On the use of regularization techniques in the inverse modeling of atmospheric carbon dioxide

The global distribution of carbon sources and sinks is estimated from atmos pheric CO2 measurements using an inverse method based on the Geophysical Fl uid Dynamics Laboratory SKYHI atmospheric general circulation model. Applyi ng the inverse model without any regularization yields unrealistically larg e CO2 fluxes in the tropical regions. We examine the use of three regulariz ation techniques that are commonly used to stabilize inversions: truncated singular value decomposition, imposition of a priori flux estimates, and us e of a quadratic inequality constraint. The regularization techniques can a ll be made to minimize the unrealistic fluxes in the tropical regions. This brings inversion estimated CO2 fluxes for oceanic regions in the tropics a nd in the Southern Hemisphere into better agreement with independent estima tes of the air-sea exchange. However, one cannot assume that stabilized inv ersions give accurate estimates, as regularization merely holds the fluxes to a priori estimates or simply reduces them in magnitude in regions that a re not resolvable by observations. By contrast, estimates of flux and uncer tainty for the temperate North Atlantic, temperate North Pacific, and borea l and temperate North American regions are far less sensitive to the regula rization parameters, consistent with the fact that these regions are better constrained by the present observations.