thumb|Weather radar in [[Norman, Oklahoma with rainshaft]]
thumb|Weather (WF44) radar dish
thumb|[[University of Oklahoma OU-PRIME C-band, polarimetric, weather radar during construction]]
A weather radar, also called weather surveillance radar (WSR) and Doppler weather radar, is a type of radar used to locate precipitation, calculate its motion, and estimate its type (rain, snow, hail etc.). Modern weather radars are mostly pulse-Doppler radars, capable of detecting the motion of rain droplets in addition to the intensity of the precipitation. Both types of data can be analyzed to determine the structure of storms and their potential to cause severe weather.
During World War II, radar operators discovered that weather was causing echoes on their screens, masking potential enemy targets. Techniques were developed to filter them, but scientists began to study the phenomenon. Soon after the war, surplus radars were used to detect precipitation. Since then, weather radar has evolved and is used by national weather services, research departments in universities, and in television stations' weather departments. Raw images are routinely processed by specialized software to make short term forecasts of future positions and intensities of rain, snow, hail, and other weather phenomena. Radar output is even incorporated into numerical weather prediction models to improve analyses and forecasts.
History
thumb|[[Typhoon Cobra as seen on a ship's radar screen in December 1944.]]
During World War II, military radar operators noticed noise in returned echoes due to rain, snow, and sleet. After the war, military scientists returned to civilian life or continued in the Armed Forces and pursued their work in developing a use for those echoes. In the United States, David Atlas at first working for the Air Force and later for MIT, developed the first operational weather radars. In Canada, J.S. Marshall and R.H. Douglas formed the "Stormy Weather Group" in Montreal. Marshall and his doctoral student Walter Palmer are well known for their work on the drop size distribution in mid-latitude rain that led to understanding of the Z-R relation, which correlates a given radar reflectivity with the rate at which rainwater is falling. In the United Kingdom, research continued to study the radar echo patterns and weather elements such as stratiform rain and convective clouds, and experiments were done to evaluate the potential of different wavelengths from 1 to 10 centimeters. By 1950 the UK company EKCO was demonstrating its airborne 'cloud and collision warning search radar equipment'.
thumb|left|1960s radar technology detected [[Early May 1965 tornado outbreak|tornado-producing supercells over the Minneapolis-Saint Paul metropolitan area.]]
Between 1950 and 1980, reflectivity radars, which measure the position and intensity of precipitation, were incorporated by weather services around the world. The early meteorologists had to watch a cathode-ray tube. In 1953 Donald Staggs, an electrical engineer working for the Illinois State Water Survey, made the first recorded radar observation of a "hook echo" associated with a tornadic thunderstorm.
The first use of weather radar on television in the United States was in September 1961. As Hurricane Carla was approaching the state of Texas, local reporter Dan Rather, suspecting the hurricane was very large, took a trip to the U.S. Weather Bureau WSR-57 radar site in Galveston in order to get an idea of the size of the storm. He convinced the bureau staff to let him broadcast live from their office and asked a meteorologist to draw him a rough outline of the Gulf of Mexico on a transparent sheet of plastic. During the broadcast, he held that transparent overlay over the computer's black-and-white radar display to give his audience a sense both of Carla's size and of the location of the storm's eye. This made Rather a national name and his report helped in the alerted population accepting the evacuation of an estimated 350,000 people by the authorities, which was the largest evacuation in US history at that time. Just 46 people were killed thanks to the warning and it was estimated that the evacuation saved several thousand lives, as the smaller 1900 Galveston hurricane had killed an estimated 6000-12000 people.
During the 1970s, radars began to be standardized and organized into networks. The first devices to capture radar images were developed. The number of scanned angles was increased to get a three-dimensional view of the precipitation, so that horizontal cross-sections (CAPPI) and vertical cross-sections could be performed. Studies of the organization of thunderstorms were then possible for the Alberta Hail Project in Canada and National Severe Storms Laboratory (NSSL) in the US in particular.
