On the Display of the Atmospheric Circulation with Streamfunctions

Abstract

The zonally averaged conservation equations for water, linear zonal momentum, and potential heat (gz+cpT) are written in a form analogous to the mass continuity equation. This is possible when atmospheric storage terms are negligible which is generally the case during the solstice seasons. It follows that the fluxes of these properties can be represented by Stokes streamfunctions. Patterns of streamfunctions in the vertical-meridional plane for mass, water (all 3 phases combined), momentum, and heat have been prepared from the “Atmospheric Circulation Statistics” of Oort and Rasmusson (1971). They are shown for the seasons December–January–February and June–July–August, and for the area between 10S-75N. The following details are of interest: The presented data are not new in any sense. Only the mode of presentation is new. Contrary to the total mass transport, which is almost entirely conservative, all other transports have sources and sinks. They are treated as vertical flux divergences and thus are amenable to the streamfunction concept. The streamfunction pattern can be considerably modified by linear combination with the mass continuity equation, characterized by a scale function: This function is zero for water transport, a2Ω cos2ϕ for momentum transport, and gz0+cpT0 for heat transport (z0, T0 averages over total atmosphere). This choice minimizes the back-and-forth transport of properties by the cell circulation. Boundary conditions are that the upper surface of the atmosphere be a streamline for mass, water, and momentum transport. For potential heat, the value at the upper surface at a certain latitude is the net radiation flux across this surface, integrated between this latitude and the pole. The streamlines represent the total flux of the respective property in whatever form. For instance, vertical fluxes of water comprise mean and eddy components of all scales as well as net contributions of solid and liquid water flux. The streamlines of transports with sources and sinks begin and end at the earth's surface (water, momentum, and heat) or additionally at the upper surface of the atmosphere (heat). There are no closed isolines. The mixed character of the various fluxes is qualitatively described. Fluxes of different properties cross each other or go in opposite directions. Further, fluxes of the same property on different scales may go in opposite directions, particularly in the vertical. The total horizontal flux divergences are compared with some independent flux estimates at the earth's surface. Although there are still significant imbalances, the general agreement is fair.