Active Remote Sensing Equation - the basis of RADAR, LIDAR, and SODAR measurements -

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Active Remote Sensing Equation- the basis of
RADAR, LIDAR, and SODAR measurements -

• Tobias Otto

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Content

• the active remote sensing equation
• derivation of the radar equation
• derivation of the lidar equation
• how to apply the active remote sensing equation
  for
• calibration
• system performance analysis

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The Active Remote Sensing Equation

• is an analytical expression for the power
  received by an active remote sensing system,i.e.
  RADAR, LIDAR or SODAR (RAdio / LIght / SOnic
  Detection and Ranging)
• merges all the knowledge about
• the system (relevant system parameters),
• the propagation path, and
• the targets that are remotely sensed
• is frequently applied for active remote sensing
  instrument
• design and performance analysis,
• calibration, conversion of the received power
  into a meaningful measurement,i.e. an observable
  that ideally solely depends on the targets itself

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The Active Remote Sensing Equation
range
active remote system
target
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Content

• active remote sensing equation
• derivation of the radar equation
• derivation of the lidar equation
• how to apply the active remote sensing equation
  for
• calibration
• system performance analysis

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Radar Equation for a Point Target
Pt
Gt
s
Pr
Gr
Pt .. transmitted power (W) Gt .. antenna gain on
transmit R .. range (m) s .. radar cross section
(m2) Gr .. antenna gain on receive Pr .. received
power (W)
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Radar Equation for a Point Target
Pt
Gt
s
Pr
Gr
Pt .. transmitted power (W) Gt .. antenna gain on
transmit R .. range (m) s .. radar cross section
(m2) Gr .. antenna gain on receive Pr .. received
power (W)
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From Point to Volume Targets

• the radar equation for a point target needs to be
  customised and expandedto fit the needs of each
  radar application(e.g. moving target indication,
  synthetic aperture radar, and also meterological
  radar)
• active remote sensing instruments have a limited
  spatial resolution,they do not observe single
  targets (raindrops, ice crystals etc.),instead
  they always measure a volume filled with a lot of
  targets
• ? volume target (distributed target) instead of
  a point target
• to account for this, the radar cross section is
  replaced with the sum of the radar cross sections
  of all scatterers in the resolution volume V
  (range-bin)

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Radar Resolution
? ?r is typically between 3m - 300m,and the
antenna beam-width is between 0.5 - 2 for
weather radars
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Range Resolution of a pulsed Active Remote
Sensing Instrument
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Range Resolution of a pulsed Active Remote
Sensing Instrument
1 2 3
e.g. pulse duration 1 µs 300 m
f0
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Range Resolution of a pulsed Active Remote
Sensing Instrument
1 2 3

• each sample consists of the sum of the
  backscattered signals of a volume withthe length
  ct/2

• for a pulsed active remote sensing instrument,
  the optimum sampling rate of the backscattered
  signal is 2/t (Hz)

Now we sample the backscattered signal.
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Radar Equation for Volume Targets
tan(a) a (rad) for small a
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Isotropic Scattering Cross Section s

• Depends on
• frequency and polarisation of the electromagnetic
  wave
• scattering geometry / angle
• electromagnetic properties of the scatterer
• target shape

? hydrometeors can be approximated as spheres
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Isotropic Scattering Cross Section s
Monostatic isotropic scattering cross section of
a conducting (metallic) sphere
Rayleigh region a ltlt ?
normalised radar cross section
electrical size
Optical region a gtgt ?
Figure D. Pozar, Microwave Engineering, 2nd
edition, Wiley.
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Radar Cross Section s

• hydrometeors are small compared to the
  wavelengths used in weather radar observations
  weather radar wavelength 10cm ? max. 6mm raindrop
  diameter
• Rayleigh scattering approximation can be
  appliedradar cross section for dielectric
  spheres

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Radar Equation for Weather Radar
radar constant
radar reflectivity factor z, solely a property of
the observed precipitation
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Radar Reflectivity Factor z

• spans over a large range to compress it into a
  smaller range of numbers, engineers prefer a
  logarithmic scale

raindrop diameter /m3 Z water volume per cubic meter
1 mm 4096 36 dBZ 2144.6 mm3
4 mm 1 36 dBZ 33.5 mm3
Knowing the reflectivity alone does not help too
much. It is also important to know the drop size
distribution.
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Raindrop-Size Distribution N(D)
where N(D) is the raindrop-size distribution that
tells us how many drops of each diameter D are
contained in a unit volume, i.e. 1m3. Often, the
raindrop-size distribution is assumed to be
exponential
Marshall and Palmer (1948) N0 8000
m-3mm-1 ? 4.1R-0.21 with the rainfall rate R
(mm/h)
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Reflectivity Rainfall Rate Relations
raindrop volume
terminal fall velocity

