A weather radar is a type of radar used to locate precipitation, calculate its motion, estimate its type (rain, snow, hail, etc.), and forecast its future position and intensity. Modern weather radars are mostly pulse-doppler radars, capable of detecting the motion of rain droplets in addition to intensity of the precipitation. Both types of data can be analyzed to determine the structure of storms and their potential to cause severe weather.
Between 1980 and 2000, weather radar networks became the norm in North America, Europe, Japan and other developed countries. Conventional radars were replaced by Doppler radars, which in addition to position and intensity of could track the relative velocity of the particles in the air. In the United States, a network consisting of 10 cm wavelength radars, called NEXRAD or WSR-88D (Weather Service Radar 1988 Doppler), was started in 1988. In Canada, Environment Canada constructed the King City station, with a five centimeter research Doppler radar, by 1985;McGill University dopplerized its radar (J. S. Marshall Radar Observatory) in 1993. This led to a complete Canadian Doppler network between 1998 and 2004. France and other European countries switched to Doppler network by the end of the 1990s to early 2000s. Meanwhile, rapid advances in computer technology led to algorithms to detect signs of severe weather and a plethora of "products" for media outlets and researchers.
After 2000, research on dual polarization technology has moved into operational use, increasing the amount of information available on precipitation type (e.g. rain vs. snow). "Dual polarization" means that microwave radiation which is polarized both horizontally and vertically (with respect to the ground) is emitted. Wide-scale deployment is expected by the end of the decade in some countries such as the United States, France, and Canada.
Since 2003, the U.S. National Oceanic and Atmospheric Administration has been experimenting with phased-array radar as a replacement for conventional parabolic antenna in order to provide more time resolution in atmospheric sounding. This would be very important in severe thunderstorms as their evolution can be better evaluated with more timely data.
Weather radars send directional pulses of microwave radiation, on the order of a microsecond long, using a cavity magnetron or klystron tube connected by a waveguide to a parabolic antenna. The wavelengths of 1 to 10 cm are approximately ten times the diameter of the droplets or ice particles of interest, because Rayleigh scattering occurs at these frequencies. This means that part of the energy of each pulse will bounce off these small particles, back in the direction of the radar station.
Shorter wavelengths are useful for smaller particles, but the signal is more quickly attenuated. Thus 10 cm (S-band) radar is preferred to but is more expensive than a 5 cm C-band system. 3 cm X-band radar is used only for very short distance purposes, and 1 cm Ka-band weather radar is used only for research on small-particle phenomena such as drizzle and fog.
Radar pulses spread out as they move away from the radar station. This means that the region of air any given pulse is moving through is larger for areas farther away from the station, and smaller for nearby areas, decreasing resolution at far distances. At the end of a 150-200 km sounding range, the volume of air scanned by a single pulse might be on the order of a cubic kilometer.
The volume of air that a given pulse takes up at any point in time may be approximately calculated by the formula , where v is the volume enclosed by the pulse, h is pulse width (in e.g. meters, calculated from the duration in seconds of the pulse times the speed of light), r is the distance from the radar that the pulse has already traveled (in e.g. meters), and is the beam width in radians). This formula assume the beam is symmetrically circular, "r" is much greater than "h" so "r" taken at the beginning or at the end of the pulse is almost the same, and the shape of the volume is a cone frustum of depth "h".
Between each pulse, the radar station serves as a receiver and listens for return signals from particles in the air. The duration of the "listen" cycle is on the order of a millisecond, which is a thousand times longer than the pulse duration. The length of this phase is determined by the need for the microwave radiation (which travels at the speed of light) to propagate from the detector, to the weather target, and back again, a distance which could be several hundred kilometers. The horizontal distance from station to target is calculated simply from the amount of time that lapses from the initiation of the pulse to the detection of the return signal. (The time is converted into distance by multiplying by the speed of light). If pulses are emitted too frequently, the returns from one pulse will be confused with the returns from previous pulses, resulting in incorrect distance calculations.
Assuming the Earth is round, with knowledge of the variation of the index of refraction through air and the distance to the target, one can calculate the height above ground of the target.
After each scanning rotation, the antenna elevation is changed for the next sounding. This scenario will be repeated on many angles in order to scan all the volume of air around the radar within the maximum range. Usually, this scanning strategy is completed within 5 to 10 minutes in order to have data within 15 km above ground and 250 km distance of the radar.
