A New Methodology for Thermodynamic Retrievals in Tropical Cyclones from Airborne Doppler Radar

Dynamic and thermodynamic retrievals from multi-Doppler radar analyses have improved our understanding of many mesoscale weather phenomena, including supercell thunderstorms, squall lines, and tropical cyclones. In the general formulation, radar derived winds are used in the momentum and thermodynamic equations to solve for buoyancy and pressure perturbations relative to a hydrostatic reference environment. Following the pioneering work of Gal-Chen (1978), various improvements to the thermodynamic retrieval methodology have been proposed, including a cylindrical coordinate version for use with tropical cyclones (Viltard and Roux 1998). However, the concept of a reference environment becomes difficult to define in a rapidly rotating tropical cyclone where the first-order temperature and pressure perturbations are associated with the system-scale vortex in thermal wind balance.

A modified thermodynamic retrieval will be presented based on a separation of the balanced, azimuthal mean vortex flow from the higher-order wind perturbations. In the modified formulation, the reference environment is assumed to be a mean vortex in both gradient wind and hydrostatic balance. The reference virtual potential temperature and pressure fields therefore depend on both height and radius, linking the radial and vertical momentum equations. Buoyancy and pressure perturbations are then retrieved relative to the balanced vortex using a spline-based variational approach called SAMURAI. Airborne Doppler radar and in situ kinematic and thermodynamic data from aircraft and dropsondes are incorporated into the retrieval. The new formulation is believed to provide better insight into the nature of convection and pressure asymmetries in tropical cyclones. Analytic results testing the methodology will be presented, with some discussion of potential application to tornadoes or dust devils. Thermodynamic retrievals using real data from the RAINEX and PREDICT/GRIP/IFEX field campaigns will be presented in a companion paper (Foerster and Bell).