A New Method to Retrieve Circulations in Tropical Cyclones from Single-Doppler Radar Observations Based on the Helmholtz Decomposition

Doppler weather radars are useful for investigating the inner-core structure of tropical cyclones (TCs). The Doppler velocity from a single radar has no information on the wind component normal to the radar beam. Therefore, closure assumptions are needed to estimate the circulations of the TCs from single-Doppler radar observations. The Generalized Velocity Track Display (GVTD) technique used to estimate the TC circulations adopts the closure assumption of no asymmetric radial winds in the TC vortex.

The present study proposes a new closure assumption introducing asymmetric radial winds to improve the axisymmetric-circulations estimation in TCs with asymmetric structure in the GVTD retrieval formula. Our new method can consider the asymmetric radial winds by using streamfunction based on the Helmholtz decomposition theorem of horizontal winds, named GVTD-X. As with GVTD, the GVTD-X technique retrieves TC circulations based on the Fourier decomposition of winds in the azimuthal direction and the least-square fit of the Doppler velocity from the single radar observation.

GVTD-X and GVTD are applied to analytical vortices and a real typhoon. For the analytical vortices with asymmetric winds in wavenumber-2 vortex Rossby waves, the axisymmetric tangential wind of V_T0 retrieved by GVTD-X (GVTD) has a relative error of less than 2% (10%) near the radius of maximum wind speed. For the real typhoon, the GVTD-estimated V_T0 has periodical fluctuations with an amplitude of about 5 m s^-1 near the elliptical eyewall. The period of the fluctuations is approximately synchronized with the counterclockwise rotating period of the elliptical shape of the eyewall, suggesting spurious signals due to the closure assumption in GVTD. The GVTD-X technique most reduces the periodical fluctuations in the estimated V_T0. We find that the new method can reduce the spurious signals of the GVTD-retrieved axisymmetric circulation in cases of asymmetric vortices. Moreover, the GVTD-X technique reasonably retrieved asymmetric tangential and radial winds in the elliptical eyewall of the real typhoon during an eyewall replacement cycle (Fig. 1), which is consistent with previous modeling studies.

Reference:

Tsujino et al. (accepted in Monthly Weather Review; https://doi.org/10.1175/MWR-D-23-0043.1)