Is Buoyancy a Relative Quantity?

Abstract

Basic concepts of buoyancy are reviewed and considered first in light of simple parcel theory and then in a more complete form. It is shown that parcel theory is generally developed in terms of the density (temperature) difference between an ascending parcel and an ‘‘environment’’ surrounding that parcel. That is, buoyancy is often understood as a relative quantity that apparently depends on the choice of a base-state environmental profile. However, parcel theory is most appropriately understood as a probe of the static stability of a sounding to finite vertical displacements of hypothetical parcels within the sounding rather than as a useful model of deep convection. The thermal buoyancy force, as measured by the temperature difference between a parcel and the base state, and vertical perturbation pressure gradient force together must remain independent of the base state. The vertical perturbation pressure gradient force can be decomposed to include a term due to thermal buoyancy and another due to the properties of motion in the flow. Some thought experiments are presented to illustrate the ambiguous relevance of the base state. It is concluded that buoyancy is not a relative quantity in that it cannot be dependent on the choice of an essentially arbitrary reference state. Buoyancy is the static part of an unbalanced vertical pressure gradient force and, as such, is determined locally, not relative to some arbitrary base state outside of a parcel. This has direct application to the diagnosis of buoyancy from numerical simulations—done properly, such a diagnosis must include not only the thermal buoyancy term but also the perturbation pressure gradient force due to buoyancy.