Due to the Earth curvature and change of index of refraction with height, the radar cannot “see” below the height above ground of the minimal angle or closer to the radar than the maximal one. This image shows the height of a series of typical angles done by a 5 cm weather radar in Canada. They range from 0.3 to 25 degrees.
Because the targets are not unique in each volume, the radar equation has to be developed beyond the basic one:
In this case, we have to add the cross sections of all the targets:
where is the light speed, is temporal duration of a pulse and is the beam width in radians.
In combining the two equations :
Which leads to:
Notice that the return now varies inversely to instead of . In order to compare the data coming from different distances from the radar, one has to normalize them with this ratio.
Return echoes from targets, reflectivity, are analyzed for their intensities in order to establish the precipitation rate in the scanned volume. The wavelengths used (1 to 10 cm) ensure that this return is proportional to the rate because they are within the validity of Rayleigh scattering which states that the targets must be much smaller than the wavelength of the scanning wave (by a factor of 10).
Reflectivity perceived by the radar (Ze) varies by the 6th power of the rain droplets' diameter (D), the square of the dielectric constant (K) of the targets and the drop size distribution (e.g. N[D] of Marshall-Palmer) of the drops. This gives a truncated Gamma function,
of the form:
Precipitation rate (R), on the other hand, is equal to the number of particles, their volume and their fall speed (v[D]) as:
So Ze and R have similar functions that can be resolved giving a relation between the two of the form:
Radar returns are usually described by colour or level. The colours in a radar image normally range from blue or green for weak returns, to red or magenta for very strong returns. The numbers in a verbal report increase with the severity of the returns.
Strong returns (red or magenta) may indicate not only heavy rain but also thunderstorms, hail, strong winds, or tornadoes, but they need to be interpreted carefully, for reasons described later in this article.
Aircraft will try to avoid level 2 returns when possible, and will always avoid level 3 unless they are specially-designed research aircraft.
Doppler weather radars are using this phase difference (pulse pair difference) to calculate the precipitation's motion. The intensity of the successively returning pulse from the same scanned volume where targets have slightly moved is :
v = target speed =
This speed is called the radial Doppler velocity because it gives only the radial variation of distance versus time between the radar and the target. The real speed and direction of motion has to be extracted by the process described below.
The phase between pulse pairs can vary from - and +, so the unambiguous Doppler velocity range is
This is called the Nyquist velocity. This is inversely dependent on the time between successive pulses: the smaller the interval, the larger is the unambiguous velocity range. However, we know that the maximum range from reflectivity is directly proportional to :
The choice becomes increasing the range from reflectivity at the expense of velocity range, or increasing the latter at the expense of range from reflectivity. In general, the useful range compromise is 100 to 150 km for reflectivity. This means for a wavelength of 5 cm, like on the image, an unambiguous velocity range of 8.3 to 12.5 m/s but the double for a 10 cm radar like the NEXRAD.
Some techniques using two alternating pulse repetition rates (PRF) permit to extend the Doppler range. The velocities noted with the first pulse rate could be equal or different with the second. For instance, if the maximum velocity with a certain rate is 10 m/s and the one with the other rate is 15 m/s. The data coming from both will be the same up to 10 m/s and differ afterward. It is then possible to find a mathematical relation between the two returns and calculate the real velocity beyond the limitation of the two PRF.
As the beam is scanning 360 degrees around the radar, data will comes from all those angles and be the radial projection of the actual wind on the individual angle. The intensity pattern formed by this scan can be represented by a cosine curve, as seen on the right. One can then calculate the direction and the strength of the motion of particles as long as there is enough coverage on the radar screen.
However, the rain drops are falling. As the radar only sees the radial component and has a certain elevation from ground, the radial velocities are contaminated by some fraction of the falling speed. This component is negligible in small elevation angles, but must be taken into account for higher scanning angles.
Most liquid hydrometeors have a larger horizontal axis due to the drag coefficient of air while falling (water droplets). This causes the water molecule dipole to be oriented in that direction so radar beams are generally polarized horizontally to receive the maximal return.
