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 atmospheric CO2 measurements using an inverse method based on the Geophysical Fluid Dynamics Laboratory SKYHI atmospheric general circulation model. Applying the inverse model without any regularization yields unrealistically large CO2 fluxes in the tropical regions. We examine the use of three regularization techniques that are commonly used to stabilize inversions: truncated singular value decomposition, imposition of a priori flux estimates, and use of a quadratic inequality constraint. The regularization techniques can all be made to minimize the unrealistic fluxes in the tropical regions. This brings inversion estimated CO2 fluxes for oceanic regions in the tropics and in the Southern Hemisphere into better agreement with independent estimates of the air-sea exchange. However, one cannot assume that stabilized inversions give accurate estimates, as regularization merely holds the fluxes to a priori estimates or simply reduces them in magnitude in regions that are not resolvable by observations. By contrast, estimates of flux and uncertainty for the temperate North Atlantic, temperate North Pacific, and boreal and temperate North American regions are far less sensitive to the regularization parameters, consistent with the fact that these regions are better constrained by the present observations.