Weather Radar

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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

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

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Weather RadarImportant Relationships
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 C3x108
m/sec 3x105 km/sec
Received Power
r ct/2
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Important Radar Parameters

• Peak Power - Pt - (instantaneous power emitted in
  a pulse)
• 10 lt Pt lt 5000 kW, 5x106 W
• Minimum detectable signal
• Much smaller than emitted energy 10-13 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

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Important Radar Parameters (Cont.)

• Radio frequency - ?Radio wavelength - ? -
  (????c/??
• 3 lt ???????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.

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INSERT TABLE 1.1 FROM BATTAN
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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 lt c/2fr lt 75 km
• Pulse duration 0.1 lt ? lt 5 µs
• vs. pulse interval 500 lt t lt 5000 µsec

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INSERT FIG. 1.3 FROM BATAN
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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
0
Angular Separation
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Summary of Important Radar Parameters and
Typical Values(c.f. The appendix of Battan)

• Peak Power
• 100-1000kW or 8090 dBm
• Minimum Detectable Signal
• 10-13 W or 100 dBm
• Radio Frequency
• The popular weather radar 510 cm
• Pulse Repetition Frequency
• PRF 1000 sec-1
• Pulse duration 0.1 lt ? lt 5 µsec
• Beam width 1o-3o

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INSERT THE APPENDIX
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Radar Range EquationDerivation

• 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

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Radar Range EquationDerivation - 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.
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Radar Range EquationDerivation - cont.

• Assume the target scatters the power intercepted
  isotropically, then the power returned Pr to the
  antenna with aperture area Ae is given as

Thus,
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Radar Range EquationDerivation - 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).
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INSERT FIG. 4.2 FROM BATTAN
Hail with a water coating scatters more radiation
back.
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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.

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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
propertiesof the precipitation, we must now find
an expressionfor ?.
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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 ? ltlt 1, e.g. for r01mm and 10cm radar,
?0.06 scattering is in the Rayleigh region, and
? for a sphere or radius ro is given as
m is the complex index of refraction and n is the
ordinary refractive index and k the absorption
coefficient.
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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.

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INSERT TABLE 4.1
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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.
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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.
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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.

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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).

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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.
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Relationship Between Z and Rainfall Rate

• For a Marshall-Palmer distribution function

for R in mm/hr and Z in mm6/m3.
For snow, Z 2000 R2
The minimum detectable rainfall rate 0.1 mm/hr.
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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
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Radar Scan Modes
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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.

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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.

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PPI
RHI
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HTI
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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.

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Nomenclature from the Glossary of Meteorology http//amsglossary.allenpress.com/glossary ground clutterRadar 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.
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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.
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http//www.met.tamu.edu/class/Metr475/lab6.html
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230 km range PPI
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• PPI velocities

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http//coriolis.tamu.edu/class/Metr475/Lab475.html
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RADAR Take Home Messages1. 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. 6. Bright band at freeing
level.7. Attenuation 1/l implies 10 cm radar
sees farther, but needs a bigger dish.