1. 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 2004 1 2 3
FastOpt 4

2. Overview Motivation Top-down vs. bottom-up approach CCDAS set-up
Calculation and propagation of uncertainties
Data fit
Global results
Conclusions and outlook

3. Motivation
after Joos, 1996

4. Fluxes in Gt C yr-1, pools in Gt C,
Motivation
Sketch of the global carbon cycle
Where are the sources/sinks?
Which are the important processes?
How do they evolve?
Fluxes in Gt C yr-1, pools in Gt C,
after Prentice et al., 2001.

5. „top-down“ vs. „bottom-up“
Advantages:
Fluxes consistent with
atm. data
Estimation of uncertainties
Disadvantages:
No process information
Coarse resolution
atmospheric
inversion
(Transport Model)
atm. CO2 data
net CO2
flux at the
surface
Advantages:
Process understanding
-> prognostic modeling
High resolution
Disadvantages:
Global validation difficult
Parameter validity
Process Model
climate and other
driving data

6. Combined Method CCDAS – Carbon Cycle Data Assimilation System
Misfit 1
Forward Modeling:
Parameters –> Misfit
Inverse Modeling:
Parameter optimization
Misfit to
observations
CO2 station
concentration
Atmospheric Transport
Model: TM2
Fluxes
Biosphere Model:
BETHY
Model parameter

7. CCDAS set-up Background fluxes:
Pre-step
Assimilated
eddy flux
CO2 & H2O
Monte Carlo
Param. Inversion
full BETHY
params
& uncert.
Background fluxes:
Fossil emissions (Marland et al., 2001 und Andres et al., 1996)
Ocean CO2 (Takahashi et al., 1999 und Le Quéré et al., 2000)
Land-use (Houghton et al., 1990)
Transport Model TM2 (Heimann, 1995)

8. 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)

9. 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)
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 = b average soil resp. (at each grid point)
t=1h
t=1h
t=1day
b<1: source
b>1: sink

10. Pre-Step
Inversion of terrestrial ecosystem parameter values against eddy covariance measurements by Monte Carlo sampling

11. 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

12. Estimated parameters and their standard deviations
a priori SD:
0.1
0.25
0.5

13. A Posteriori parameter PDF for Loobos site
ga,v: vegetation factor of atmospheric conductance
Evm: activation energy of Vm

14. Propagation of unctertainties to modelled fluxes

15. Carbon sequestration at the Loobos site during 1997 and 1998
Knorr & Kattge, 2004

16. CCDAS Step 2: Station network
41 stations from Globalview (2001), no gap-filling, monthly values
Annual uncertainty values from Globalview (2001).

17. Calibration Step
Flow of information in CCDAS. Oval boxes represent the various
quantities. Rectangular boxes denote mappings between these fields.

18. Prognostic Step Oval boxes represent the various quantities.
Rectangular boxes denote mappings between these fields.

19. Methodology Minimize cost function such as (Bayesian form): where
is a model mapping parameters to observable quantities
is a set of observations
error covariance matrix
 need of (adjoint of the model)

20. Calculation of uncertainties
Error covariance of parameters
= inverse Hessian
Covariance (uncertainties) of prognostic quantities

21. Gradient Method cost function J (p) 1st derivative (gradient) of
J (p) to model parameters p:
yields direction of steepest
descent.
2nd derivative (Hessian)
of J (p):
yields curvature of J.
Approximates covariance of
parameters.
Model parameter space (p)
Figure from Tarantola, 1987

22. Data fit

23. Seasonal cycle Barrow Niwot Ridge observed seasonal cycle
optimised modeled seasonal cycle

24. Global Growth Rate Calculated as: observed growth rate
Atmospheric CO2 growth rate
Calculated as:
observed growth rate
optimised modeled growth rate

25. Parameters I 3 PFT specific parameters (Jmax, Jmax/Vmax and b)
18 global parameters
57 parameters in all plus 1 initial value (offset)
Param
Initial
Predicted
Prior unc. (%)
Unc. Reduction (%)
fautleaf
c-cost
Q10 (slow)
t (fast)
0.4
1.25
1.5
0.24
1.27
1.35
1.62
2.5
0.5 70 75 39 1 72 78
(TrEv)
(TrDec)
(TmpDec)
(EvCn)
(DecCn)
(C4Gr)
(Crop)
1.0
1.44
0.35
2.48
0.92
0.73
1.56
3.36 25 95 62 91 90

26. Parameters II
Relative Error Reduction

27. Some values of global fluxes
Value Gt C/yr
(prior)
GPP
Growth resp.
Maint. resp.
NPP
135.7
23.5
44.04
68.18
134.8
22.35
72.7
40.55
134.3
22.31
72.13
40.63
135.3
22.39
73.28
40.46
Fast soil resp.
Slow soil resp.
NEP
53.83
14.46
-0.11
27.4
10.69
2.453
27.6
10.71
2.318
27.21
10.67
2.587

28. Carbon Balance Euroflux (1-26) and other eddy covariance sites*
latitude N
*from Valentini et al. (2000) and others
Euroflux (1-26) and other
eddy covariance sites*
net carbon flux
gC / (m2 year)

29. Uncertainty in net flux
Uncertainty in net carbon flux
gC / (m2 year)

30. Uncertainty in prior net flux
Uncertainty in net carbon flux from prior values
gC / (m2 year)

31. NEP anomalies: global and tropical
global flux anomalies
tropical (20S to 20N) flux anomalies

32. IAV and processes Major El Niño events Major La Niña event
Post Pinatubo period

33. Interannual Variability I
Normalized CO2 flux and ENSO
ENSO and terr. biosph. CO2:
Correlations seems strong with
a maximum at ~4 months lag,
for both El Niño and La Niña
states.
Lag correlation
(low-pass filtered)

34. Interannual Variabiliy II
Lagged correlation on grid-cell basis at 99% significance
correlation coefficient

35. 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)

36. 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

37. Including the ocean Global land flux Seasonality at MLO Observations
High resolution standard model
Low resolution model
Low-res incl. ocean basis functions

38. 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.

39. 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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