Several research groups recently demonstrated [e.g., Fisher and Lary, 1995; Elbern et al., 1997; Khattatov et al., 1999> that concentrations of some non-observed chemical species can be constrained to a certain extent by the observed ones through our knowledge of atmospheric photochemistry. By utilizing mathematical relationships between chemically coupled species, observations of a subset of chemicals can be used to determine the future state of the whole system. The goal of this manuscript is to provide a mathematical formalism for assessing uncertainties of such an analysis. Practical applications of this study include designing future instruments and measurement strategies optimized to deliver the maximum amount of information given limited resources. In addition, it opens possibilities for testing our knowledge of atmospheric photochemistry by comparing predicted and measured concentrations and their estimated uncertainties. ¿ 2001 American Geophysical Union