If we decide to send simultaneously two pulses with orthogonal polarization: vertical and horizontal, we receive two sets of data proportional to the two axis of the droplets that are independent:
With this new knowledge added to the reflectivity, velocity, and spectrum width produced by Doppler weather radars, researchers have been working on developing algorithms to differentiate precipitation types, non-meteorological targets, and to produce better rainfall accumulation estimates. In the U.S., NCAR and NSSL have been world leaders in this field.
NOAA has set up a test bed for dual-polametric radar at NSSL and plans to equip all its 10 cm wavelength NEXRAD radars with dual-polarization by the end of the decade. McGill University J. S. Marshall Radar Observatory in Montreal, Canada has converted their instrument (1999) and the data are used operationally by Environment Canada in Montreal. Another Environmental Canada radar in King City (North of Toronto) was dual-polarized in 2005, this one works on a 5 cm wavelength which gives new challenges, specifically greater attenuation. Environmental Canada is working on converting all of its radars to dual-polarization. Finally, Météo-France is working on the subject and hopes to set up their first polarized radars in 2008.
For more details:
All data from radar scans are displayed according to the need of the users. Different outputs have been developed through time to reach this. Here is a list of common and specialized outputs available.
Since data are obtained one angle at a time, the first way of displaying them as been the Plan Position Indicator (PPI) which is only the layout of radar return on a two dimensional image. One has to remember that the data coming from different distances to the radar are at different heights above ground.
This is very important as a high rain rate seen near the radar is relatively close to what reach the ground but what is seen from 160 km (100 miles) away is about 1.5 km above ground and could be far different from the amount reaching the surface. It is thus difficult to compare weather echoes at different distance from the radar.
PPIs are afflicted with ground echoes near the radar as a supplemental problem. These can be misinterpreted as real echoes. So other products and further treatments of data have been developed to supplement its shortcomings.
USAGE: Reflectivity, Doppler and polarimetric data can use PPI.
N.B.: In the case of Doppler data, two points of view are possible: relative to the surface or the storm. When looking at the general motion of the rain to extract wind at different altitudes, it is better to use data relative to the radar. But when looking for rotation or wind shear under a thunderstorm, it is better to use the storm relative images that subtract the general motion of precipitation leaving the user to view the air motion as if he would be sitting on the cloud.
To avoid some of the problems on PPIs, the CAPPI or Constant Altitude Plan Position Indicator has been developed by researchers in Canada. It is basically a horizontal cross-section through radar data. This way, one can compare precipitation on an equal footing at difference distance from the radar and avoid ground echoes. Although data are taken at a certain height above ground, a relation can be inferred between ground stations reports and the radar data.
CAPPIs call for a large number of angles from near the horizontal to near the vertical of the radar in order to have a cut that is as close as possible at all distance to the height needed. But even then, after a certain distance, there isn’t any angle available and the CAPPI becomes the PPI of the lowest angle. The zigzag line on the angles diagram above shows the data used to produce a 1.5 and 4 km height CAPPIs. Notice that the section after 120 km is using the same data.
USAGE: Mostly for reflectivity data. McGill University is producing Doppler CAPPIs but the nature of velocity make the output a bit noisy as velocities can change rapidly in direction with height contrary to a relatively smooth pattern in reflectivity.
Real time examples:
Another solution to the PPI problems is to produce images of the maximum reflectivity in a layer above ground. This solution is usually taken when the number of angles available is small or variable. The American National Weather Service is using such Composite as their scanning scheme can vary from 4 to 14 angles, according to their need, which would make very coarse CAPPIs. The Composite make sure that no strong echo is missed in the layer and a treatment using Doppler velocities eliminate the ground echoes. Comparing base and composite products, one can locate virga and updrafts zones.
Real time example: NWS Burlington radar, one can compare the BASE and COMPOSITE products
One of the main use of radar is to be able to assess the amount of precipitations fallen over large basins for hydrological purpose. For instance, river flood control, sewer management and dam construction are all areas where planners want accumulation data. It ideally completes surface stations data which they can use for calibration.
To produce radar accumulations, we have to estimate the rain rate over a point by the average value over that point between one PPI, or CAPPI, and the next; then multiply by the time between those images. If one wants for a longer period of time, one has to add up all the accumulations from images during that time.
