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Estimating parameters in inversions for regional carbon fluxes

Estimating parameters in inversions for regional carbon fluxes. Nir Y Krakauer 1* , Tapio Schneider 1 , James T Randerson 2 1. California Institute of Technology 2. Earth Systems Science, University of California, Irvine * niryk@caltech.edu. Motivation & outline.

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Estimating parameters in inversions for regional carbon fluxes

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  1. Estimating parameters in inversions for regional carbon fluxes Nir Y Krakauer1*, Tapio Schneider1, James T Randerson2 1. California Institute of Technology 2. Earth Systems Science, University of California, Irvine * niryk@caltech.edu

  2. Motivation & outline • Inferring carbon fluxes from patterns in atmospheric CO2 concentrations is an inverse problem • Parameters in the inversion set-up may not be well constrained by prior information, yet the values chosen significantly affect the inferred flux patterns • Here, we explore generalized cross-validation as a method for choosing values for parameters

  3. The linear inverse problem Measurements of CO2 concentrations, with error variance matrix Cb the (unknown) flux magnitudes Ax ≈ b A transport operator that relates concentration patterns to flux magnitudes x ≈ x0 A prior guess for the flux distribution, with prior uncertainty variance matrix Cx

  4. Ambiguities in parameter choice • Solving the inverse problem requires specifying Cb,Cx,x0 • Adjustable parameters include: Weight CO2 measurements equally or differentially? How much weight to give the measurements vs. the prior guesses? • Different parameter values lead to varying results for, e.g., the land-ocean and America-Eurasia distribution of the missing carbon sink

  5. Generalized cross-validation (GCV) • Craven and Wahba (1979): a good value of a regularization parameter in an inverse problem is the one that provides the best invariant predictions of left-out data points • Choose the parameter values that minimize the “GCV function”: T = effective degrees of freedom GCV=

  6. The TransCom 3 inversion • Estimates mean-annual fluxes from 11 land and 11 ocean regions • Data: 1992-1996 mean CO2 concentrations at 75 stations, and the global mean rate of increase Gurney et al 2002

  7. Parameters we varied • λ: How closely the solution would fit the prior guess x0 • controls size of the prior-flux variance Cx • higher λ: solution will be closer to x0 (more regularization) • TransCom value: 1 • τ: How much preference to give data from low-variance (oceanic) stations • controls structure of the data variance Cb • 0: all stations weighted equally • TransCom value: 1

  8. Results: the GCV function

  9. Results: inferred CO2 flux (Pg C/ yr)

  10. Results: Ocean

  11. Results: equatorial land

  12. overall flux distribution TransCom parameter values GCV parameter values

  13. Conclusion • Parameter choice accounts for part of the variability in CO2 flux estimates derived from inverse methods • GCV looks promising for empirically choosing parameter values in global-scale CO2 inversions • GCV-based parameter choice methods should also be of use for smaller-scale (regional and local) studies

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