A two‐dimensional zonally averaged time dependent model is developed to describe the transport and chemical transformations of species in the troposphere and the stratosphere. The constituents are advected by the residual Eulerian circulation, which is shown to equal the diabatic circulation under certain circumstances. Prescribed values of temperatures and diabatic heating rates are used to calculate the diabatic velocities. Slow diffusion, with Kyy = 3 × 109 cm2 s−1 and Kzz = 103 cm2 s−1, is included in the tracer transport calculations in the stratosphere, to simulate mixing due to wave transience. High diffusion coefficients are used in the troposphere. We show that the observed distribution of ozone is adequately reproduced in the model. In early spring, when the ozone columns attain the maximum values at middle and high latitudes, deviations from observations are 5–10% for all latitudes in the northern hemisphere. Stratospheric water vapor, which is extremely sensitive to the latitude of transport across the tropopause, is also well reproduced. Studies of the global atmospheric lifetimes for CF2Cl2, CFCl3, and CCl4 confirm that the strength of the global circulation is realistic in the model. Model experiments are performed with the recently measured low values of oxygen cross sections in the Herzberg continuum as well as with previous high values. In most cases, including ozone calculations, the low values improve the model results.