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Improving Understanding of Global and Regional Carbon
Dioxide Flux Variability through Assimilation of in Situ and Remote Sensing Data in a Geostatistical Framework
Kim Mueller1
Sharon Gourdji1
Anna M. Michalak1,2
1Department of Civil and Environmental Engineering2Department of Atmospheric, Oceanic and Space Sciences
The University of Michigan
Synthesis Bayesian Inversion
Meteorological Fields
TransportModel
Sensitivity of observations to
fluxes (H)
Residual covariance
structure (Q, R)
Prior flux
estimates (sp)
CO2
Observations (y)
Inversion
Flux estimates and covariance
ŝ, Vŝ
BiosphericModel
AuxiliaryVariables
Slide from Anna Michalak
Key Questions
Is there another inversion approach available to estimate: Spatial and temporal autocorrelation structure
of fluxes and/or flux residuals? Sources and sinks of CO2 without relying on
prior estimates? Significance of available auxiliary data? Relationship between auxiliary data and flux
distribution? Realistic grid-scale flux variability
Geostatistical Approach to Inverse Modeling
Geostatistical inverse modeling objective function:
H = transport information, s = unknown fluxes, y = CO2 measurements
X and define the model of the trend R = model data mismatch covariance Q = spatio-temporal covariance matrix for the flux deviations
from the trend
1 1,
1 1( ) ( ) ( ) ( )
2 2T TL s β y Hs R y Hs s Xβ Q s Xβ
Deterministic component Stochastic component
Global Gridscale CO2 Flux Estimation Estimate monthly CO2 fluxes (ŝ) and their uncertainty on
3.75° x 5° global grid from 1997 to 2001 in a geostatistical inverse modeling framework using: CO2 flask data from NOAA-ESRL network (y) TM3 (atmospheric transport model) (H) Assume spatial correlation but no temporal correlation a
priori (Q)
Three models of trend flux (Xβ) considered: Simple monthly land and ocean constants Terrestrial latitudinal flux gradient and ocean constants Terrestrial gradient, ocean constants and auxiliary
variables
January 2000 June 2000
0.1
0.2
0.3
0.4
0.5
0.6
0.7January 2000 June 2000
W
-2.0
-1.5
- 1
0
0.5
1
-0.5
Inversion Results –
Transcom Regions
TransCom, Gurney et al. 2003
Southern Ocean
Boreal Asia
South Pacific South Indian
Europe
North Pacific
North Atlantic
Temperate Asia
South Atlantic
Tropical Indian
Tropical East Pacific
Northern Africa
Tropical Atlantic
Tropical West Pacific
Australia
Boreal North America
South America
Southern Africa
Temperate North America
Tropical America
Tropical Asia
Northern Ocean
(SoOc)
(SoIn)
(BoAs)
(SoPa)
(NoPa)
(TrIn)
(TeAs)
(NoAt)
(SoAt)
(TEPa)
(Euro)
(TrAt)
(BNAm)
(NoAf)
(TWPa)
(SoAf)(TrAm)
(TNAm)
(Aust)
(SoAm)
(TrAs)
(NoOc)
Regional comparison of seasonal cycle
GtC/yr
GtC/yr
1 3 5 7 9 11
0
10
BNAm1 3 5 7 9 11
TNAm1 3 5 7 9 11
TrAm1 3 5 7 9 11
SoAm1 3 5 7 9 11
NoAf SoAf
10
0
10
BoAs TeAs TrAs Aust Euro
1 3 5 7 9 11
−2
0
2
NoPa1 3 5 7 9 11
TWPa1 3 5 7 9 11
TEPa1 3 5 7 9 11
SoPa1 3 5 7 9 11
NoOc NoAt
Jan
Mar
May
Jul
Sep
Nov
−2
0
2
TrAt SoAt SoOc TrIn SoIn
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
Jan
Mar
May
Jul
Sep
Nov
11 Land Regions
11 Ocean Regions
Geostatistical Best Estimates (ŝ)+/- 2σŝ
TransCom Estimates (Baker et al., 2006)+/- 2 σ
Aggregated Bottom Up Es
Regional comparison of inter annual variability
GtC/yr
GtC/yr
98 99 00 01
−2
0
2
BNAm98 99 00 01
TNAm98 99 00 01
TrAm98 99 00 01
SoAm98 99 00 01
NoAf98 99 00 01
SoAf
98 99 00 01
−2
0
2
BoAs98 99 00 01
TeAs98 99 00 01
TrAs98 99 00 01
Aust98 99 00 01
Euro
−0.5
0
0.5
NoPa TWPa TEPa SoPa NoOc NoAt
98 99 00 01
−0.5
0
0.5
TrAt98 99 00 01
SoAt98 99 00 01
SoOc98 99 00 01
TrIn98 99 00 01
SoIn
11 Land Regions
11 Ocean Regions
98 99 00 01
Geostatistical Best Estimates (ŝ)+/- 2σŝ
TransCom Estimates (Baker et al., 2006)
Key Questions
Is there another inversion approach available to estimate: Spatial and temporal autocorrelation structure
of fluxes and/or flux residuals? Sources and sinks of CO2 without relying on
prior estimates? Significance of available auxiliary data? Relationship between auxiliary data and flux
distribution? Realistic grid-scale flux variability
…. Sharon
Key Questions
Is there another inversion approach available to estimate: Spatial and temporal autocorrelation structure
of fluxes and/or flux residuals? Sources and sinks of CO2 without relying on
prior estimates? Significance of available auxiliary data? Relationship between auxiliary data and flux
distribution? Realistic grid-scale flux variability
Sample Auxiliary Data
Gourdji et al. (in prep.)
