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 Rmax and Vmax AS IT RELATES TO THE PULSE REPETITION FREQUENCY

METEOROLOGIST JEFF HABY

The Pulse Repetition Frequency (PRF) is the number of radiation pulses emitted by radar in 1 second. For example, if the radar emits 400 pulses in one second then the PRF is 400 pulses/second. Think of pulses like the pulses of a strobe light. A strobe light alternates between light and dark and there is light a certain number of times within a given period of time. Radar is similar except the number of pulses is much more per second than a strobe light and radar emits microwave type wavelength radiation. Another difference is that the radar spends less than 1% of the time emitting radiation and over 99% of the time sensing for returned radiation. Radar can sample the troposphere very fast because the speed of light is fast (about 300,000,000 meters per second).

Rmax stands for the maximum range the radar can detect. If the radar emitted a pulse of energy and waited as long as needed for returning radiation then the radar could detect to any range. However, since the speed of light is so fast compared to the distances we need to measure returns in the troposphere the radar is not required to wait more than a tiny fraction of a second for return energy to come back. Thus, the radar can be set to emit and listen for 100s of pulses per second and we can still measure ranges that cover a broad area. However, the faster the PRF becomes the smaller of a range that can be detected. If the PRF is set too fast then there is not as much time to sample the troposphere in one pulse before the next pulse is sent out. Energy returned from one pulse after another pulse has been sent will be range folded.

Suppose the PRF is 500 pulses per second. The formula for Rmax is C / (2 * PRF). C stands for the speed of light. With a PRF of 500 pulses/s, the Rmax is = 300,000,000 m/s / (1,000 s^-1) = 300,000 m which is equal to 300 km. Thus the radar can sample up to 300 km during each pulse. If a return is beyond 300 km then it will be range folded and will show up at a distance closer to the radar than the return really is because the radar thinks it is getting returns from a second pulse it already sent out.

Suppose we increase the PRF to 1,200 pulses per second. Rmax then becomes 300,000,000 m/s / (2,400 s^-1) = 125 km. From these two examples you can see that as the PRF increases, then the Rmax becomes a smaller range. This makes sense because the faster pulses are emitted the less time there is for the pulse to travel and come back to the radar before the next pulse is emitted. If we want to detect echoes beyond 125 km we will need to decrease the PRF from 1,200 to a smaller number.

When a reflectivity image is put into motion we can see where the precipitation areas are moving toward and how fast they are moving. However, we can not see the motions within the precipitation areas very well. To help with that problem Doppler radar has come along.

Vmax stands for the maximum velocity the radar can detect. Precipitation particles that are sensed are either moving closer to the radar over time, further from the radar over time or stay the same distance from the radar over time. It is this motion we want to detect because from it the motions inside rain clouds can be sensed.

The motion of precipitation particles or other particles is determined by the phase shift that occurs from radar radiation striking the particle. Suppose you throw a ball at a wall that is moving at you and then throw another ball at the same velocity at a wall that is moving away from you. The ball you threw at the wall that is moving toward you will rebound faster off the wall back toward you. Thus, the velocity of the ball changes relative to you depending on if the wall is moving further or closer to you even if you throw it at the same velocity toward the wall both times. This principle does not work with light because the speed of light is a constant. However, the frequency (number of light waves passing a point over time) and wavelength (distance from beginning to end of each wave) does change. It is from the phase shift of light that is used by radar to determine whether an object is moving toward or away from the radar and the magnitude of that motion.

Suppose the PRF is 500 pulses per second using a 0.1 meter wavelength radar. The formula for Vmax = (PRF * wavelength) / 4. With a PRF of 500 pulses/s, the Vmax is = (500 s^-1 * 0.1 m) / 4 = 12.5 m/s. Thus the radar can only sample motions that are equal to or less than 12.5 m/s. If the actual velocity of an object is 17.5 m/s that echo will be velocity folded and will have a value of (17.5 - 12.5 = 5 m/s). If we want to detect higher velocities without them being folded the PRF needs to be increased.

Suppose we increase the PRF to 1,200 pulses per second. Vmax becomes (1,200 s^-1 * 0.1 m) / 4 = 30 m/s. From these two examples you can see that as the PRF increases, then the Vmax becomes higher. Think of a strobe light once again and the strobe light shining on a bouncing ball. If the strobe light flickers more quickly (higher PRF) and we watch it in slow motion then we can predict where the ball will be each time the light shines on it again. However, if the pulses are longer (PRF decreased) to the point where the light shines again slower than the time it takes the ball to make one bounce we will not know whether the ball is rising or falling (it has folded and we can no longer be sure where it will be when the light shines on the ball on the next pulse). The phase shift of light is smaller the higher the PRF is. As the PRF decreases the phase shift becomes more. Once the phase shift becomes too much then the velocity will be folded.