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 Gourdji1Anna 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)

InversionFlux 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 2

T 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 AtlanticTemperate Asia

South Atlantic

Tropical Indian

Tropical East Pacific

Northern Africa

Tropical AtlanticTropical 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 trendPhysical 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 trendPhysical 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

Ann

ual A

vera

ge N

on-F

ossi

l Fue

l Flu

x (G

tC/y

r)

BN

Am

TNA

m

TrA

m

SoA

m

NoA

f

SoA

f

BoA

s

TeA

s

TrA

s

Aus

t

Euro

Transcom Land Regions

-1.5

-1

-0.5

0

0.5

1

Ann

ual A

vera

ge N

on-F

ossi

l Fue

l Flu

x (G

tC/y

r)

NoP

a

TWPa

TEPa

SoPa

NoO

c

NoA

t

TrA

t

SoA

t

SoO

c

TrIn

SoIn

Transcom Ocean Regions

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3A

nnua

l Ave

rage

Non

-Fos

sil F

uel F

lux

(GtC

/yr)

BN

Am

TNA

m

TrA

m

SoA

m

NoA

f

SoA

f

BoA

s

TeA

s

TrA

s

Aus

t

Euro

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

Ann

ual A

vera

ge N

on-F

ossi

l Fue

l Flu

x (G

tC/y

r)

NoP

a

TWPa

TEPa

SoPa

NoO

c

NoA

t

TrA

t

SoA

t

SoO

c

TrIn

SoIn

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?

kimlm@umich.edu & sgourdji@umich.edu