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Wen-Chau Lee, Xiaowen Tang, and Ben J.-D. Jou

Abstract

The concept and mathematical framework of the distance velocity–azimuth display (DVAD) methodology is presented. DVAD uses rV d (Doppler velocity scaled by the distance from the radar to a gate, r) as the basis to display, interpret, and extract information from single Doppler radar observations. Both linear and nonlinear wind fields can be represented by the same Cartesian polynomial with different orders. DVAD is mathematically concise and superior to the velocity–azimuth display (VAD) in interpreting and deducing flow characteristics. The rV d pattern of a two-dimensional linear wind field is exclusively in the form of a bivariate quadratic equation representing conic sections (e.g., ellipse, parabola, and hyperbola) centered at the radar depending only on divergence and deformation. The presence of a constant background flow translates the conic sections to a different origin away from the radar. It is possible to graphically estimate the characteristics of a linear wind field from the conical sections without performing a VAD analysis. DVAD analysis can deduce quantitative flow characteristics by a least squares fitting and/or a derivative method, and is a natural way to account for nonlinearity. The rV d pattern behaves similar to a type of velocity potential in fluid mechanics where (rV d ) is a proxy of the true wind vector and is used to estimate the general flow pattern in the vicinity of the radar.

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Wen-Chau Lee, Ben J-D. Jou, Pao-Liang Chang, and Frank D. Marks Jr.

Abstract

This paper is the third of a series that focuses on the applications of the ground-based velocity track display (GBVTD) technique and the GBVTD-simplex center finding algorithm developed in the previous two papers to a real tropical cyclone (TC). The evolution and structure of Typhoon Alex (1987), including full tangential winds, mean radial winds, one component of the mean flow, and their derived axisymmetric angular momentum and perturbation pressure fields are reconstructed from 16 volume scans (6.5 h of data with a 2-h gap) from the Civil Aeronautic Administration (CAA) Doppler radar while Typhoon Alex moved across the mountainous area in northern Taiwan.

This analysis retrieves a plausible and physically consistent three-dimensional primary circulation of a landfalling TC using a single ground-based Doppler radar. Highly asymmetric wind structures were resolved by the GBVTD technique where the maximum relative tangential wind at z = 2 km evolved from 52 m s−1 (before landfall), to less than 40 m s−1 (after landfall), to less than 35 m s−1 (entering the East China Sea). Alex’s eye began to fill with precipitation while its intensity decreased rapidly after landfall, a characteristic of circulations disrupted by terrain. The mean radial wind field revealed a layer of low-level inflow in agreement with past TC observations. The outward slope of the eyewall reflectivity maximum was consistent with the constant angular momentum contours within the eyewall. After Alex entered the East China Sea, its circulation became more axisymmetric.

The axisymmetric perturbation pressure field was retrieved using the gradient wind approximation, which, when used in conjunction with one or more surface pressure measurements within the analysis domain, can estimate the central pressure. The retrieved perturbation pressure fields at two time periods were compared with surface pressures reported in northern Taiwan. Considering the assumptions involved and the influence of terrain, good agreement (only 1–2-mb deviation) was found between them. This agreement indicates the relative quality of the GBVTD-retrieved axisymmetric circulation and suggests GBVTD-retrieved quantities can be useful in operational and research applications.

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