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

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. Two models of the photochemistry of the Martian atmosphere, with and without nitrogen chemistry, are considered. The oxygen nonthermal escape ratio of 1.2 x 10(exp 8)/cu cm/s 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-micrometer 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.