• the reflectivity measured by weather radars can
  be related to the liquid water content as well as
  to the rainfall rate
• power-law relationship
• the coefficients a and b vary due to changes in
  the raindrop-size distribution or in the terminal
  fall velocity.
• Often used as a first approximation is a 200
  and b 1.6

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Summary of the assumptions in the radar equation

• In the derivation of the radar equation for
  weather radars, the following
• assumptions are implied
• the hydrometeors are homogeneously distributed
  within the range-bin
• the hydrometeors are dielectric spheres made up
  of the same material with diameters small
  compared to the radar wavelength
• multiple scattering among the hydrometeors is
  negligible
• incoherent scattering (hydrometeors exhibit
  random motion)
• the main-lobe of the radar antenna beam pattern
  can be approximatedby a Gaussian function
• far-field of the radar antenna, using linear
  polarisation
• so far, we neglected the transmission term
  (attenuation)

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Content

• active remote sensing equation
• derivation of the radar equation
• derivation of the lidar equation
• how to apply the active remote sensing equation
  for
• calibration
• system performance analysis

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Lidar Equation for Volume Targets
laser
laser beam
receiver
receiver field of view
telescope area
Pr .. received power (W) Pt .. transmitted power
(W) AL .. laser beam cross section (m2) c ..
speed of light (ms-1) t .. temporal pulse length
(s) R .. range (m) s .. isotropic scattering
cross section (m2) A .. area of the primary
receiver optics (m2)
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Lidar Equation for Volume Targets
laser
laser beam
receiver
receiver field of view
telescope area
Pr .. received power (W) Pt .. transmitted power
(W) AL .. laser beam cross section (m2) c ..
speed of light (ms-1) t .. temporal pulse length
(s) R .. range (m) s .. isotropic scattering
cross section (m2) A .. area of the primary
receiver optics (m2) ? .. receiver efficiency
(how many of the incoming photons are
detected) O(R) .. receiver-field-of-view overlap
function T(R) .. transmission term (attenuation)
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Lidar Equation for Volume Targets
laser
laser beam
receiver
receiver field of view
telescope area
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Lidar Equation for Volume Targets
laser
laser beam
receiver
receiver field of view
telescope area
with the backscatter coefficient ß (m-1sr-1)
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Lidar Equation for Volume Targets
Both the backscatter coefficient and the
transmission term (attenuation) contain
significant contributions from molecular
scattering (gases like oxygen, nitrogen) ?
Rayleigh scattering and particle scattering
(liquid and solid air pollution particles such as
sulfates, mineral dust, sea-salt, pollen but
also larger hydrometeors as rain, ice, hail and
graupel) ? resonance or optical
scattering Difficult to differentiate with power
measurements only.
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Summary Radar and Lidar Equation
monostatic, i.e. co-located transmitter and
receiver
active remote system
C active remote sensing system constant M(R) range
dependent measurement geometry B(R) target
characteristics T(R) transmission term
(attenuation)
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Summary Radar and Lidar Equation
Radar Radar observations of the atmosphere
mainly contain contributions from hydrometeors
which areRayleigh scatterers at radar
frequencies. This allows the definition of the
reflectivity z, a parameter that is only
dependent on the hydrometeor microphysics and
independent on the radar wavelength,i.e. the
reflectivity within the same radar resolution
volume measured by different radarsshould be
equal Lidar Both the backscatter coefficient ß
and the transmission term T contain significant
contributions from molecular scattering (gases
like oxygen, nitrogen) ? Rayleigh scattering
and particle scattering (liquid and solid air
pollution particles such as sulfates, mineral
dust, sea-salt, pollen but also larger
hydrometeors as rain, ice, hail and graupel) ?
resonance or optical scattering Lidar
measurements of the atmosphere comprise
contributions from all three scattering regimes
Rayleigh, resonance and optical scattering ? it
requires more than a simple power measurement to
separate them. For this reason, lidar
measurements are also strongly dependent on the
lidar frequency and can not beeasily compared to
each other.
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Measurement example from Cabauw, Netherlands
UV-Lidar
Transportable Atmospheric Radar
Uncalibrated attenuated backscatter
Calibrated reflectivity not corrected for
propagation effects.
C active remote sensing system constant M(R) range
dependent measurement geometry B(R) target
characteristics T(R) transmission term
Which terms of the active remote sensing equation
contribute the figures oflidar backscatter and
radar reflectivity shown above?
data available at http//www.cesar-database.nl
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Content