Variance-Ratio Test uses atmospheric data to assess significant improvement in fit of more complex trend
Physical understanding combined with results of VRT to choose final set of auxiliary variables:
% Ag LAI SST% Forest fPAR dSSt/dt% Shrub NDVI Palmer Drought Index% Grass Precipitation GDP Density
Land Air Temp. Population Density
Variance-Ratio Test uses atmospheric data to assess significant improvement in fit of more complex trend
Physical understanding combined with results of VRT to choose final set of auxiliary variables:
% Ag LAI SST% Forest fPAR dSSt/dt% Shrub NDVI Palmer Drought Index% Grass Precipitation GDP Density
Land Air Temp. Population Density
Variance-Ratio Test and Auxiliary Variables
Three models of trend flux (Xβ) considered: Monthly land and ocean constants (simple) Terrestrial latitudinal flux gradient and ocean constants
(modified) Latitudinal gradient, ocean constants and auxiliary
variables (variable)
ˆ
Deterministiccomponent
Stochasticcomponent
Building up the best estimate in January 2000
Gourdji et al. (in prep.)
Ts QHX ˆ ˆ
Uncertainty Reduction from Simple to Variable Trend
Gourdji et al. (in prep.)
%
Regional comparison of seasonal cycle
Gourdji et al. (in prep.)
Comparison of annual average non-fossil fuel flux
Gourdji et al. (in prep.)
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
An
nu
al A
vera
ge
No
n-F
oss
il F
uel
Flu
x (G
tC/y
r)
BN
Am
TN
Am
TrA
m
So
Am
No
Af
So
Af
Bo
As
Te
As
TrA
s
Au
st
Eu
ro
Transcom Land Regions
-1.5
-1
-0.5
0
0.5
1
An
nu
al A
vera
ge
No
n-F
oss
il F
uel
Flu
x (G
tC/y
r)
No
Pa
TW
Pa
TE
Pa
So
Pa
No
Oc
No
At
TrA
t
So
At
So
Oc
TrI
n
So
In
Transcom Ocean Regions
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3A
nn
ual
Ave
rag
e N
on
-Fo
ssil
Fu
el F
lux
(GtC
/yr)
BN
Am
TN
Am
TrA
m
So
Am
No
Af
So
Af
Bo
As
Te
As
TrA
s
Au
st
Eu
ro
Transcom Land Regions
Variable Trend Best Estimates +/- 2
Simple Trend Best EstimatesModified Trend Best EstimatesTranscom (Baker et al., 2006) +/- 2
Rodenbeck et al. (2003) +/- 2
-1.5
-1
-0.5
0
0.5
1
Transcom Ocean Regions
An
nu
al A
vera
ge
No
n-F
oss
il F
uel
Flu
x (G
tC/y
r)
No
Pa
TW
Pa
TE
Pa
So
Pa
No
Oc
No
At
TrA
t
So
At
So
Oc
TrI
n
So
In
Variable Trend Best Estimates +/- 2
Simple Trend Best EstimatesModified Trend Best EstimatesTranscom (Baker et al., 2006) +/- 2
Rodenbeck et al. (2003) +/- 2
Takahashi Oceanic Exchange (2002)
Conclusions Atmospheric data information and geostatistical approach can:
Quantify model-data mismatch and flux covariance structure Identify significant auxiliary environmental variables and
estimate their relationship with flux Constrain continental-scale fluxes independently of biospheric
model and oceanic exchange estimates Uncertainties at grid scale are high, but uncertainties of
continental and global estimates are comparable to synthesis Bayesian studies
Upscaling fluxes a posteriori minimizes the risk of aggregation errors associated with inversions that estimate fluxes directly at large scale
Auxiliary data inform grid-scale flux variability; seasonal cycle at larger scales is consistent across models
Use of auxiliary variables within a geostatistical framework can be used to derive process-based understanding directly from an inverse model
North American CO2 Flux Estimation Estimate North American
CO2 fluxes at 1°x1° resolution & daily/weekly/monthly timescales using: CO2 concentrations
from 3 tall towers in Wisconsin (Park Falls), Maine (Argyle) and Texas (Moody)
STILT – Lagrangian atmospheric transport model
Auxiliary remote-sensing and in situ environmental data
Pseudodata and recovered fluxes (Source: Adam Hirsch, NOAA-ESRL)
Acknowledgements
Collaborators: Advisor: Anna Michalak Research group: Alanood Alkhaled, Abhishek Chatterjee, Sharon
Gourdji, Charles Humphriss, Meng Ying Li, Miranda Malkin, Kim Mueller, Shahar Shlomi, and Yuntao Zhou
Data providers: NOAA-ESRL cooperative air sampling network Christian Rödenbeck, MPIB Kevin Schaefer, NSIDC
Funding sources:
QUESTIONS?