1. Weather Radar Radar - acronym for RADio Detection and Ranging
PS: Radar and lidar: major active remote sensing
Passive R.S. does not have ranging capability
Main components of a radar/lidar are:
Transmitter – “magnetron” which generates short pulses of electromagnetic energy (microwave)
Note: lidar uses shorter wavelength (UV, vis, NIR)
Antenna which emits and receives focused the energy into a narrow beam
Receiver which detects that portion of the transmitted energy that has been reflected (scattered) by objects with refractive characteristics different from air

2. Diagram of Radar Transmission and Reception (Fig. 1
Diagram of Radar Transmission and Reception (Fig. 1.1 from Batan and Fig. 8.1 from Stephens)

3. Basic Operation Principles
Electromagnetic energy is transmitted into the atmosphere. Once reaching a target (cloud droplets, ice crystals, rain drops, snowflakes, aerosol particles, insects, birds, airplane, etc.), the energy is absorbed and scattered. A portion of backscattered energy is received and processed by a radar to display as an echo.
Two types of radar
Conventional radar – incoherent radar (1-2o beam width)
Detect only the intensity or the amplitude of
the electromagnetic energy – an incoherent sys
Doppler radar – coherent (phase) radar
Detect both the amplitude and phase of the
electromagnetic energy.

4. Weather Radar: Important Relationships
range - r
Transmitter
Target
pulse of
energy
time for light to reach target = r/c
time for light to reach receiver = r/c
total time = 2r/c; r = ct/2
where c is the speed of light
C=3x108 m/sec = 3x105 km/sec
Received Power
r = ct/2

5. Important Radar Parameters
Peak Power - Pt - (instantaneous power emitted in a pulse)
10 < Pt < 5000 kW, 5x106 W
Minimum detectable signal
Much smaller than emitted energy ~ W
Because of the large range of the energy dealt with in a radar system (10-13 ~106), the power is often expressed in decibels (dB). Difference between two power level p1 and p0 is given by
p(dB) = 10 log10(p1/p0)
So, the dynamic range of a radar ~ 190 dB
in electronic term, po = 1 mW (10-3 W), unit dBm
Minimum detectable ~ -100 dBm
Peak power ~ 90 dBm
magnetron—A self-excited oscillator used as a radar transmitter tube. Magnetrons are characterized by high peak power, small size, efficient operation, and low operating voltage. Emitted electrons interact with an electric field and a strong magnetic field to generate microwave energy. Because the direction of the electric field that accelerates the electron beam is perpendicular to the axis of the magnetic field, magnetrons are sometimes referred to as crossed-field tubes. Unlike a klystron, a magnetron is not a coherent transmission source, but has a randomly changing phase from pulse to pulse. A coaxial magnetron uses a different architecture and has better stability, higher reliability, and longer life. Magnetrons are used in inexpensive radars and microwave ovens.
klystron—A power amplifier tube used to amplify weak microwave energy (provided by a radio- frequency exciter) to a high power level for a radar transmitter. A klystron is characterized by high power, large size, high stability, high gain, and high operating voltages. Electrons are formed into a beam that is velocity modulated by the input waveform to produce microwave energy. A klystron is sometimes referred to as a linear beam tube because the direction of the electric field that accelerates the electron beam coincides with the axis of the magnetic field, in contrast to a crossed-field tube such as a magnetron. Klystrons provide a coherent transmitted signal appropriate for Doppler radar and pulse-compression applications. They are used in many operational radars, for example, NEXRAD (Next Generation Weather Radar) and TDWR (Terminal Doppler Weather Radar).

6. Important Radar Parameters (Cont.)
Radio frequency -  Radio wavelength -  - (c/
3 < GHz (1 GHz = 109 sec-1)
(wavelengths from 1 to 30 cm)
Detection capability of hydrometeor depends critically on radio frequency/wavelength.
In general, the smaller the size of the particles, the shorter the wavelength required to detect. e.g. the popular 10 cm (3 GHz or S-band) radar can detect rain drops but not cloud droplets which may be detected by 95 or 35 GHz radar.

7. INSERT TABLE 1.1 FROM BATTAN
Names are trivial (military codes). Select wavelengths to match optical windows in atmosphere.

