WEATHER RADAR SYSTEMS Draft of Lecture 3

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WEATHER RADAR SYSTEMS Draft of Lecture 3
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MEASUREMENT OF RADAR REFLECTIVITY

• Reflectivity is the most important measurement
  performed by weather radar
• Reflectivity is correlated with precipitation
  activity
• A reflectivity map is closest to a weather
  picture
• Early weather radars had only reflectivity
  measuring capability
• Reflectivity of precipitation is caused by the
  scattering of radar energy by particles suspended
  in air
• Scatterers have unknown sizes, shape, orientation
  positions, velocities, composition
• The important task is to measure and relate the
  echo power to precipitation activity
• This is done under certain assumptions, depending
  on the capability of the radar and complexity of
  the measurement models

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SHAPE OF RAINDROPS

• Drop shape depends on a balance of surface
  tension, gravity and drag forces
• In typical rain, smaller drops are more numerous
• Smaller droplets tend to have spherical shape
• Spherical shape is a good approximation for
  raindrops

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SCATTERING BY SMALL PARTICLES

• NORMALIZED RADAR CROSS SECTION OF SPHERE vs SIZE

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SCATTERING BY SINGLE RAINDROP

• Raindrops are Rayleigh scatterers (D/? ltlt 1) for
  practical radar wavelengths
• Scattering depends strongly on drop diameter D
  and wavelength ?
• Backscattering cross section ?b of a small (D ?
  ?/16) spherical drop of water is (Rayleigh
  scattering approximation)

For a given radar ? is constant ? ?b ? D6
m complex refractive index of scatterer n
jk) At ?10 cm For water n 9, k 0.63 to
1.47 (20 to 0 C) For ice n 1.78, k 2.4?103
to 5.5?104 (0 to 20 C) Km2 0.91 to 0.93
for ? 1 to 10 cm, constant with temperature
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REFLECTIVITY AND REFLECTIVITY FACTOR

• Energy backscattered from all particles in a
  resolution volume will be received at a given
  instant (with appropriate weighting)
• Resolution volume contains numerous drops of
  varying sizes
• Important parameter is backscattering cross
  section per unit volume of space
• Reflectivity
• Z reflectivity factor
• Di is the diameter of ith raindrop in the volume
  element ?V
• Summation is over the drops in the volume ?V
• ?V should be large enough to represent the drop
  statistics, but small enough to ensure
  homogeneity
• In case of radar ?V may represent the resolution
  volume

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REFLECTIVITY FACTOR

• Z cannot be directly evaluated from particle
  sizes, which are unknown
• Evaluated statistically for large ensembles of
  scatteres
• Reflectivity factor has SI units m6/m3 or m6 m3
  (dimensionally m3)
• A more practical unit is mm6/m3 or mm6 m3
  (differs from SI by a factor of 1018)
• In practice Z varies over wide range
• To avoid deling with large values, Z is most
  often expressed in dB
• dBZ 10 log10 Z , with Z expressed in mm6/m3
• Examples
• Clouds 0 dBZ
• Drizzle 25 dBZ
• Very heavy rain with hail gt60 dBZ

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NWS REFLECTIVITY LEVELS
Level Reflectivity interval (dBZ) Rainfall category
1 18-30 Light (Mist)
2 30-41 Moderate
3 41-46 Heavy
4 46-50 Very heavy
5 50-57 Intense
6 gt57 Extreme (with hail)
National Weather Service, USA
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WEATHER RADAR RANGE EQUATION
Effective power along beam
Spherical spread
Volume of resolution volume
Reflec-tivity
Reverse spherical spread
Antenna collecting area

• ? reflectivity backscattering cross section
  of droplets per unit volume

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WEATHER RADAR RANGE EQUATION
Equivalent reflectivity factor

• Units ? (m), Ze (m6/m3), ? (m2/m3)

2ln2 is a shape factor due to nonideal antenna
calculated for half-power (3-dB) beamwidth of
Gaussian-shaped beam pattern
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EFFECT OF LOSSES

• System Loss Facor (Ls) Denotes fraction of
  energy lost between points where Pt is specified
  and where Pr is measured. Accounts for losses
  that are not included in any other variable in
  the radar equation.
• Atmospheric Loss actor (La one-way, La2 2-way)
  Loss of radar signals due to weather and other
  factors. Includes lens effect of 1 dB (2-way,
  worst case 0 elevation at 450 km range)
• Receiver Filtering Loss Factor (Lf) Accounts for
  spectral components of transmitted signal that do
  not pass through the finite bandwidth of the
  receiver filter
• Signal power at the output of radar receiver

Gs Receiver power gain, usually measured with a
continuous wave or monotone signal
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RANGE EQUATION PRACTICAL FORM

• Using more practical units,

Where the units are
Pro (mW)
Pt (W)
? (µs)
?b ()
Ze (mm6/m3)
? (cm)
r (km)
The range equation is used to determine the
reflectivity Ze. All other quantities are known.
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RAIN RATE ESTIMATION

• Radar reflectivity can be estimated from range
  equation
• Reflectivity is a good indicator of rainfall
  intensity (rain rate)
• However, quantitative rain estimate is more
  difficult
• The relation between reflectivity and rain rate
  is complex (not definite / unique / exact)
• Rain rate may vary by a factor of 3 or more for a
  given reflectivity factor

Rain rate Volume of water passing through unit horizontal area per unit time, depends on drop fall speeds in addition to diameters and numerical density of drops
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RAIN RATE ESTIMATION

• Drop terminal velocity wt(D) 386.6 D0.67 m/s
  where D is in m
• Rain rate R ? D3.67 for given drop diameter D
• But reflectivity Z ? D6
• Hence Z-R relation is not unique, depends on drop
  size distribution

N(D) is the number of drops / unit volume, having
diameter between D and D ?D Unit number/(m3
mm) or m-3 mm-1
and
If drop size distribution N(D) is known then Z-R
relation is unique
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MARSHALL-PALMER DISTRIBUTION

• N0 8000 m-3 mm-1
• D Drop diameter in mm
• 4.1 R-0.21
• R rain rate in mm h-1
• Actual drop size distribution and Z-R relation
  may vary substantially

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REFLECTIVITY-RAIN RATE RELATION
Z-R relationship is often expressed
directly Typical form Z a Rb where a,b are
constants, and R and Z are expressed in mm h1
and mm6 m3 respectively Examples for stratiform
rain a 200, b 1.6 (Marshall-Palmer
distribution) a 400, b 1.4 (Laws and
Parsons) a 300, b 1.5 (Joss and Waldvogel)
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REFLECTIVITY-RAIN RATE RELATION
Multiplicity of Z-R relationships