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 they have been neglectedin traditional estimates of the global energy cycle on the ground that they can be treatedas molecular heat fluxes. This view may cause quantitative underestimates of the efficiency ofthe global circulation of the atmosphere. In Part I of this two-part study we revisit the classicaltheory, beginning with the local energy equations. Similar to Lorenz we introduce a barotropicreference pressure p_r and define a generalized field equation for the integrand of availablepotential energy, without reference to hydrostasy. The emerging energy quantity is new in thatit comprises not only the classical correlation between efficiency factor and enthalpy but alsoan additional potential that depends upon p_r. We then perform mass-averaging over the scaleof contemporaneous global models (40–400 km) and come up with averaged field energy equations, valid at the gridscale. Additional global and time-averaging of these removes all divergencesand tendencies and yields two equations for the global energy reservoirs. The availablepotential energy reservoir is fed by gridscale plus sub-gridscale generation. The kinetic energyreservoir is tapped by gridscale plus sub-gridscale dissipation. Exchange between the reservoirsis carried by both gridscale and sub-gridscale conversion terms (C^grid, C^sub). Generation, conversionand dissipation fluxes are complete, as compared to the approximate quantities in thetraditional formulation of the energy cycle. This approach allows to fully exploit Lorenz’soriginal concept. The gridscale equations derived will be the basis for evaluating numericallythe classical Lorenz terms plus a couple of new global conversion fluxes, notably C^sub, to bepresented in Part II of this study.