8. Radar Important Parameters (Cont.)
Pulse repetition frequency (fr) (PRF)
Typical PRF for weather radar fr = 1000 s-1
but may range between 200 – 2000 s-1
Maximum range of detection for a radar set
half the interval between pulses times the speed of light:
c/2fr ~ 150 km for fr = 1000 s-1
range: 750km < c/2fr < 75 km
Pulse duration: 0.1 <  < 5 µs
vs. pulse interval 500 < t < 5000 µsec

9. INSERT FIG. 1.3 FROM BATAN

10. Important Radar Parameters - cont.
Beam width - angular separation between points where the transmitted intensity has fallen to 1/2 its maximum value (i.e., 3 dB below the maximum)
The smaller the beam width, the better the resolution. Typical width for weather radar 1o-3o
Imax
Beam Width
.5 *Imax
Intensity
Angular Separation

11. Side lobes < 1%

12. Summary of Important Radar Parameters and “Typical Values” (c. f
Summary of Important Radar Parameters and “Typical Values” (c.f. The appendix of Battan)
Peak Power
~ kW or 80~90 dBm
Minimum Detectable Signal
~ W or –100 dBm
Radio Frequency
The popular weather radar 5~10 cm
Pulse Repetition Frequency
PRF ~ 1000 sec-1
Pulse duration: 0.1 <  < 5 µsec
Beam width: 1o-3o

13. INSERT THE APPENDIX

15. Radar Range Equation Derivation
The Radar Range Equation relates received power to the backscatter cross section of the target.
Note: the radar equations given here invoke some assumptions and thus differ from the more precise eqs. used in operation. More exact ones found in
Radar Observation of the Atmosphere by Battan.
Assume the radar transmits peak power Pt isotropically without attenuation. Using the inverse-square law, the power intercepted P by a target of area At at a distance r from the transmitter is

16. Radar Range Equation Derivation - cont.
But, the antenna focuses the energy into a narrow beam, thereby increasing the power relative to an isotropic source. Thus the power intercepted is
where G is a dimensionless number (ratio of peak
intensity to uniform) called the antenna axial Gain.

17. Radar Range Equation Derivation - cont.
Assume the target scatters the power intercepted isotropically, then the power returned Pr to the antenna with aperture area Ae is given as
But the gain and aperture area
are related approximately as
Thus,

18. Radar Range Equation Derivation - cont.
But, most targets do not scatter isotropically, and as a convenient artifice the back scatter cross-section  is introduced such that
and  ≠ At.
The ratio /At vary with target property and size and the frequency of a radar. For small target (w.r.t. radar wavelength), the ratio increases exponentially with particle size (Rayleigh approximation).

19. Hail with a water coating scatters more radiation back.
INSERT FIG. 4.2 FROM BATTAN

20. Weather Radar Equation
Rain, snow and cloud particles are examples of distributed targets - many scattering elements that are simultaneously illuminated by the transmitted pulse.
The volume containing those particles that are simultaneously illuminated is called the resolution volume given by the beam width and pulse length.
Power returned from a given range fluctuates because precipitation particles move.
Instead of using the instantaneous power received, the radar range equation is formulated in terms of the average signal received from a given volume.

21. Weather Radar Equation - cont.
For averages over about 10-2 s, the average received power may be written as:
where the summation is over the backscatter
cross-sections within the resolution volume.
In order to relate the received power to properties of the precipitation, we must now find an expression for .

22. Rayleigh Scattering
Define the scattering size parameter  for a sphere as
the ratio of the circumference of the sphere to the wavelength. Also called “electrical size.”
For  << 1, e.g. for r0~1mm and 10cm radar, =0.06 scattering is in the Rayleigh region, and  for a sphere or radius ro is given as
where
m is the complex index of refraction and n is the ordinary
refractive index and k the absorption coefficient.

23. Weather Radar and Rayleigh Scattering
the refractive terms  depends upon , T and composition of the scatterer. For the meteorological range of temperatures and for common wavelengths
liquid water - ||2 ≈ 0.93
ice ||2 ≈ 0.21
Thus, an ice sphere has a radar cross-section only about 2/9 that of a water sphere of the same size.
For water-coated hailstone, k and  varies strongly with water content, ranging from well below the values for ice to significantly higher than those for pure water. The later often displayed as a “bright band” in the radar screen, often associated with light precipitation in mix-phase clouds.

24. INSERT TABLE 4.1
Radar signal K^2 falls as temp decreases for shorter wavelengths, but not 3 & 10 cm.

25. Weather Radar Equation - cont.
Assuming Rayleigh scattering spheres of diameter D
Introduce the radar reflectivity factor Z, where
where the summation extends over a unit volume,
and N(D)dD is the number of drops per unit volume
of a given diameter.

26. Weather Radar Equation - cont.
After accounting for the scattering volume and the beam pattern, the most useful weather radar range equation is:
radar
target
where  is the pulse duration and  is the beam width in radians.
Note that in some instances, Rayleigh scattering may not be fulfilled. In such instances, Z should be replaced by Ze, the effective radar reflectivity factor.

