## 1. Introduction

The velocity information received by Doppler weather radars has been widely used in weather analysis, wind field retrieval, data assimilation, etc. However, due to the restriction of pulse repetition frequency in sampling, velocity aliasing would appear in some severe weather and have a bad effect on data analysis and application. According to the Nyquist sampling theorem, the maximum unambiguous velocity (i.e. Nyquist velocity) is given by

where *λ* is the Doppler radar wavelength and *f* is the pulse repetition frequency. If the true radial velocity is outside this range, the measured velocity will be aliased into

where *V*_{m} and *V*_{t} are the measured and true velocity respectively, and integer *n* (positive or negative) is termed the Nyquist number which represents aliasing intervals the measured velocity deviates from the true value. The purpose of velocity dealiasing is to determine the correct Nyquist number and restore the measured velocity to the true value for each data gate.

There have been mainly two approaches to deal with the velocity aliasing problem. One focuses on the radar system to prevent the aliasing from occurring. For example, radar wavelength and pulse repetition frequency can be increased to raise the Nyquist velocity according to Eq. (1). Furthermore, aliasing can be reduced significantly by alternately using two different pulse repetition frequencies (Dazhang *et al.*, 1984; Hildebrand *et al.*, 1996). However, constrained by hardware techniques, they are not always compatible with the operational use of existing radar system, and may involve significant hardware costs. As a result, more studies refer to the ‘software’ approach that builds algorithms to achieve the true velocity from the aliasing on the basis of wind velocity field analysis.

Most software techniques are based on the assumption that the wind field is temporally and spatially continuous so aliasing is identified as abrupt change. One-dimensional methods along radials (Ray and Ziegler, 1977; Bargen and Brown, 1980), two-dimensional methods along radials and azimuths (Merritt, 1984; Eilts and Smith, 1990), three-dimensional methods along radials, azimuths and elevations (Bergen and Albers, 1988), and four-dimensional methods along radials, azimuths, elevations and time (James and Houze, 2001), all deal with the aliasing discontinuities of velocity fields. However, these methods need starting points as references to search the irregular gradients. For isolated areas, additional information provided by radiosonde, wind field model, and Vertical Azimuth Display (VAD) or modified VAD (MVAD) wind profile is required to serve as independent references (Hennington, 1981; Merritt, 1984; Eilts and Smith, 1990; Tabary *et al.*, 2001). However, these auxiliary data can not usually be acquired or be available in operation due to their sparseness or mismatch in space and time compared with the radar data. Moreover, noise removal is usually needed in these techniques to correctly discriminate large gradients around aliasing boundaries from those related to noise and clutter, which might smooth real aliasing discontinuity and damage original information of the wind field.

In fact, zero velocity isodops are very important for velocity field analysis when a Plan Position Indicator (PPI) display is given. Because the radar origin is certainly on zero isodops, when it is taken as a start point, there can be found two zero isodops extending to the maximum range with approximately opposite orientations. For a linear wind field as in most cases, when zero isodops are recognized, they separate a non-aliasing field into two regions. The sign of radial velocities in either region should be unique—positive or negative—while opposite to the sign in the other region. This simple concept can be introduced in dealiasing through zero isodop searching and velocity sign comparison. As a result, compared with the typical methods focusing on spatial continuity checking, a new automated dealiasing algorithm based on searching for zero isodop is proposed in this article. The new algorithm is described in detail in section 2. In section 3, the algorithm is applied to real cases. A summary follows in section 4.