Fitting Parametric Vortices to Aliased Doppler Velocities Scanned from Hurricanes

Abstract

n alias-robust least squares method that produces less errors than established methods is developed to produce reference radial velocities for automatically correcting raw aliased Doppler velocities scanned from hurricanes. This method estimates the maximum tangential velocity VM and its radial distance RM from the hurricane vortex center by fitting a parametric vortex model directly to raw aliased velocities at and around each selected vertical level. In this method, aliasing-caused zigzag discontinuities in the relationship between the observed and true radial velocities are formulated into the cost function by applying an alias operator to the entire analysis-minus-observation term to ensure the cost function to be smooth and concave around the global minimum. Simulated radar velocity observations are used to examine the cost function geometry around the global minimum in the space of control parameters (VM, RM). The results show that the global minimum point can estimate the true (VM, RM) approximately if the hurricane vortex center location is approximately known and the hurricane core and vicinity areas are adequately covered by the radar scans, and the global minimum can be found accurately by an efficient descent algorithm as long as the initial guess is in the concave vicinity of the global minimum. The method is used with elaborated refinements for automated dealiasing, and this utility is highlighted by an example applied to severely aliased radial velocities scanned from a hurricane.