The NSSL, created in 1964, began experimentation on dual polarization signals and on Doppler effect uses. In May 1973, a tornado devastated Union City, Oklahoma, just west of Oklahoma City. For the first time, a Dopplerized 10 cm wavelength radar from NSSL documented the entire life cycle of the tornado. The researchers discovered a mesoscale rotation in the cloud aloft before the tornado touched the ground – the tornadic vortex signature. NSSL's research helped convince the National Weather Service that Doppler radar was a crucial forecasting tool. In Canada, Environment Canada constructed the King City station, with a 5 cm 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 had switched to Doppler networks by the early 2000s. Meanwhile, rapid advances in computer technology led to algorithms to detect signs of severe weather, and many applications for media outlets and researchers.
After 2000, research on dual polarization technology 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 was done by the end of the decade or the beginning of the next in some countries such as the United States, France, and Canada. In April 2013, all United States National Weather Service NEXRADs were completely dual-polarized.
Principle
Sending radar pulses
thumb|upright=1.25|A radar beam spreads out as it moves away from the radar station, covering an increasingly large volume.
Weather radars send directional pulses of microwave radiation, on the order of one microsecond long, using a cavity magnetron or klystron tube connected by a waveguide to a parabolic antenna. The wavelengths of 1 – 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 towards the radar station.
alt=Large spherical weather radar dome on Mont Ventoux against clear sky.|thumb|Weather radar dome on [[Mont Ventoux, France, housing a fixed microwave antenna used for long-range atmospheric monitoring.]]
Shorter wavelengths are useful for smaller particles, but the signal is more quickly attenuated. Thus 10 cm (S-band) radar is preferred but is more expensive than a 5 cm C-band system. 3 cm X-band radar is used only for short-range units, and 1 cm Ka-band weather radar is used only for research on small-particle phenomena such as drizzle and fog.
The volume of air that a given pulse takes up at any point in time may be approximated by the formula <math>\, {v = h r^2 \theta^2}</math>, 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 <math>\,\theta</math> is the beam width (in radians). This formula assumes 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".
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.
Determining height
thumb|upright=1.5|The radar beam path with height
Since the Earth is round, the radar beam in vacuum would rise according to the reverse curvature of the Earth. However, the atmosphere has a refractive index that diminishes with height, due to its diminishing density. This bends the radar beam slightly toward the ground and with a standard atmosphere this is equivalent to considering that the curvature of the beam is 4/3 the actual curvature of the Earth. Depending on the elevation angle of the antenna and other considerations, the following formula may be used to calculate the target's height above ground:
:<math>H = \sqrt{r^2+(k_ea_e)^2+2rk_{e}a_{e}\sin(\theta_e)} - k_{e}a_{e} + h_{a},</math>
where:
:r = distance radar–target,
:k<sub>e</sub> = 4/3,
:a<sub>e</sub> = Earth radius,
:θ<sub>e</sub> = elevation angle above the radar horizon,
:h<sub>a</sub> = height of the feedhorn above ground.
Effective volume coverage
thumb|Scanned volume by using multiple elevation angles
A weather radar network uses a series of typical angles that are set according to its needs. After each scanning rotation, the antenna elevation is changed for the next sounding. This scenario will be repeated on many angles to scan the entire volume of air around the radar within the maximum range. Usually, the scanning strategy is completed within 5 to 10 minutes to have data within 15 km above ground and 250 km distance of the radar. For instance in Canada, the 5 cm weather radars use angles ranging from 0.3 to 25 degrees. The accompanying image shows the volume scanned when multiple angles are used.
Due to the Earth's curvature and change of index of refraction with height, the radar cannot "see" below the height above ground of the minimal angle (shown in green) or closer to the radar than the maximal one (shown as a red cone in the center).
Calibrating return intensity
Because the targets are not unique in each volume, the radar equation has to be developed beyond the basic one. Assuming a monostatic radar where <math> G_t=A_r (\mathrm{or} \, G_r) =G</math>:
:<math>P_r = P_t