27. Weather Radar Equation - cont.
where C is a constant determined by radar parameters
and dielectric characteristics of the target
Power in decibels is related to the reflectivity factor as measured on the decibel scale.
Pr - measured in milliwatts, 10 log Pr is the power in dBm (decibels relative to a milliwatt).
Z is measured in mm6/m3 and 10 log Z is the reflectivity factor in dBz.

28. Major Assumptions behind the Radar Equation
The targets are spheroid
For non-spherical targets, polarization needs to be taken into account. The effect is measured by “depolarization ratio” of the cross-polarized component (Pc) over parallel-polarized component (Pp).

29. No attenuation between the target and radar
Pending the wavelength of radar beam, attenuation may be caused by radome, atmospheric gases, clouds, and precipitation due to both absorption and scattering.
For radar of 10 cm or longer wavelength, all attenuations are insignificant.
For radar of a few cm, gas attenuation is negligible, but cloud and rain attenuations need to be considered.
For radar of less than 3 cm, all attenuations needs to be considered. Ice cloud attenuation is less than water clouds by two orders of magnitude and is thus often neglected.
Because of attenuation, the shorter the wavelength, the shorter the detection range.

30. Relationship Between Z and Rainfall Rate
For a Marshall-Palmer distribution function
for R in mm/hr and Z in mm6/m3.
Some empirical data on R and Z give
For snow, Z = 2000 R2
The minimum detectable rainfall rate ≈ 0.1 mm/hr.

31. Relationship of dBz to rain rates.
Rain (mm/hr)
0.1
1.0
10.0
100.0
Z (mm6/m3) 5
200
7950
316,000
dBz 7 23 29 55
Some empirical data on R and Z give

32. Radar Scan Modes

33. Radar Displays PPI - Plan position Indicator (rotating scan)
Maps the received signals on polar coordinates in the plan view. The antenna scans 360° at fixed elevation angle. At every azimuth the voltage output of the receiver as a function of range is used to intensity-modulate a tube with polar coordinates (Rogers and Yau, 1989). This produces a plane view of the distribution of precipitation.
Without careful calibration, PPI records are only useful to show the location and time of occurrence of precipitation.

35. Radar Displays - cont. RHI - Range Height Indicator
This display is generated when the antenna scans in elevation with fixed azimuth, thereby showing the details of the vertical structure of precipitation.
CAPPI - Constant Altitude PPI
Azimuth and altitude are varied systematically to survey region surrounding the radar site.

36. PPI
RHI

37. HTI

38. Radar Displays - cont. Doppler Radar
The frequency of the transmitted signal for certain radars is constant. The frequency of the returned signal is compared with the transmitted signal, and the frequency (Doppler) shift is interpreted as the radial velocity of the precipitation r(hat) unit vector in radar pointing direction.

39. Nomenclature from the Glossary of Meteorology
ground clutter—Radar echoes from trees, buildings, or other objects on the ground. Such echoes may be caused by the reflection of energy back to the radar in the main lobe or sidelobes of the antenna pattern and, in weather radar applications, interfere with the meteorological echoes at the same range.
anomalous propagation—(Sometimes abbreviated AP or anaprop.) A propagation path of electromagnetic radiation that deviates from the path expected from refractive conditions in a standard atmosphere. In standard propagation conditions, radiation transmitted horizontally at the earth's surface is bent downward along a path with a radius of curvature equal to 4/3 times the radius of the earth. Subrefractive propagation causes less bending of the ray and superrefractive propagation causes greater downward bending than in the standard conditions. AP clutter is an extended region of ground echoes caused by superrefraction. See effective earth radius.

40. The combination of a low tilt angle and an inversion at and near the Earth's surface promotes an abundance of ground clutter. Below left is an example radar images using the lowest tilt angle (0.5 degrees) taken in the morning when a radiation inversion was in place. Right more typical NEXRAD ground clutter.

44. 230 km range PPI

45. PPI velocities

47. tornado

48. RADAR Take Home Messages 1. P(dB) = 10 log (P/Po) 2
RADAR Take Home Messages 1. P(dB) = 10 log (P/Po) 2. c ~ 300 m/ms; Pulse Rep. Freq ~ 1000 Hz; Distance between pulses = ½ 300 x 103 ms = 150 km. This is the range limit without overlap. 3. Doppler (phase coherent) provides radial velocity. 4. Atmospheric window 1.0 to 30 cm. Longer wavelengths cannot see cloud droplets. 5. Ice scatters only about 2/9 of liquid water Bright band at freeing level. 7. Attenuation ~ 1/l implies 10 cm radar sees farther, but needs a bigger dish.