Doppler Weather Radar: Radial Velocity, the PPI Sweep and the Nyquist Limit

Two very different questions, one dish

A weather radar answers two separate questions with the same pulse of microwaves. Reflectivity -- how much energy bounces back -- tells you how much precipitation is out there and roughly how intense it is. Doppler velocity -- how the returned pulse's frequency has shifted -- tells you how fast that precipitation is moving toward or away from the radar. A storm can look identical in reflectivity and be either a harmless shower or a tornado-producing supercell; it is the velocity data that tells them apart, by revealing the rotation.

The physics is the ordinary Doppler effect applied to a round trip: the pulse travels out to the target and the echo travels back, so the frequency shift is doubled compared with a one-way Doppler shift, and it scales with the radial component of the target's velocity, the emitted frequency, and the speed of light:

delta_f = 2 · v_r · f / c
v_r = radial velocity (component of motion along the radar beam), f = radar frequency, c = speed of light

Only the radial component is visible -- and that is a real limitation

A radar sees only the component of a target's velocity directly along the beam. Rain moving purely tangentially -- sideways across the radar's line of sight, say directly overhead moving east while the radar sits to the south -- registers zero Doppler velocity even though the actual wind speed might be considerable, because none of that motion is toward or away from the dish. This is why a single Doppler radar cannot fully reconstruct a 3D wind field on its own: it fundamentally cannot see motion perpendicular to its beam, and meteorologists either rely on the geometry of a rotation signature (a tight adjacent pair of strong inbound and outbound velocities is the classic radar signature of a tornado vortex) or combine data from two or more radars viewing the same storm from different angles to recover the full wind vector.

The PPI display: one elevation, one full circle

Weather radar antennas scan in a Plan Position Indicator (PPI) pattern: the dish sweeps a full 360 degrees in azimuth at a fixed elevation angle, then steps up to a slightly higher elevation and sweeps again, building up a stack of shallow cones that approximate a 3D volume scan every 5 to 10 minutes. On the display, distance from the centre is range and angle around the centre is compass bearing, with colour typically encoding either reflectivity (how much precipitation) or, on a separate product, Doppler velocity (red for motion away from the radar, green or blue for motion toward it, by meteorological convention).

The Nyquist limit and velocity folding

A radar can only unambiguously measure a Doppler shift up to half the pulse repetition frequency (PRF) -- the Nyquist velocity -- because a phase shift greater than half a cycle between successive pulses is indistinguishable from a smaller shift in the opposite direction. A target moving faster than the Nyquist velocity does not simply read as 'too fast to measure'; it folds, appearing on the display as a much slower velocity of the wrong sign, which is a classic and sometimes dangerous radar artifact if not corrected for.

V_Nyquist = PRF · wavelength / 4
target moving faster than V_Nyquist → folds to an apparently slower, wrong-sign velocity

Raising the PRF widens the unambiguous velocity range but shrinks the unambiguous range distance (a longer wait between pulses is needed to let distant echoes return before the next pulse goes out, and vice versa) -- a fundamental trade-off radar engineers call the Doppler dilemma, usually solved in practice by transmitting at two different PRFs and cross-checking the results to resolve folded velocities.

Frequently asked questions

Try it live

Everything above runs in your browser — open Doppler Weather Radar and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.