Implementing convection into Lorenz's global cycle. Part I. Gridscale averaging of the energy equations

Sub-gridscale processes take place throughout the global atmosphere. Yet th ey have been neglected in traditional estimates of the global energy cycle on the ground that they can be-treated as molecular heat fluxes. This view may cause quantitative underestimates of the efficiency of the global circu lation of the atmosphere. In Part I of this two-part study we revisit the c lassical theory, beginning with the local energy equations. Similar to Lore nz we introduce a barotropic reference pressure p(r) and define a generaliz ed field equation for the integrand of available potential energy, without reference to hydrostasy. The emerging energy quantity is new in that it com prises not only the classical correlation between efficiency factor and ent halpy but also an additional potential that depends upon p(r). We then perf orm mass-averaging over the scale of contemporaneous global models (40-400 km) and come up with averaged field energy equations, valid at the gridscal e. Additional global and time-averaging of these removes all divergences an d tendencies and yields two equations for the global energy reservoirs. The available potential energy reservoir is fed by gridscale plus sub-gridscal e generation. The kinetic energy reservoir is tapped by gridscale plus sub- gridscale dissipation. Exchange between the reservoirs is carried by both g ridscale and sub-gridscale conversion terms (C-grid,C-sub). Generation, con version and dissipation fluxes are complete, as compared to the approximate quantities in the traditional formulation of the energy cycle. This approa ch allows to fully exploit Lorenz's original concept. The gridscale equatio ns derived will be the basis far evaluating numerically the classical Loren z terms plus a couple of new global conversion fluxes, notably C-sub, to be presented in Part II of this study.