¶ General Information on RAdio Detecting And Ranging (RADAR)
¶ How Radars Work
Radars normally consist of four main components:
- Transmitter -Generates high-frequency signal
- Antenna -Send and receive power
- Receiver -Amplifies the power received back from the target
- Display -Allow user to observe the return signals
Modern weather radars send out short pulses of energy and then wait for the signal to travel out, reflect of a target, and then return back to the antenna, Fig. 1. After an appropriate wait period, another pulse is sent out and so on. Once the energy strikes an object, the energy is scattered in all directions, only a small portion is returned to the radar. The receiver detects and amplifies the weak signal. This whole process can occur up to 1300 times each second. The vast majority of the time is spent waiting for the return signal. The radar only transmits energy for a very short period (7 seconds/hour) (NWS 2005). More information on radar hardware and radar in general can be found in Radar for Meteorologists by Ronald E. Rhinehart or almost any other Radar Meteorology book.
¶ Electromagnetic Waves
The energy that a radar emits has both electric and magnetic components, hence the name electromagnetic. Both components travel at right angles to each other and to the direction of propagation. The frequency of electromagnetic radiation is related to its wavelength by
frequency = speed_of_light / wavelength
. Different wavelengths and frequencies of the electromagnetic spectrum are classified into bands, shown in Table 1. Major uses for some of these bands are shown in Table 2.
| Band | Uses |
|---|---|
| L-Band | Clear air turbulence studies |
| S-Band | Near and far range weather observation due to low attenuation |
| C-Band | Shorter range weather as signal is more easily attenuated than S |
| X-Band | Cloud development. Can detect smaller particles but attenuate very easily |
| K-Band | Same as X-Band, but more sensitive |
*Attenuation—In radar meteorology, any process which reduces power density in radar signals.
The speed of the electromagnetic (EM) radiation depends on the material through which it is traveling. The refractive index, which is the ratio of the speed of light in a vacuum to the speed of light through a certain medium, of the atmosphere is proportional to the atmospheric pressure and vapor pressure and inversely proportional to the temperature. EM radiation will propagate at different speeds through different refractive indices. Since the important part of the refractive index is in the fourth, fifth, and sixth decimal places, the refractive index was defined to be easier to work with.
Refractivity=(refractive_index-1)*10e6
The propagation of the EM radiation is more dependent on the gradient of refractivity rather than the absolute value at a point. Depending on the refractivity gradients, the path of the EM radiation can "bend" towards the ground more than normal, this is referred to as Superrefraction. Superrefraction allows the radar to detect ground targets at longer ranges than normal. This condition is called anomalous propagation (AP). Subrefraction occurs when the path of the EM radiation does not "bend" as much as normal. Subrefraction is less common, but can still cause problems detecting targets in the atmosphere.
¶ Radar Variables
This section is to give a brief description of the different kinds of radars and the parameters that can be observed or calculated from the data.
¶ Doppler Radar
- Reflectivity (ZH) - Proportional to the amount of power returned from the radar. This is dependent on the drop size distribution and drop diameters to the sixth power.
- Doppler Velocity (VR) - The radial velocity either towards or away from the radar. Some of the problems associated with doppler velocities can be found here
- Spectral Width - Standard deviation of the velocities in a sample volume. Large values can often be associated with areas of turbulence due to the large range of velocities.
¶ Polarimetric Radar
Most weather radar can transmit EM radiation with a single horizontal pulse (i.e. The electric field is aligned perpendicular to the ground). A polarimetric radar is able to transmit with both a horizontal and vertical pulse. These pulses can be sent out together or as an alternating pattern shown in Fig. 3.
¶ Polarimetric Variables
- Differential Reflectivity (ZDR) - Ratio of horizontal to vertical linear reflectivities. It is a good indicator of drop shape.
- Specific Differential Phase (KDP) - Second order difference of phase between a horizontally and vertically polarized wave. Has a propagation effect and can be a good indicator of rain rate.
- Correlation Coefficient (ρHV) - Correlation between the horizontal and vertical power returns. Can be a good indicator of regions of mixed precipitation
- Linear Depolarization Ratio (LDR) - Ration of vertical power returned of a horizontal pulse, or vice versa. Good indicator of regions of mixed precipitation and can also be used for hail detection.
¶ Display Types
There are many ways to display radar data. Below are a few of the most common types of displays.
