A New Closure Assumption and Formulation Based on the Helmholtz Decomposition for Improving Retrievals for Vortex Circulations from Single-Doppler Radar Observations

Abstract

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 the radius by solving all 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 to small errors in storm center location. 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. Significance Statement In tropical cyclone (TC) wind retrievals from single-Doppler weather radar observations, closure assumptions are required for the retrieval equations. The present study proposes a new closure allowing asymmetric radial winds and improving retrievals for TC winds in the previously developed technique. The relative error of the axisymmetric tangential wind in idealized vortices from the new approach is less than 2% at the radius of the maximum wind speed. In applying to a real TC with an elliptical eyewall, we found that the new approach can largely suppress an artificial evolution of the tangential winds in the previous retrieval technique.