• active remote sensing equation
• derivation of the radar equation
• derivation of the lidar equation
• how to apply the active remote sensing equation
  for
• calibration
• system performance analysis

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Calibration of Active Remote Sensing Measurements
C active remote sensing system constant M(R) range
dependent measurement geometry B(R) target
characteristics T(R) transmission term
(attenuation)
AMS Glossary of Meteorology The process whereby
the magnitude of the output of a measuring
instrument (e.g., the level of mercury in a
thermometer or the detected backscatter power of
a meteorological radar) is related to the
magnitude of the input force (e.g., the
temperature or radar reflectivity) actuating that
instrument. For the calibration of a radar /
lidar measurement (output mean received
power),we need to know - the range dependent
measurement geometry (range normalisation, easy
and accurate) - the active remote sensing system
constant can be determined analytically
using the system specifications, however for
an accurate calibration, extensive measurements
of the system are needed because it can vary
e.g. due to aging of hardware components,
hardware changes it needs to be constantly
monitored
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Content

• active remote sensing equation
• derivation of the radar equation
• derivation of the lidar equation
• how to apply the active remote sensing equation
  for
• calibration
• system performance analysis

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Radar performance
What is the minimum reflectivity detectable by a
meteorological radar?
Determined by the minimum received power that can
be discerned from the noise floor, i.e. the
minimum detectable signal (Pmds).
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Radar performance
Result of radar performance calculation of an
arbitrary weather radar
How could we increase the sensitivity? ? reduce
the range resolution (B ?) ? increase transmit
power (Pt ?) ? reduce the noise floor of the
system (Pmds ?) ? reduce the radar wavelength (?
?)
If we use a small wavelength (e.g. cloud radar at
35 GHz), we are able to detect very weak echoes
(e.g. fog). Are those radars also suited for the
observation of heavy rain? ? attenuation by rain
increases with frequency ? radar has a limited
dynamic range, i.e. there is a zmin but also a
zmax given by the dynamic range of the receiver
(a cloud radar receiver can be saturated by heavy
precipitation)
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IDRA reflectivity measurement of insects in summer
Why are there only insects close to the radar,
because theradar microwaves are keeping them
warm and cosy?
Of course not, insects are weak echoes. The radar
can not detect them at far ranges because the
echo is from a certain range on below the
sensitivity (zmin) of the radar.
data available at http//www.cesar-database.nl
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Summary
The active remote sensing equation is an
expression for the mean received power only. But
beside power (amplitude), electromagnetic waves
are also characterised by their frequency, phase
and polarisation. Those are the properties that
are exploited to gather more independent
measurements of the atmosphere in order to
separate e.g. transmission from
backward-scattering, or for lidar particle from
molecular scattering.
Advanced active remote sensing instruments ?
Doppler radar / lidar ? dual-polarisation radar
/ lidar ? multi-frequency radar / lidar ? Raman
lidar, taking advantage of the inelastic / Raman
scattering which leads to a change of the
molecules quantum state (the energy level), such
that the frequency of the scattered photon is
shifted a Raman lidar needs a high average laser
power and has additional receiver chanels for the
Raman backscatter spectrum of gases such as N2 or
H2O
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Active Remote Sensing Equation- the basis of
RADAR, LIDAR, and SODAR measurements -
Tobias Otto
e-mail t.otto_at_tudelft.nlweb http//atmos.webl
og.tudelft.nlreferences R. E. Rinehart, Radar
for Meteorologists, Rinehart Publications, 5th
edition, 2010. R. J. Doviak and D. S. Zrnic,
Doppler Radar and Weather Observations,
Academic Press, 2nd edition, 1993. V. N. Bringi
and V. Chandrasekar, Polarimetric Doppler
Weather Radar Principles and Applications,
Cambridge University Press, 1st edition,
2001. C. Weitkamp, Lidar Range-Resolved
Optical Remote Sensing of the Atmosphere,
Springer, 2005.