- Planned Position Indicator (PPI) - Display on which radar echo are shown with range and azimuth displayed in polar coordinates, centered on the radar. These are taken across a constant elevation angle relative to the radar (0.5º). Because of this, the height is not constant across the domain.
- Constant Altitude Planned Position Indicator (CAPPI) - A PPI taken at a constant altitude. Involves interpolation of the radar data onto a grid at a constant height.
- Range Height Indicator - A cross section through the horizontal plane where the X and Y axes are Range and Height, respectivity.
- Vertical Point (VPT) - Radar points at 90º elevation and scans for a certain amount of time. Similar to normal MMCR and WACR operations.
¶ Other Useful Pieces of Information
¶ Z-R Relationships
¶ Radar Rainfall Estimation
The rain rate can be calculated from a radar reflectivity field based on a Z-R relationship. The most notable one being the Marshall-Palmer relationship, Z=200R1.6, where Z is the linear reflectivity (mm6 m−3) and R is the rain rate (mm/hr). The relationship between reflectivity and rain rate is most commonly given by an empirical power-law relationship, give by: z=ARb.
There can be errors of over 100% difference when comparing the radar and rain gauge rain rates. This is due to the fact that rain gauges measure rain at a single point whereas radars sample a whole volume. Other factors can also affect the difference, such as:
- Hail - Cause high reflectivities which would not correlate well with the rain rate
- Attenuation - Signal weakens as it passes through rain/hail/snow/ice/etc..
- Bright Band - Causes anomalously higher reflectivity values
In order to calculate the power-law relationship between the radar and rain gauge, the log of the general Z-R equation must be taken:
- log10(Z)=log10(A)+b*log10(R)
Since the linear reflectivity must be used,
- z=10(Z/10)
and
- log10(10(Z/10))=log10(A)+b*log10(R)
then
- Z/10= log10(A)+b*log10(R)
From this relationship, Z/10 (y-axis) is plotted vs the log10(R) (x-axis). A least-squares linear regression line is then calculated in the form of y=mx+a along with an r-squared value. Going back to the Z=ARb equation,
- A=10a
- b=m
Figure 1 shows an example of the plot in excel.
¶ Radar Snowfall Estimation
Measuring snowfall rates with radar is much more difficult for a few reasons:
- Calibrations of radar are usually set for liquid hydrometeors
- Snow and ice crystals are not spherical
- Densities of the snowflakes/ice are unknown
- Blowing snow can contaminate measurements
A few studies have provided some Z-S relationships, approximately
- z=2000R2
¶ Hydrometeor Identification
Polarimetric radar can be used to detect various other features of hydrometeors than just reflectivity, velocity, and spectral width. A way to categorize the radar data is to use Fuzzy Logic. Fuzzy logic is a form of multi-valued logic derived from fuzzy set theory to deal with reasoning that is approximate rather than precise. A paper by Hongping Liu and V. Chandrasekar titled "Classification of Hydrometeors Based on Polarimetric Radar Measurements: Development of Fuzzy Logic and Neuro-Fuzzy Systems, and In Situ Verification" give more details on the actual process. An example of a hydrometeor identification using this process is shown in Figure 1.
It can be seen that there are two classifications of snow, dry or wet. There has a few studies into the classification of snow flakes using polarimetric radar but is still in its early stages.
¶ SAPR Point Targets
¶ Point Targets
A point target is a stationary object such as a bridge, tower, railroad, etc... that the radar can observe. Since this is a stationary object that should not be growing or shrinking, the cross-sectional area (the area that the radar observes) should not change. Changes in the observables of this point target can then be attributed to changes in the radar or the atmosphere.
¶ Beam Pattern
The shape of the reflector determines the shape of the beam pattern. A radar does not radiate uniformly in all directions. There are going to be areas of higher and lower power. The beam pattern can help use determine and correct for those irregularities. An example of a beam pattern from the X-SAPR at SGP I4 can be seen in Fig. 1.
In this image, the main lobe can easily be seen (Approx. centered around 0 azimuth). Off to the sides of the main lobe are spikes in the gain called side lobes. Side lobes are secondary radiated energy maximums in a direction other than that of the main lobe. These sidelobes can oftentimes produce erroneous echo.
¶ Typical Radar Problems
¶ Anomalous Propagation (AP)
There are various conditions that can cause AP, one of them being an inversion. Figure 1 shows the temperatures from the tower at 10 and 60 m. The radar images from before, Fig. 2, and after, Fig 3., the inversion.
