The atmospheric structure upwind of the Great takes during arctic air outbreaks is represented by three layers: a lower constant flux layer in contact with the ground, a well-mixed planetary boundary layer surmounted by an inversion, and a deep stratum of overlying stable air. The set of primitive equations is averaged through the depth of the mixed layer to yield predictive equations for the horizontal components of velocity, potential temperature and specific humidity in the layer, and the height of the inversion. Interactions between the well-mixed convective layer and both the underlying and overlying layers are parameterized so that time-dependent calculations can be limited to a single layer. Precipitation from cumulus clouds within the layer is represented in terms of the mesoscale variables and latent heat is included. The equation set has been solved numerically for a 2000-point grid mesh centered on Lake Erie. Grid separation was 6 km in the cross-lake direction and 12 km along the lake... Abstract The atmospheric structure upwind of the Great takes during arctic air outbreaks is represented by three layers: a lower constant flux layer in contact with the ground, a well-mixed planetary boundary layer surmounted by an inversion, and a deep stratum of overlying stable air. The set of primitive equations is averaged through the depth of the mixed layer to yield predictive equations for the horizontal components of velocity, potential temperature and specific humidity in the layer, and the height of the inversion. Interactions between the well-mixed convective layer and both the underlying and overlying layers are parameterized so that time-dependent calculations can be limited to a single layer. Precipitation from cumulus clouds within the layer is represented in terms of the mesoscale variables and latent heat is included. The equation set has been solved numerically for a 2000-point grid mesh centered on Lake Erie. Grid separation was 6 km in the cross-lake direction and 12 km along the lake...