Vertical variations in the concentration and carbon isotope composition of soil carbon dioxide should be related to its flux (respiration) out of soils. This expectation can be quantified in terms of one-dimensional, steady state, Fickian diffusion with an in situ source (i.e., a two-component diffusive mixing model -- endmembers: carbon dioxide from the overlying atmosphere and from oxidizing organic matter). Application of this model to paleosols requires information about ancient carbon dioxide. Such information may be preserved in relevant mineral proxies. The common mineral goethite (FeOOH) contains small amounts of a Fe(III) carbonate component in apparent solid solution. This component can be a proxy for the concentration and carbon isotope ratio of carbon dioxide in wet, oxidizing paleosols. Therefore, concentration and isotopic data from pedogenic goethites that are preserved throughout a paleosol profile might be used, among other things, to estimate ancient soil respiration rates. The method requires preservation of goethite from the crucial upper portion of a paleosol profile, and this preservation could be rare. Nevertheless, the possibility that such preservation may occur is suggested by the fact that goethite data from some paleosols studied to date exhibit the model-predicted linear relationship between the isotopic composition and the reciprocal of concentration for soil carbon dioxide. In one such instance, vertical variations in the concentration of the Fe(III) carbonate component indicated a pre-vascular tropical soil respiration rate that may have been as high as about 7 millimole/square meter/hour.

However, there are also data which suggest that three-component mixing of carbon dioxide may occur in some soils (third component: addition of carbon dioxide from in situ dissolution of carbonate minerals). Such a happenstance in an ancient soil would complicate the problem of recovering paleo-respiration rates from pedogenic goethite and indicates that paleosols must be evaluated on a case-by-case basis.