A New Closure Assumption and Formulation Based on the Helmholtz Decomposition in the Generalized Velocity Track Display

Abstract

Doppler weather radars are powerful tools for investigating the inner-core structure and intensity of tropical cyclones (TCs). The Doppler velocity can provide quantitative information on the vortex structure in the TCs. The Generalized Velocity Track Display (GVTD) technique has been used to retrieve the axisymmetric circulations and asymmetric tangential flows in the TCs from ground-based single-Doppler radar observations. GVTD can have limited applicability to asymmetric vortices due to the closure assumption of no asymmetric radial flows. The present study proposes a new closure formulation that includes asymmetric radial flows, based on the Helmholtz decomposition. Here it is assumed that the horizontal flow is predominantly rotational and expressed with a streamfunction, but limited inclusion of wavenumber-1 divergence is available. Unlike the original GVTD, the decomposition introduces consistency along radius by requiring to solve equations simultaneously. The new approach, named GVTD-X, is applied to analytical vortices and a real TC with asymmetric structures. This approach makes the retrieval of axisymmetric flow relatively insensitive to the contamination from asymmetric flows and the error in the storm center locations. For an analytical vortex with a wavenumber-2 asymmetry, the maximum relative error of the axisymmetric tangential wind retrieved by GVTD-X is less than 2% at the radius of the maximum wind speed. In practical applications, errors can be evaluated by comparing results for different maximum wavenumbers. When applied to a real TC, GVTD-X largely suppressed an artificial periodic fluctuation that occurs in GVTD from the aliasing of the neglected asymmetric radial flows.