Maximum likelihood estimation of covariance parameters for Bayesian atmospheric trace gas surface flux inversions

[1] This paper introduces a Maximum Likelihood (ML) approach for estimating the statistical parameters required for the covariance matrices used in the solution of Bayesian inverse problems aimed at estimating surface fluxes of atmospheric trace gases. The method offers an objective methodology for populating the covariance matrices required in Bayesian inversions, thereby resulting in better estimates of the uncertainty associated with derived fluxes and minimizing the risk of inversions being biased by unrealistic covariance parameters. In addition, a method is presented for estimating the uncertainty associated with these covariance parameters. The ML method is demonstrated using a typical inversion setup with 22 flux regions and 75 observation stations from the National Oceanic and Atmospheric Administration-Climate Monitoring and Diagnostics Laboratory (NOAA-CMDL) Cooperative Air Sampling Network with available monthly averaged carbon dioxide data. Flux regions and observation locations are binned according to various characteristics, and the variances of the model-data mismatch and of the errors associated with the a priori flux distribution are estimated from the available data.

[1]  Gregg Marland,et al.  A 1° × 1° distribution of carbon dioxide emissions from fossil fuel consumption and cement manufacture, 1950–1990 , 1996 .

[2]  Milind Kandlikar,et al.  Bayesian inversion for reconciling uncertainties in global mass balances , 1997 .

[3]  Shamil Maksyutov,et al.  TransCom 3 CO2 inversion intercomparison: 1. Annual mean control results and sensitivity to transport and prior flux information , 2003 .

[4]  Ian G. Enting,et al.  Reconstructing the recent carbon cycle from atmospheric CO2, δ13C and O2/N2 observations* , 1999 .

[5]  P. Kitanidis,et al.  Maximum likelihood parameter estimation of hydrologic spatial processes by the Gauss-Newton method , 1985 .

[6]  Gregg Marland,et al.  Carbon Dioxide Emission Estimates from Fossil-Fuel Burning\, Hydraulic Cement Production\, and Gas Flaring for 1995 on a One Degree Grid Cell Basis , 2003 .

[7]  Philippe Ciais,et al.  Transcom 3 inversion intercomparison: Model mean results for the estimation of seasonal carbon sources and sinks , 2004, Global Biogeochemical Cycles.

[8]  A. Tarantola.  Inverse problem theory : methods for data fitting and model parameter estimation , 1987 .

[9]  I. Enting,et al.  Using high temporal frequency data for CO2 inversions , 2002 .

[10]  Martin Heimann,et al.  The global atmospheric tracer model TM3 , 1995 .

[11]  Philip E. Gill,et al.  Practical optimization , 1981 .

[12]  P. Tans,et al.  Error estimates of background atmospheric CO2 patterns from weekly flask samples , 1990 .

[13]  Thomas Kaminski,et al.  A coarse grid three-dimensional global inverse model of the atmospheric transport 1. Adjoint model and Jacobian matrix , 1999 .

[14]  Philippe Ciais,et al.  Inverse modeling of annual atmospheric CO2 sources and sinks , 1999 .

[15]  P. Tans,et al.  A geostatistical approach to surface flux estimation of atmospheric trace gases , 2004 .

[16]  Christopher B. Field,et al.  The contribution of terrestrial sources and sinks to trends in the seasonal cycle of atmospheric carbon dioxide , 1997 .

[17]  Paul J. Crutzen,et al.  An inverse modeling approach to investigate the global atmospheric methane cycle , 1997 .

[18]  Ian G. Enting,et al.  Inverse problems in atmospheric constituent transport , 2002 .

[19]  P. Kitanidis,et al.  Estimation of historical groundwater contaminant distribution using the adjoint state method applied to geostatistical inverse modeling , 2004 .

[20]  C. Sweeney,et al.  Global sea-air CO2 flux based on climatological surface ocean pCO2, and seasonal biological and temperature effects , 2002 .

[21]  P. Kitanidis.  Parameter Uncertainty in Estimation of Spatial Functions: Bayesian Analysis , 1986 .

[22]  Ian G. Enting,et al.  A synthesis inversion of the concentration and δ 13 C of atmospheric CO 2 , 1995 .

[23]  Tapio Schneider,et al.  Using generalized cross‐validation to select parameters in inversions for regional carbon fluxes , 2004 .

[24]  Thomas Kaminski,et al.  On aggregation errors in atmospheric transport inversions , 2001 .

[25]  Taro Takahashi,et al.  Towards robust regional estimates of CO2 sources and sinks using atmospheric transport models , 2002, Nature.

[26]  Sander Houweling,et al.  CO 2 flux history 1982–2001 inferred from atmospheric data using a global inversion of atmospheric transport , 2003 .

[27]  P. Kitanidis.  Quasi‐Linear Geostatistical Theory for Inversing , 1995 .

[28]  P. Ciais,et al.  Influence of transport uncertainty on annual mean and seasonal inversions of atmospheric CO2 data , 2002 .

[29]  Kevin R. Gurney,et al.  On error estimation in atmospheric CO2 inversions , 2002 .