A hough spectral model for three-dimensional studies of the middle atmosphere

A three-dimensional framework is developed for studying the middle atmosphere in relation to upper-tropospheric structure. The numerical model is formulated from the primitive equations in isentropic coordinates, which directly characterize diabatic processes forcing the Brewer-Dobson circulation. It is anchored in observed tropospheric variability, so integrations provide middle atmospheric behavior that tracks observed variations in the upper troposphere. The numerical framework is versatile and computationally efficient. It achieves enhanced performance by incorporating eigenfunctions of the primitive equations to represent structure spectrally in all three coordinates. Scale-selective dissipation can then be applied entirely at sixth order, which leaves all but the shortest vertical scales undamped. This feature allows vertical diffusion to be made small enough to represent stratospheric transport as advective (rather than diffusive) for most of the scales carried in the integration. Transport across the model's lower boundary, which is positioned near the tropopause, is calculated prognostically from diabatic processes in the middle atmosphere, in concert with tropospheric influences imposed at the bottom. Integrations in which different tropospheric influences are represented can then be used to provide an understanding of how transport and chemical composition depend on processes in the middle atmosphere and in the troposphere. Integrations forced by observed tropospheric behavior are validated against climatological structure, as well as tracer behavior deduced from satellite measurements. The isentropic formulation, together with sixth-order vertical dissipation, enable potential vorticity to be conserved quite accurately. The results throw light on the three-dimensional structure of the Brewer-Dobson circulation and how it follows from diabatic processes operating in the middle atmosphere and tropospheric processes operating below.