Relationships between CO2, thermodynamic limits on silicate weathering, and the strength of the silicate weathering feedback

Recent studies have suggested that thermodynamic limitations on chemical weathering rates exert a first-order control on riverine solute fluxes and by extension, global chemical weathering rates. As such, these limitations may play a prominent role in the regulation of carbon dioxide levels (pCO2) over geologic timescales by constraining the maximum global weathering flux. In this study, we develop a theoretical scaling relationship between equilibrium solute concentrations and pCO2 based on equilibrium constants and reaction stoichiometry relating primary mineral dissolution and secondary mineral precipitation. We test this theoretical scaling relationship against reactive transport simulations of chemical weathering profiles under open- and closed-system conditions, representing partially and fully water-saturated regolith, respectively. Under open-system conditions, equilibrium bicarbonate concentrations vary as a power-law function of pCO2(y=kxn) where n is dependent on reaction stoichiometry and k is dependent on both reaction stoichiometry and the equilibrium constant. Under closed-system conditions, bicarbonate concentrations vary linearly with pCO2 at low values and approach open-system scaling at high pCO2. To describe the potential role of thermodynamic limitations in the global silicate weathering feedback, we develop a new mathematical framework to assess weathering feedback strength in terms of both (1) steady-state atmospheric pCO2 concentrations, and (2) susceptibility to secular changes in degassing rates and transient carbon cycle perturbations, which we term 1st and 2nd order feedback strength, respectively. Finally, we discuss the implications of these results for the effects of vascular land plant evolution on feedback strength, the potential role of vegetation in controlling modern solute fluxes, and the application of these frameworks to a more complete functional description of the silicate weathering feedback. Most notably, the dependence of equilibrium solute concentrations on pCO2 may represent a direct weathering feedback largely independent of climate and modulated by belowground organic carbon respiration.