Abstract :
Sub-gridscale processes take place throughout the global atmosphere. Yet they 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 circulation of the atmosphere. In Part I of this two-part study we revisit the classical
theory, beginning with the local energy equations. Similar to Lorenz we introduce a barotropic
reference pressure pr and define a generalized field equation for the integrand of available
potential energy, without reference to hydrostasy. The emerging energy quantity is new in that
it comprises not only the classical correlation between efficiency factor and enthalpy but also
an additional potential that depends upon pr. We then perform mass-averaging over the scale
of 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 divergences
and tendencies and yields two equations for the global energy reservoirs. The available
potential energy reservoir is fed by gridscale plus sub-gridscale generation. The kinetic energy
reservoir is tapped by gridscale plus sub-gridscale dissipation. Exchange between the reservoirs
is carried by both gridscale and sub-gridscale conversion terms (Cgrid, Csub). Generation, conversion
and dissipation fluxes are complete, as compared to the approximate quantities in the
traditional formulation of the energy cycle. This approach allows to fully exploit Lorenz’s
original concept. The gridscale equations derived will be the basis for evaluating numerically
the classical Lorenz terms plus a couple of new global conversion fluxes, notably Csub, to be
presented in Part II of this study.
