Total potential energy of finite columns

The relation between enthalpy and total potential energy in a column of finite horizontal extent is investigated. The limitations of the quasistatic approximation are introduced a priori rather than a posteriori, i.e., cyclone-scale air masses are assumed to be in hydrostatic equilibrium, but any differential equation implying small-scale hydrostatic balance is deliberately avoided. It is found that the enthalpy and total potential energy are equal for columns over ocean, but in general, there is an orographic term which cannot be eliminated by redefining the zero-level of geopotential. There is also a term consequent of the departure from hydrostatic balance in the neighborhood of surface irregularities; this term is presumably negligible for columns of cyclone-scale lateral extent.