Application of Geostatistical Inverse Modeling for Data-driven Atmospheric Trace Gas Flux Estimation

Anna M. Michalak

UCAR VSP Visiting ScientistNOAA Climate Monitoring and Diagnostics Laboratory

Anna M. Michalak

Environmental and Water Resources EngineeringDepartment of Civil and Environmental EngineeringThe University of Michigan

NOAA-CMDL Air Sampling Network

Bayesian Inference Applied to Inverse Modeling for Contaminant Source Identification

sssy

ssyys

dp|p

p|p|p

Posterior probability density function of unknown parameter

Prior distribution ofunknown parameter

p(y) probability of data

Likelihood of unknownparameter given data

y : what you know (n×1)s : what you want to know (m×1)

Bayesian Inference Applied to Inverse Modeling for Trace Gas Surface Flux Estimation

sssy

ssyys

dp|p

p|p|p

Posterior probability of surface flux distribution

Prior informationabout fluxes

p(y) probability ofmeasurements

Likelihood of fluxes givenatmospheric distribution

y : available observations (n×1)

s : surface flux distribution (m×1)

Bayesian vs. Geostatistical Inverse Modeling Classical Bayesian inverse modeling objective function:

Q and R are diagonal sp is prior flux estimate in each region

Geostatistical inverse modeling objective function:

R is diagonal; Q is full covariance matrix X and define the model of the mean

pT

pTL ssQssHsyRHsy 11

2

1

2

1

XsQXsHsyRHsy 11

2

1

2

1 TTL

Geostatistical Approach to Inverse Modeling Prior flux estimates are not required Key components:

Model of the mean Prior covariance matrix

Prior based on spatial and/or temporal correlation Derived from available data

Covariance parameter optimization (RML) Model-data mismatch and prior covariance

Method yields physically reasonable estimates (and uncertainties) at any resolution

Conditional realizations can be generated

Recovery of Annually Averaged Fluxes Pseudodata study examining effect of:

Altering model-data mismatch Considering land and ocean fluxes as correlated /

independent Specifying vs. estimating fossil fuel sources

Observations at 39 NOAA-CMDL sites over 12 months (n = 433) Source flux recovered on 3.75o x 5.0o grid (m = 3456) Basis functions obtained using adjoint of TM3 model

Michalak, Bruhwiler & Tans (J. Geophys. Res. 2004, in press)

“Actual” Fluxes

Low Model-Data Mismatch

Best estimate Standard Deviation

Low Model-Data Mismatch

Best estimate “Actual” fluxes

Higher Model-Data Mismatch

Best estimate Standard Deviation

Best estimate “Actual” fluxes

Higher Model-Data Mismatch

Low Model-Data Mismatch

Best estimate “Actual” fluxes

Conclusions from Pseudodata Study Geostatistical approach to inverse modeling shows promise in

application to atmospheric inversions Geostatistical inversions can be performed at fine scale and

for strongly underdetermined problems Separate land and ocean correlation structures can be

identified from atmospheric data Current atmospheric network can be used to obtain physically

reasonable flux estimates without the use of prior estimates

Recovery of Monthly Fluxes (1997-2001) Atmospheric data study examining flux information that can

be recovered from subset of NOAA-CMDL Cooperative Air Sampling Network

Observations at 39 NOAA-CMDL sites (n ~ 451 / year) Source flux recovered on 7.5o x 10o grid (m = 10368 / year) Basis functions obtained using adjoint of TM3 model

Monthly Estimates for 2000 – Take 1

Monthly Estimates for 2000 – Take 2

TransCom 3 Regions

Fluxes for 2000 Aggregated by Region

Conclusions from Atmospheric Data Study Geostatistical approach is successful at identifying monthly

fluxes using subset of NOAA-CMDL network Geostatistical inverse modeling:

Avoids biases associated with using prior estimates and aggregating fluxes to large regions

Offers strongly data-driven flux estimates Examined network sufficient to constrain certain regions,

whereas other regions are not sufficiently sampled

Future work Incorporating and parameterizing both spatial and temporal

covariance Fixed-lag Kalman smoother Influence of auxiliary variables Gridscale flux estimates

Global inversions Regional inversions

Operational flux estimation Geostatistical inversion software