A new top boundary condition for modeling surface diffusive exchange of a generic volatile tracer: theoretical analysis and application to soil evaporation

We describe a new top boundary condition (TBC) for representing the air–soil diffusive exchange of a generic volatile tracer. This new TBC (1) accounts for the multi-phase flow of a generic tracer; (2) accounts for effects of soil temperature, pH, solubility, sorption, and desorption processes; (3) enables a smooth transition between wet and dry soil conditions; (4) is compatible with the conductance formulation for modeling air–water volatile tracer exchange; and (5) is applicable to site, regional, and global land models. Based on the new TBC, we developed new formulations for bare-soil resistance and corresponding soil evaporation efficiency. The new soil resistance is predicted as the reciprocal of the harmonic sum of two resistances: (1) gaseous and aqueous molecular diffusion and (2) liquid mass flow resulting from the hydraulic pressure gradient between the soil surface and center of the topsoil control volume. We compared the predicted soil evaporation efficiency with those from several field and laboratory soil evaporation measurements and found good agreement with the typically observed two-stage soil evaporation curves. Comparison with the soil evaporation efficiency equation of Lee and Pielke (1992; hereafter LP92) indicates that their equation can overestimate soil evaporation when the atmospheric resistance is low and underestimate soil evaporation when the soil is dry. Using a synthetic inversion experiment, we demonstrated that using inverted soil resistance data from field measurements to derive empirical soil resistance formulations resulted in large uncertainty because (1) the inverted soil resistance data are always severely impacted by measurement error and (2) the derived empirical equation is very sensitive to the number of data points and the assumed functional form of the resistance. We expect the application of our new TBC in land models will provide a consistent representation for the diffusive tracer exchange at the soil–air interface.