Doppler Radar Detection principle

8.1.1 Doppler effect
         Doppler effect is the phenomenon that Austrian physicist J.doppler first discovered from the moving source of sound in 1842, Defined as "the frequency at which the energy reaches the receiver (device) when the receiver or receiver is in a relative motion state with the energy source".

         An example is when an emergency train (car) beeps at a very high speed toward you, The tone (frequency) of the sound is increased by the compression of the wave (shorter wavelength). When the train (car) is away from you, the tone (frequency) of the sound is reduced by the expansion of the wave (longer wavelength).  
Doppler frequency (Doppler shift):

         for a moving target, The frequency shifts to the radar movement or away from the radar movement are the same, but the symbols are different: ① if the target moves Reddar to positive, ② if the target is far away from the radar frequency shift is negative.  

8.1.2 Radial speed
         radial velocity is simply defined as the component of the target motion parallel to the radar radial. It is the radial component of the target motion along the radar, either toward the radar or from the radar.
         Note: ① radial velocity is always less than or equal to the actual target speed; ② measured by wsr-88d is just the movement of the target toward or out of the radar. ③ when the target motion is perpendicular to the radar radial or stationary, the radial velocity is zero.  
         The relationship between the actual velocity of the target and the radial velocity described by wsr-88d can be described as a radial velocity equation by mathematical means
         │vr│=│v│ cosβ 
          where VR is the radial velocity, V is the actual speed, and β is the minimum angle between the actual speed V and the radar radial.

8.1.3 Doppler weather radar speed measurement
Because the Doppler frequency shift (HZ) relative emission frequency (MHz) is very small, so Doppler weather radar is usually not directly measured Doppler shift, but by measuring the bit difference between successive returned pulses to determine the target's radial velocity, this pulse phase change can be relatively easy and more accurate measurement. This technique of velocimetry is called "pulse-to-handle".
Pulse-to-handle Pulse-pair Method
In order for Doppler radar to extract the Doppler motion information of the target, we must know the initial phase of each transmitting wave, so that we can compare the phase of the successive return signal. If the initial phase of each emission wave is not known, then the phase shift between the two pulses returned will not be known, and the target object can be estimated radially along the radar.
WSR-88D and Cinrad are all-coherent radars, which means that each pulse is known for its phase at launch. The frequency of each transmit pulse is constant and its phase is the same for the internal reference signal. When the pulse returns, it is compared with the reference signal to determine the phase. The phase change of any pulse to another pulse can be calculated. The phase change is associated with the motion of the target.

Note: In fact, the radial velocity given by the radar is the average of the radial velocity obtained from multiple pulses, called the mean radial velocity, and the corresponding standard deviation is called the spectral width. The average radial velocity is usually obtained by averaging dozens of pairs of pulses.

8.1.4 Maximum non-fuzzy distance and distance folding

Distance folding: Refers to a radar to produce a radar echo of the target object of a recognition error. When the target is located outside the maximum non-fuzzy distance rmax, the radar shows the target in a position within the Rmax, which is called "distance folding" vividly.
When a distance collapse occurs, the position of the echo shown by the radar is correct, but the distance is wrong (but the correct position can be expected).
How is the distance folding happening?
The maximum non-fuzzy distance of radar is n mile (nm = nautical mile)


The characteristic of the distance folding echo: The azimuth is correct, the strength is weak; sometimes it has a strange Doppler velocity.

8.1.5 Maximum non-fuzzy speed and speed blur

8.1.6 Doppler Dilemma (The Doppler dilemma)

8.1.7 get i and Q values
The echo signal is equivalent to the frequency modulation and frequency modulation of the carrier pulses during the limited period of reception. The particle scattering process is equivalent to the amplitude modulation of the transmitting signal, and the particle radial motion is equivalent to the frequency modulation of the transmitting signal.

1) I and Q components
The I and Q components include all the necessary information to produce a reflectance factor, radial velocity, and velocity spectrum width data.
The amplitude (i.e. z) and phase of the signal are calculated directly according to the I and Q values. Thus, the pulse-to-phase shift can also be calculated directly from the I and Q values, and then the radial velocity and velocity spectral width data are generated.

The individual I values are insufficient for determining the direction of the target (toward the radar or leaving the radar). The I and Q values together provide the speed and direction of the target.

