinrich
Widmann3
Tsukuba, 1st Novembre 20043
FastOpt421
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Overview
• Motivation• Top-down vs. bottom-up approach• CCDAS set-up• Calculation and propagation of
uncertainties• Data fit• Global results• Conclusions and outlook
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Motivation
after Joos, 1996
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Motivation
• Where are the sources/sinks?
• Which are the important processes?
• How do they evolve?
Sketch of the global carbon cycle
Fluxes in Gt C yr-1, pools in Gt C,after Prentice et al., 2001.
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„top-down“ vs. „bottom-up“
net CO2
flux at thesurface
Process Model
climate and other driving data
atmospheric inversion
(Transport Model)
atm. CO2 dataAdvantages:• Fluxes consistent with
atm. data• Estimation of uncertainties
Disadvantages:• No process information• Coarse resolution
Advantages:• Process understanding
-> prognostic modeling• High resolution
Disadvantages:• Global validation difficult • Parameter validity
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Combined MethodCCDAS – Carbon Cycle Data Assimilation
System
CO2 stationconcentration
Biosphere Model:BETHY
Atmospheric Transport Model: TM2
Misfit to observations
Model parameter
Fluxes
Misfit 1 Forward Modeling:
Parameters –> Misfit
Inverse Modeling:
Parameter optimization
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CCDAS set-up
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)
eddy flux CO2 & H2O
Monte CarloParam. Inversion
full BETHY
Assimilated
params& uncert.
Pre-step
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Terminology
GPP Gross primary productivity (photosynthesis)NPP Net primary productivity (plant growth)NEP Net ecosystem productivity (undisturbed C storage)NBP Net biome productivity (C storage)
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BETHY(Biosphere Energy-Transfer-Hydrology
Scheme)
• GPP:C3 photosynthesis – Farquhar et al. (1980)C4 photosynthesis – Collatz et al. (1992)stomata – Knorr (1997)
• Plant respiration:maintenance resp. = f(Nleaf, T) – Farquhar, Ryan (1991)
growth resp. ~ NPP – Ryan (1991) • Soil respiration:
fast/slow pool resp., temperature (Q10 formulation) and soil moisture dependant
• Carbon balance:average NPP = average soil resp. (at each grid point)
<1: source>1: sink
t=1h
t=1h
t=1day
lat, lon = 2 deg
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Pre-Step
Inversion of terrestrial ecosystem parameter values against eddy covariance measurements by Monte Carlo sampling
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Case study: Loobos site, Netherlands
• temperate oceanic climate, coniferous forest• Halfhourly data of Eddy covariance measurements
from seven days during 1997 and 1998
• Diagnostics: NEE and LE
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Estimated parameters and their standard deviations
a priori SD:
0.1
0.25
0.5
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A Posteriori parameter PDF for Loobos site
ga,v: vegetation factor of atmospheric conductanceEvm: activation energy of Vm
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Propagation of unctertainties to modelled fluxes
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Carbon sequestration at the Loobos site during 1997 and 1998
Knorr & Kattge, 2004
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CCDAS Step 2: Station network
41 stations from Globalview (2001), no gap-filling, monthly values
1979-1999.
Annual uncertainty values from Globalview (2001).
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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 rrrrrrrrrrr
−−+−−= )()()( 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
DrMr
pr
need of (adjoint of the model)Jpr∇
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Calculation of uncertainties
• Error covariance of parameters
1
2
2−
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
=ji,
p pJ
rr
∂∂
C = inverse Hessian
T
pX p)p(X
p)p(X
rrr
rrr
rr
∂∂
∂∂
≈ 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.
pr
pr
ppJrr
∂∂− )(
cost function J (p) pr
Model parameter space (p)pr
2nd derivative (Hessian)of J (p):
yields curvature of J.Approximates covariance ofparameters.
pr
22 ppJrr
∂∂ )(
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Data fit
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Seasonal cycle
Barrow Niwot Ridge
observed seasonal cycle
optimised modeled seasonal cycle
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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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Some values of global fluxes
1980-2000 (prior)
1980-2000 1980-1990 1990-2000
GPPGrowth resp.Maint. resp.NPP
135.723.544.0468.18
134.822.3572.740.55
134.322.3172.1340.63
135.322.3973.2840.46
Fast soil resp.Slow soil resp.NEP
53.8314.46-0.11
27.410.692.453
27.610.712.318
27.2110.672.587
Value Gt C/yr
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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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Uncertainty in net flux
Uncertainty in net carbon flux 1980-200gC / (m2 year)
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Uncertainty in prior net flux
Uncertainty in net carbon flux from prior values 1980-2000gC / (m2 year)
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NEP anomalies: global and tropical
global flux anomalies
tropical (20S to 20N) flux anomalies
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IAV and processes
Major El Niño events
Major La Niña event
Post Pinatubo period
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Interannual Variability I
Normalized CO2 flux and ENSO
Lag correlation(low-pass filtered)
ENSO and terr. biosph. CO2:Correlations seems strong with a maximum at ~4 months lag,for both El Niño and La Niña states.
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Interannual Variabiliy II
Lagged correlation on grid-cell basis at 99% significance
correlation coefficient
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Low-resolution CCDAS
• A fully functional low resolution version of CCDAS, BETHY runs on the TM2 grid (appr. 10° x 7.8°)
• 506 vegetation points compared to 8776 (high-res.)• About a factor of 20 faster than high-res. Version -> ideal
for developing, testing and debugging• On a global scale results are comparable (can be used
for pre-optimising)
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Including the ocean • A 1 GtC/month pulse lasting for three months is used as
a basis function for the optimisation• Oceans are divided into the 11 TransCom-3 regions• That means: 11 regions * 12 months * 21 yr / 3 months =
924 additional parameters• Test case:
all 924 parameters have a prior of 0. (assuming that our background ocean flux is correct)
each pulse has an uncertainty of 0.1 GtC/month giving an annual uncertainty of ~2 GtC for the total ocean flux
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Including the ocean
Seasonality at MLOGlobal land flux
Observations
Low-res incl. ocean basis functions Low resolution model
High resolution standard model
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Conclusions
• Eddy covariance measurements can be used to assign prior values and uncertainty distribution for CCDAS step 2.
• CCDAS with 58 parameters can fit 20 years of CO2 concentration data; ~15 directions can be resolved
• Terr. biosphere response to climate fluctuations dominated by El Nino.
• A tool to test model with uncertain parameters and to deliver a posterior uncertainties on parameters and prognostics.
• With the ability of including ocean basis functions in the optimisation procedure CCDAS comprises a ‘normal’ atmospheric inversion.
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Future
• Explore more parameter configurations.• Include missing processes (e.g. fire).• Upgrade transport model and extend data.• Include more data constraints (eddy fluxes, isotopes,
high frequency data, satellites) -> scaling issue.• Projections of prognostics and uncertainties into future.• Extend approach to a prognostic ocean carbon cycle
model.
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For more information, please visit:http://www.ccdas.org