Effects of atmospheric composition on apparent activation energy of silicate weathering: I. Model formulation

We have developed a weathering model to comprehensively understand the determining factors of the apparent activation energy of silicate weathering in order to better estimate the silicate-weathering flux in the Precambrian. The model formulates the reaction rate of a mineral as a basis, then the elemental loss by summing the reaction rates of whole minerals, and finally the weathering flux from a given weathering profile by integrating the elemental losses along the depth of the profile. The rate expressions are formulated with physicochemical parameters relevant to weathering, including solution and atmospheric compositions. The apparent activation energies of silicate weathering are then represented by the temperature dependences of the physicochemical parameters based on the rate expressions. It was found that the interactions between individual mineral-reactions and the compositions of solution and atmosphere are necessarily accompanied by those of temperature-dependence counterparts. Indeed, the model calculates the apparent activation energy of silicate weathering as a function of the temperature dependence of atmospheric CO2(ΔHCO2′). The dependence of the apparent activation energy of silicate weathering on ΔHCO2′ may explain the empirical dependence of silicate weathering on the atmospheric composition. We further introduce a compensation law between the apparent activation energy and the pre-exponential factor to obtain the relationship between the silicate-weathering flux (FCO2), temperature and the apparent activation energy. The model calculation and the compensation law enable us to predict FCO2 as a function of temperature, once ΔHCO2′ is given. The validity of the model is supported by agreements between the model prediction and observations of the apparent activation energy and FCO2 in the modern weathering systems. The present weathering model will be useful for the estimation of FCO2 in the Precambrian, for which ΔHCO2′ can be deduced from the greenhouse effect of atmospheric CO2.