Understanding the vertical structure of potential vorticity in tropical depressions

Potential vorticity (PV) has been used to understand the intensification and motion of a variety of tropical vortices. Here, atmospheric reanalyses and idealized models are used to understand how the vertical structures of moist convective heating and adiabatic advection jointly shape the vertical structures of PV in tropical depressions. Observationally based estimates reveal a top-heavy PV structure in tropical depressions, contrasting with bottom-heavy structures of absolute vorticity and diabatic PV generation. These distinct vertical structures are reproduced in an axisymmetric model which employs the weak temperature gradient approximation for conceptual simplicity and is forced by stratiform and deep convective heating. When applied in isolation, the stratiform and deep convective heatings produce PV maxima at 500 hPa and near the surface, respectively. When these two heatings are applied simultaneously, interactions between the stratiform and deep convective modes enhance the adiabatic advective tendencies produced by the transverse circulation, making the PV distribution more top-heavy. In the lower and middle troposphere, radial advection also greatly reduces the radius of the PV structure relative to that of the imposed heating, consistent with structures in observed tropical depressions; the implications of these differences in radial structures for using the flux form of the relevant conservation equations (e.g. for PV substance or absolute vorticity) are discussed