(12)Important Radar Characteristic
Range Height Relationship
The range-height relationship is important in determining the vertical location from which backscatter is occurring.
If the earth had no atmosphere, one would expect that a beam launched from the ground would travel in a straight line. Since the earth is curved a horizontally launched beam would be extend further above the surface with distance from the earth. Another way to express this is to say that the beam exhibit a relative curvature with respect to the earth’s surface of 1/R, where R is the radius of the earth. However, the earth does have an atmosphere and in general the radar reflective index decreases slightly with height, as indicated by the discussion of Equation 8. In fact, when the various contributions to dn/dz are considered it is found that the rate of decrease is almost linear through the troposphere and equal to about -4x10-8 m-1. A consequence of this is that the radar beam is refracted towards the earth as shown in Figure 10.
From Figure 10 we can clearly see that a horizontally-pointed radar beam will propagate further over the horizon than we would otherwise expect. The curvature of any given ray relative to the earth’s surface is given by:
(12)
where R is the radius of the earth, n is the radar refracrive index, z is the height of the ray above the earth’s surface at a distance s from the source around the surface, f is the angle at the intersection of the radar beam and a circle with radius R+z which is concentric to the earth (see Figure 10).
We can quantitatively calculate the magnitude of the effect by combining the refraction curvature effect and the earth’s curvature. This is gives what is called the radar effective radius, R/ .
(13a)
Thus:
(13b)
Using a value of dn/dz of -4x10-8m-1, we find that R/ is approximately 4/3R (the magnitude of this effect obviously varies according to meteorological conditions). Replacing R with R/ in Equation 12 compensates for the bending of the ray due to atmospheric effects (in the standard atmosphere) and the equation simplifies to df /ds=1/R/ . That is, the rays would travel in straight lines with height affected only by the earth’s curvature. This is useful to simplify the illustration of radar radiation pattern and ray traces.
The result above also tells us that the general effect of radar refraction in the "standard atmosphere" is to make the earth seem bigger, and thus flatter than it really is. This is illustrated in Figure 11.
Beam Filling
To analyze a return from a radar pulse, one must have some knowledge of what proportion of the beam is filled with scatterers in order to draw conclusions about their number density and type. This is particularly important in operational use of radar for evaluation of precipitation intensity, but it is also important in clear-air studies if a quantitative analysis of the contents of the pulse volume is to be made. Ideally the entire beam should be filled. In this case the total incident power, and thus reflectivity, can be most easily determined.
Figure 12 illustrates this concept. The figure is for the case of precipitation detection but the principle remains the same for other types of backscatter. In case A, the beam is completely filled and so the true intensity is detected. In case B, only a small percentage of the beam is filled and thus the overall returned power is not representative of the intensity of scattering in the filled region.
Because the radar beam spreads out in the vertical and horizontal as it gets further from the antenna, accurate analysis of radar returns becomes more difficult as range increases.
Range-Width Relationship
As mentioned above, the width of the radar beam increases with distance from the antenna. As the beam gets wider, the radar detects scatterers over a gradually increasing volume. This has an important consequence to the measurement of Doppler velocities since it becomes more likely that the scatterers detected may not be moving homogeneously. Since only radial velocities are detected, there is a real possibility that the velocity signals detected at larger ranges may cancel each other out to some extent.
Figure 13 depicts a theoretical example in which radar measured radial velocities may cancel one another. In this illustration a sea breeze front is moving onshore. The winds behind the front are from the southeast, while those ahead of it are from the southwest. In this example, the front is far enough away from and oriented at such an angle to the radar, that the wind field changes substantially across the beam width. The measured Doppler velocities of any passively-carried scatterers will vary according to where they are along the beam width. In this particular case, the radial components of the wind are nearly opposing, so some cancellation will occur.
Range Folding
As mentioned in the weather radar background section, weather radar emits pulses of radiation and then listens for any returned signals. The time lag between transmission and the returned signal is used to determine the location of the scatterers.
Range folding occurs when scatterers are very distant but have a large enough radar cross section to produce a detectable return. In this case the return from a prior pulse may be detected during the listening period for the current pulse. Hence the scatterers appear to be much closer than they really are. Both reflectivity and radial velocity data are affected by this.
The occurrence of range folding can usually be detected by radar software and reflectivity data can be "unfolded" using special algorithms. However, velocity data cannot be accurately unfolded and hence the effective range with which Doppler radars can detect velocity data is limited by the frequency of the radar pulses; the higher the pulse rate, the shorter the range within which the velocity field can be determined.
In the case of the WSR-88D, range folding of velocity data is detected and the NEXRAD products display the folded data using a special color to indicate the problem.