Chemical Source Inversion Using Assimilated Constituent Observations

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Chemical Source Inversion Using Assimilated
Constituent Observations

• Andrew Tangborn
• Global Modeling and Assimilation Office

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How are data assimilation and chemical source
inversion related?

• 1. Underdetermined systems fewer constraints
  than unknowns.
• 2. Use Bayesian methods require error
  statistics.
• 3. If errors are normally distributed and
  unbiased optimal scheme results in weighted
  least squares estimate.

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How are they different?

• 1. Different goals state estimate vs. source
  estimate.
• 2. Use different errors source errors vs. model
  and
• State errors.

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Example Kalman Filtering (KF) and Greens
function (GF) Inversion

• Inputs
• chemical tracer observations
• winds
• chemical source/sinks
• Initial state
• Error estimates

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Algorithms

• KF
• Kalman gain
  observation operator
• ca cf K(co Hcf)
• observations
• analysis
• forecast

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• KF
• Where K PfHT (RHPfHT)-1
• is a weighted by obs error (R)
• and forecast error (HPfHT) covariances.
• The forecast error covariance
• Pf MPaMT Q
• is evolved in time from analysis error using the
  discretized model (winds) M
• and added model error Q

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• GF
• Greens function Inverse of source
  error cov.
• xinv (GTXGW)-1 (GTXcoWz)
• Inverse of R
  obs first guess source
• inverted source
• G calculated by running model forward using unit
  sources at
• each grid point.

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• Differences between KF and GF
• KF Initial condition (analysis) used in
• forecast contains earlier observation
• information.
• GF Initial condition does not explicitly
• contain observation data.
• KF Uses model (wind) and observation errors.
• State errors are propagated in time.
• GF Uses source and observation errors.
• State errors are never calculated.

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Combing KF and GF

• Carry out KF assimilation of tracer observations.
• Use both the analysis and analysis error
  covariance as the observations and observation
  error in the GF
• co ca
• X (Pa)-1
• Now X contains information on model errors
• (including wind errors) and co is spread to
  all grid points through assimilation.

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Numerical Experimentsadvection diffusion in 2p x
2p domainwith constant and random source errors
Model source
True Source
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Tracer Fields
True field
Model solution
Analysis field
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Source InversionError Standard Deviation
No Assimilation
With assimilation
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Conclusions

• Data Assimilation can add information to source
  inversion.
• Improvements likely come through improved and
  more complete error covariance information and
  spreading observation information to more grid
  points.