Uniqueness of a solution of a steady state photochemical problem: Applications to Mars

Abstract

Based on the conservation of chemical elements in chemical reactions, a rule is proved that the number of boundary conditions given by densities and/or nonzero velocities should not be less than the number of chemical elements in the system, and the boundary conditions for species given by densities and velocities should include all elements in the system. Applications of this rule to Mars are considered. It is shown that the problem of the CO2‐H2O chemistry in the lower and middle atmosphere of Mars, say, in the range of 0–80 km does not have a unique solution, if only CO2 and H2O densities are given at the lower boundary, and the remaining boundary conditions are fluxes. Two examples of models of this type are discussed. These models fit the same boundary conditions, are balanced with a relative accuracy of 10−4 for H2 (and much better for other species), and predict O2, CO, and H2 mixing ratios which differ by orders of magnitude. One more species density, e.g., that of O2, should be specified at the boundary to obtain a unique solution. The situation is better if the upper boundary is extended to the exobase where thermal escape velocities of H and H2 can be specified. In this case, however, either the oxygen nonthermal escape rate (and hence the total hydrogen escape rate) or the O2 (or other species) density at the surface should be given as a boundary condition. Two models of the photochemistry of the Martian atmosphere, with and without nitrogen chemistry, are considered. The oxygen nonthermal escape rate of 1.2×108 cm−2 s−1 is given at 240 km and is balanced with the total hydrogen escape rate within an uncertainty of 1% for both models. Both models fit the measured O2 and CO mixing ratios, the O3 abundance, and the O2 1.27‐μm dayglow almost within the uncertainties of the measured values, though the model without nitrogen chemistry fits better. The importance of nitrogen chemistry in the lower and middle atmosphere of Mars depends on a fine balance between production of NO and N in the upper atmosphere which is not known within the required accuracy.