Application of Geostatistical Inverse Modeling for Data-driven Atmospheric Trace Gas Flux Estimation
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Application of Geostatistical Inverse Modeling for Data-driven Atmospheric Trace Gas Flux Estimation. Anna M. Michalak UCAR VSP Visiting Scientist NOAA Climate Monitoring and Diagnostics Laboratory. Anna M. Michalak

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Anna m michalak ucar vsp visiting scientist noaa climate monitoring and diagnostics laboratory

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

Anna M. Michalak

UCAR VSP Visiting Scientist

NOAA 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
NOAA-CMDL Air Sampling Network Data-driven Atmospheric Trace Gas Flux Estimation


Bayesian inference applied to inverse modeling for contaminant source identification
Bayesian Inference Data-driven Atmospheric Trace Gas Flux EstimationApplied to Inverse Modelingfor Contaminant Source Identification

Likelihood of unknown

parameter given data

Posterior probability density function of unknown parameter

Prior distribution of

unknown parameter

p(y) probabilityof 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
Bayesian Inference Applied to Inverse Modeling for Trace Gas Surface Flux Estimation

Likelihood of fluxes given

atmospheric distribution

Posterior probability of surface flux distribution

Prior information

about fluxes

p(y) probabilityofmeasurements

y : available observations (n×1)

s: surface flux distribution (m×1)


Bayesian vs geostatistical inverse modeling
Bayesian vs. Geostatistical Inverse Modeling Surface Flux Estimation

  • 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


Geostatistical approach to inverse modeling
Geostatistical Approach to Inverse Modeling Surface Flux Estimation

  • 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
Recovery of Annually Averaged Fluxes Surface Flux Estimation

  • 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
Surface Flux EstimationActual” Fluxes


Low model data mismatch
Low Model-Data Mismatch Surface Flux Estimation

Best estimate

Standard Deviation


Low model data mismatch1
Low Model-Data Mismatch Surface Flux Estimation

Best estimate

“Actual” fluxes


Higher model data mismatch
Higher Model-Data Mismatch Surface Flux Estimation

Best estimate

Standard Deviation


Higher model data mismatch1
Higher Model-Data Mismatch Surface Flux Estimation

Best estimate

“Actual” fluxes


Low model data mismatch2
Low Model-Data Mismatch Surface Flux Estimation

Best estimate

“Actual” fluxes


Conclusions from pseudodata study
Conclusions from Pseudodata Study Surface Flux Estimation

  • 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
Recovery of Monthly Fluxes (1997-2001) Surface Flux Estimation

  • 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 2
Monthly Estimates for 2000 – Take 2 Surface Flux Estimation


Transcom 3 regions
TransCom 3 Regions Surface Flux Estimation


Fluxes for 2000 aggregated by region
Fluxes for 2000 Aggregated by Region Surface Flux Estimation


Conclusions from atmospheric data study
Conclusions from Atmospheric Data Study Surface Flux Estimation

  • 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
Future work Surface Flux Estimation

  • 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