Anna M. Michalak UCAR VSP Visiting Scientist NOAA Climate Monitoring and Diagnostics Laboratory
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Transcript of 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 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
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XsQXsHsyRHsy 11
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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