2) determine the target direction
Once the I and Q values of the two successive return pulses are determined, their phase vectors can be drawn separately on the Cartesian coordinate system.
The method of judging the relationship between the phase vector rotation and the target motion is: the direction of phase Vector 2 is transferred from the angle of phase vector 1 along less than 180 °, 1) if the counterclockwise rotation means that the target object moves toward the radar, the negative velocity (according to the Convention); 2) If clockwise rotation means that the target is moving away from the radar, The target motion rate is proportional to the size of the angle (phase shift) between the phase vector 1 and the phase Vector 2.
Note: The direction and size of the radial velocity determined by the above method is the first guess value, the first guess is the true radial velocity of the target when the pulse pair phase is less than 180 °, and the first guess cannot reflect the true radial velocity of the target in the case of successive pulse-to-bit difference exceeding 180°, the velocity is "fuzzy", It is necessary to pass the correction of the speed-backward fuzzy algorithm to get the real speed.

3) Example of calculating radial velocity with phase vectors
(1) Do not appear in the situation of blurred speed

From # # to # # of pulses to phase shift to 135°, the rotation of the phase vector is clockwise, indicating that the target is moving to the radar at a speed of up to a few kn. The first guessing speed is the number of KN.
(2) The main points to remember when the actual phase shift exceeds 180° are:
Doppler weather radar always assumes that the phase shift associated with the target motion is the minimum angle between the Pulse # # and # #. What happens when the actual phase shift is more than 180°? Whenever the actual phase shift exceeds 180 °, the radar uses a corner (phase shift) corresponding to the same voltage difference of less than 180 °, resulting in a blurring of the target motion velocity. In other words, the radar's "first guess" of the target's radial velocity is smaller than the live one, and the direction is the opposite of the actual target's actual direction of motion.
For example: The actual 270° phase shift is considered a phase shift of 90°.

4) Get modulation function

In the CINRAD-SC,CC,CCJ and CD-type radar receivers, the intermediate frequency channel has two paths, one for the logarithmic channel and the other for the linear channel. If the echo signal in the logarithmic channel is amplified by logarithmic output echo intensity signal, the quadrature signal I and q are output after linear amplification and phase detection in the linear channel. The logarithmic amplified output, I and Q signals are fed into the signal processing system, and finally the Echo power p, the radial velocity v and the velocity spectrum W are obtained.
While the wsr-88d and Cinrad-sa and SB types have no logarithmic channels, the echo power, radial velocity, and spectral width are all represented by the I and Q signals

8.1.8-based data generation
The Doppler radar base includes reflectivity factor, mean radial velocity and spectral width.
There are too many statistical uncertainties to estimate the cardinality of a single pulse and pulse pair to produce accurate data. Therefore, a large number of pulse echoes must be statistically processed to meet the required accuracy, the number of pulses required depends on the characteristics of the radar system and the type of data required (reflectivity factor or speed).
The following is a brief description of the formation of wsr-88d and CINRAD-SA radar base data.
1) reflectance factor data

2) Average radial velocity data
Doppler velocity information is obtained by pulse-to-handle method. Take 3 steps to get:
(1) In order to make each 0.25km distance library speed estimation error is not less than 1m/s, need to 40~50 a pulse pair.
(2) to find the pulse pair phase vector and. This step uses the phase vector to represent the pulse pair (note that unlike the phase vector with the front face representing a single pulse), the angle from the positive direction of the x-axis is calculated to represent the phase shift of the pulse pair, and the size of the phase vector represents the scalar product of the phase vector corresponding to each independent pulse. The vector summation of the pulse pair phase vector and the large number of phase vectors (higher echo power) have a relatively large influence on the average radial velocity estimation. Therefore, the velocity estimation is an average estimate of the weighted return power. Larger scattering bodies return higher power and have large weights at average speed.
(3) Give each 0.25km distance to the library an average radial velocity until 230km.

3) Speed Spectrum width data
The velocity spectrum width is a measure of the degree of dispersion of velocity in a distance library. The spectral width is mathematically proportional to the variance of the velocity of each scattering body within a distance library. The spectral width can be used as a tool for speed estimation quality control. When the spectral width increases, the reliability of the velocity estimation is reduced.
Some typical meteorological characteristics and conditions can lead to relatively high spectral width, including: (1) near the interface of air mass, such as the frontal boundary and the flow boundary of thunderstorms, etc. (2) thunderstorms, (3) Shear area, (4) turbulence, (5) wind shear, (6) different diameters of rain and snow at different landing velocities.
Some non-meteorological conditions can also increase the spectral width: (1) antenna speed (slow and wide fast narrow), (2) distance (far and wide near narrow), (3) signal-to-noise ratio.

Resolution of the base data
The reflectance factor in the base data is obtained by averaging four sampled volumes along the radar radial resolution equivalent to the length of 4 sample volumes, and the azimuth direction resolution is the same as the sampling volume at the azimuth direction. The resolution of the average radial velocity and spectral width is consistent with the size of the radar sample volume. For SA and SB-type radars, the resolution of the reflectance factor in the base data is 1kmx1°, while the resolution of the radial velocity and spectral width is 0.25kmx1°.

Doppler Radar Detection principle