Effective Buoyancy, at the Surface and Aloft

The Archimedean buoyancy of a fluid parcel is typically offset by the `virtual mass' effect due to environmental inertia, yielding an `effective buoyancy' less than the Archimedean value. Despite its ubiquity, however, this effect is only vaguely understood and rarely quantified. We address this by deriving analytical expressions for the effective buoyancy of parcels both at the surface and aloft, finding a dependence on aspect ratio which is markedly enhanced for surface parcels. We present intuition for these effects, and then discuss applications to convective parameterizations, the `gray-zone' of numerical modeling, and the over-estimation of vertical acceleration in the hydrostatic approximation.