A hierarchy of models is developed to test the accuracy of the family solution of the photochemical equations of the stratosphere. Results of the explicit solution of the equations for a simplified mid-winter disturbance near the 850 K isentropic surface are compared with the solutions for models containing 26, 20, 16, 14, 12, 10, and 8 families for a 12-day integration. In general, it is found that the family approach can yield quite accurate solutions, providing enough families are retained. However, large errors, of order 20%, are produced in some radical concentrations such as OH for models with a small number of families. The minimum number of families consistent with economy in the solution of the equations while maintaining scientific accuracy is discussed. In particular, it is recommended that exact dynamical tracers be incorporated into family models to reduce computer memory requirements by parameterizing long time scale species such as H2O, CH4 and H2 in terms of the tracer. Other species such as N2O, total chlorine, and total nitrogen may also be so parameterized according to how the model is to be used.

Even for models with an extensive set of families, the concentrations of radical species are significantly in error at dawn, suggesting the need for caution in comparisons with measurements made using occultation techniques. This may not lead to significant errors in the calculation of reservoir species such as O3 on time scales up to a few weeks but can seriously perturb the qualitative features of other important molecules such as ClONO2 and ClO, and this could lead to significant errors in the calculation of O3 in the longer term. The results have important implications for the development of three-dimensional models of stratospheric chemistry. Some examples of the chemical schemes of those models which have been described in the literature are studied to determine their strengths and weaknesses. The schemes are shown to produce good results for species such as O3 and HNO3 but show signs of weaknesses, particularly in the radical species. Some changes to these schemes are suggested, with a view toward producing an improved three-dimensional model in the future. ¿American Geophysical Union 1991