Aviation is a heavy user of radar data. One map particularly important in this field is the Echotops for flight planning and avoidance of dangerous weather. Most country weather radars are scanning enough angles to have a 3D set of data over the area of coverage. It is relatively easy to estimate the maximum altitude at which precipitation is found within the volume. However, those are not the tops of clouds as they extended to higher altitudes than the precipitation.
To know the vertical structure of clouds, in particular thunderstorms or the level of the melting layer, a vertical cross sections product of the radar data is available to meteorologist. This is done by displaying only the data along a line, from coordinates A to B, taken from the different angles scanned.
When a weather radar is scanning in only one direction vertically, it obtains high resolution data along a vertical cut of the atmosphere. The output of this sounding is called a Range Height Indicator (RHI) which is excellent for viewing the detailed vertical structure of a storm. This is different from the vertical cross section mentioned above by the fact that the radar is making a vertical cut along specific directions and does not scan over the entire 360 degrees around the site. This kind of sounding and product is only available on research radars.
Over the past few decades, radar networks have been extended to allow the production of composite views covering large areas. For instance, all major countries (e.g., the United States, Canada, much of Europe) produce images that include all of their radars. This is not as trivial a task.
In fact, such a network can consist of different types of radar with different characteristics like beam width, wavelength and calibration. These differences have to be taken into account when matching data across the network, particularly to decide what data to use when two radars cover the same point. If one uses the stronger echo but it comes from the most distant radar, one uses returns that are from higher altitude coming from rain or snow that might evaporate before reaching the ground (virga). If one uses data from the closest radar, it might be attenuated passing through a thunderstorm. Composite images of precipitations using a network of radars are made with all those limitations in mind.
Here are some national radar networks :
To help meteorologists to spot dangerous weather, mathematical algorithms have been introduced in the weather radar treatment programs. These are particularly important in the analyzing the Doppler velocity data as they are more complex. The polarization data will even need more algorithms.
Main algorithms for reflectivity:
Main algorithms for Doppler velocities:
Radar data interpretation depends on many hypotheses about the atmosphere and the weather targets. They are :
One has to keep in mind that those hypotheses are not necessarily met in many circumstances and be able to recognize when the truth from the false echoes.
The first assumption is that the radar beam is moving through air that cools down at a certain rate with height. The position of the echoes depend heavily on this hypothesis. However, the real atmosphere can vary greatly from the norm.
This type of false return is relatively easy to spot on a time loop if it is due to night cooling or marine inversion as one sees very strong echoes developing over an area, spreading in size laterally but not moving and varying greatly in intensity. However, inversion of temperature exist ahead of warm fronts and the abnormal propagation echoes are then mixed with real rain.
The extreme of this problem is when the inversion is very strong and shallow and the radar beam reflects many time on the ground as it has to follow a waveguide path. This will create multiple bands of strong echoes on the radar images.
If we want to reliably estimate the precipitation rate, the targets have to be 10 times smaller than the radar wave according to Rayleigh scattering. This is because the water molecule has to be excited by the radar wave in order to give a return. This is relatively true for rain or snow as 5 or 10 cm radars are used.
However, for very large hydrometeors, since the wavelength is of the order of stone, the return level off according to the Mie scattering. A return of more than 55 dBZ is likely to come from hail but won’t vary proportionally to the size. On the other hand, very small targets like cloud droplets are too small to be excited and don’t give a recordable return on usual weather radars.
As demonstrated at the start of the article, radar beams have a physical dimension and data are sampled every degree, not continuously, along each angle of elevation. This results in an averaging of the values of the returns for reflectivity, velocities and polarization data on the resolution volume scanned.
In the figure to the right, at the top is a view of a thunderstorm taken by a wind profiler when is passed overhead. This is like a vertical cross section through the cloud with 150 m vertical and 30 m horizontal resolution. We can see that the reflectivity has large variations in a short distance. Now compare this with a simulated view of what a regular weather radar would see at 60 km (40 miles) at the bottom. Everything has been smoothed out.
This shows how the output of weather radar is only an approximation of the reality. Naturally, resolution can be improved by newer equipment but some things cannot. As mentioned previously, the volume scanned increases with distance so the possibly that the beam is only partially filled increases too. This leads to underestimation of the precipitation rate at larger distances and fools the user into thinking that rain is lighter as it moves away.
