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
1
Diagram of Radar Transmission and
Reception (Fig. 1.1 from Batan and Fig.
8.1 from Stephens)
2
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.
3
Weather Radar:
Important Relationships
range - r
pulse of
energy
Received
Power
Transmitter
Target
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
r = ct/2
4
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 ~ 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
5
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.
6
INSERT TABLE 1.1 FROM BATTAN
7
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
8
INSERT FIG. 1.3 FROM BATAN
9
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
Intensity
Imax
Beam Width
.5 *Imax
0
Angular Separation
10
11
Summary of Important Radar Parameters
and “Typical Values”
(c.f. The appendix of Battan)
• Peak Power
~ 100-1000kW or 80~90 dBm
• Minimum Detectable Signal
~ 10-13 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
12
INSERT THE APPENDIX
13
14
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
15
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.
16
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,
17
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).
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Hail with a water coating scatters more radiation back.
INSERT FIG. 4.2 FROM BATTAN
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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.
20
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 .
21
Rayleigh Scattering
Define the scattering size parameter  for a sphere as
2 r0
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.
22
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.
23
INSERT TABLE 4.1
24
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.
25
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).
Pc
Dp (dB)  10 log
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.
Some empirical data on R and Z give
For snow, Z = 2000 R2
The minimum detectable rainfall rate ≈ 0.1 mm/hr.
30
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
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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.
33
34
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.
35
PPI
RHI
36
HTI
37
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.
   (1  v / c)
2 
  V  rˆ

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Nomenclature from the Glossary of Meteorology
http://amsglossary.allenpress.com/glossary
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
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effective earth radius.
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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41
http://www.met.tamu.edu/class/Metr475/la
b6.html
42
43
230 km range PPI
44
PPI velocities
45
http://coriolis.tamu.edu/class/Metr475/Lab
475.html
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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.
6. Bright band at freeing level.
7. Attenuation ~ 1/ implies 10 cm radar sees
farther, but needs a bigger dish.
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