Nyquist Velocity

Forward speeds are on the right half of the speedometer, while reverse speeds are on the left. Speeds of less than 50 mph are clear-cut (unambiguous), and cause no confusion. However, speeds of 50 mph or more are ambiguous and cause a phenomenon known as velocity aliasing. Velocity aliasing is a process that causes a Doppler radar to display untrue velocity values because of the motion of the target. Consider the following scenario. A train departs the station traveling forward at 40 mph (fig. 2-23, view A). Beyond city limits, its cruising speed is increased another 20 mph (fig. 2-23, view B). Suddenly something is wrong! The speedometer reads 40 mph in reverse. The train did not change direction; it has simply exceeded the limits of its instrument. The train’s speed appears aliased as 40 mph in reverse, obviously an ambiguous velocity. While radars don’t use speedometers, they do measure phase shifts and experience velocity aliasing in much the same way as the train. Consider the 360° of one wavelength as the radar’s speedometer. When phase shifts are less than 180° (one-half wavelength), they are clearly detectable. However, shifts of 180° or more are ambiguous. The radar is unsure if motion is inbound toward the antenna at 60 knots, or outbound at 40 knots. Look at figure 2-24. In views (A) and (B), the target’s motion poses no problem to the radar as both motions produce phase shifts of less than 180° (one- half wavelength), regardless of direction. Illustration (C) depicts a phase shift? of 180°. Here is where the problems begin. Remember, that to unambiguously measure the phase shift, the shift must be less than one- half the wavelength (180°). In this case, we cannot distinguish whether the 180° shift represents motion toward or away from the radar. This measurement is ambiguous. Illustration (D) depicts a phase shift of 270° resulting from energy striking a target that is moving away from the radar. Since a shift of 270° is more than one-half wavelength (180°), it is ambiguous. This 270° shift is seen as a 90° phase shift of motion toward the radar. This can result in an aliased velocity being displayed. While aliased velocities are subject to misinterpretation, the WSR-88D has a unique way of dealing with them. Computer programs are designed to recognize that direction reversal is impossible. They determine that wind speeds are exceeding radar tolerance and calculate the amount of aliasing occurring. All necessary corrections are then applied to the products you receive. Nyquist Velocity As just explained, velocity detection is wavelength dependent. As soon as the one-half wavelength limit is passed, the determination of velocity becomes ambiguous. Anytime we speak of wavelength, the same arguments hold for frequency, since they are inversely related. Ultimately, the pulse repetition frequency (PRF) of a radar determines the maximum speed that can be detected without confusion. The maximum unambiguous velocity that can be detected at a given PRF is called the Nyquist velocity. Nyquist Figure 2-23.—(A) Speedometer showing true velocity. (B) Speedometer showing ambiguous velocity. 2-20