When a secondary lobe hits a very reflective target, like a mountain or a strong thunderstorm, some of the energy is sent back to the radar. This energy is relatively weak but arrives at the same time the central peak is illuminating a different azimuth. The echo is thus misplaced by the processing program. This has the effect of actually broadening the real weather echo making a smearing of weaker values on each side of it. This causes the user to overestimate the extent of the real echoes.
In the sky there is more than rain and snow. Other objects can be misinterpreted as rain by a weather radar. The main ones are:
Each of them has their own characteristics that make it possible to distinguish them to the trained eye but they may fool a layman. It is possible to eliminate some of them with post-treatment of data using reflectivity, Doppler, and polarization data.
Micro-waves used in weather radars can be absorbed by rain, depending on the wavelength used. For the 10 centimeter radars, this attenuation is negligible. That is the reason why countries with high water content storms are using 10 centimeter wavelength like in the United States with NEXRAD. The cost of a larger antenna, klystron and other related equipments is offset by this benefit.
For a 5 centimeter radar, absorption becomes important in very heavy rain and this attenuation leads to underestimation of echoes in and beyond a strong thunderstorms line. Canada and other northern countries use this less costly kind of radars as their precipitations are usually less intense. However, users have to remember this effect when interpreting data. The images above show how a strong line of echoes seems to vanish as it moves over the radar. To compensate for this behaviour, radar sites are often chosen to somewhat overlap in coverage in order to give different points of view of the same storms.
Shorter wavelengths are even more attenuated and are only useful on short range radar. Many television stations in the United States have 3-centimeter radars to cover their audience area. Knowing their limitations and using them with the local NEXRAD can supplement the data available to a meteorologist.
As we have seen previously, the reflectivity depends on the diameter of the target and its capacity to reflect. Snow flakes are large but weakly reflective while rain drops are small but highly reflective.
When snow falls through a layer above freezing temperature, it melts and eventually becomes rain. Using the reflectivity equation, one can demonstrate that the returns from the snow before melting and the rain after, are not too different as the change in dielectric constant compensate for the change in size. However, during the melting process, the radar wave “sees” something akin to very large droplets as snow flakes become coated with water.
This gives enhanced returns that can be mistaken for stronger precipitations. On a PPI, this will show up as an intense ring of precipitations at the altitude where the beam crosses the melting level while on a series of CAPPIs, only the ones near that level will have stronger echoes. A good way to confirm a bright band is to make a vertical cross section through the data like in the picture above.
It is assumed that the beam hits the weather targets and returns directly to the radar. If fact, there is energy reemitted in all directions. Most of it is weak, and multiple reflections diminish it even further so what can eventually return to the radar from such an event is negligible. In some cases though, this cannot be.
For instance, when the beam hits hail, the energy spread toward the wet ground will be reflected back to the hail and then to the radar. The resulting echo is weak but noticeable. Due to the extra path length it has to go through, it arrives later at the antenna and is placed further than its source. This gives a kind of triangle of false weaker reflections placed radially behind the hail.
These two images show what can be achieved already to clean up radar data. The output on the left is made with the raw returns and it is difficult to spot the real weather. Since rain and snow clouds are usually moving, one can use the Doppler velocities to eliminate a good part of the clutter (ground echoes, reflections from buildings seen as urban spikes, anomalous propagation, etc..). The image on the right has been filtered using this property in a somewhat complex technique.
However, not all non-meteorological targets remain still; one can think of birds for instance. Others, like the bright band, depend on the structure of the precipitations. Polarization offers a direct typing of the echoes which could be used to filter more false data or produce separate images for specialized purposes. This recent development in this field is bound to improve the quality of radar products.
Another question is the resolution. As mentioned previously, radar data are an average of the scanned volume by the beam. Resolution can be improved by larger antenna or denser networks. A program by the Center for Collaborative Adaptive Sensing of the Atmosphere (CASA): aims to supplement regular NEXRAD using many low cost X band (3 cm) weather radar mounted on cellular telephone towers. These radars will subdivide the large area of the NEXRAD into smaller domains to look at altitudes below its lowest angle. These will give details not currently available.
Timeliness is also a point needing improvement. With 5 to 10 minutes time between complete scans of weather radar, a lot of things can be missed in the development of a thunderstorm. A Phased-array radar is being tested at the National Severe Storms Lab in Norman, Oklahoma, to speed up the gathering of data.