short course on radar meteorology
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Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 1
A short course on radar meteorology
Tobias Otto
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 2
Radar Meteorology
Reference: AMS Glossary
Radar: Radio Detection And Ranging
An electronic instrument used for the detection and ranging of distant objects of such composition that they scatter or reflect radio energy.
Meteorology:
The study of the physics, chemistry, and dynamics of the Earth's atmosphere.
Radar Meteorology:
The study of the atmosphere and weather using radar as the means of observation and measurement.
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 3
Microwaves
HF 3 - 30 MHzVHF 30 - 300 MHzUHF 300 - 1000 MHzL 1 - 2 GHzS 2 - 4 GHzC 4 - 8 GHzX 8 - 12 GHzKu 12 - 18 GHzK 18 - 27 GHzKa 27 - 40 GHzV 40 - 75 GHzW 75 - 110 GHzmm 110 - 300 GHz
KNMI Windprofiler
IDRA
Cloud Radar
WLAN
mobilephones
Reference: Radar-frequency band nomenclature (IEEE Std. 521-2002)
KNMIWeatherRadar
PARSAX
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 4
T. Otto
electromagnetic waves
frequency ≈ 2.4 GHzwavelength ≈ 12 cm
scattering
absorption
Microwaves and Water
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 5
PARSAX on top of EWI faculty
T. Otto
receivedpower
time
radar
Water and Radar
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 6
Information in microwaves
1. Amplitudecan be related to the strength of precipitation / rain rate
Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation.
AA
xy
z
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 7
Information in microwaves
Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation.
xy
z
1. Amplitudecan be related to the strength of precipitation / rain rate
2. FrequencyDoppler shift, relative radial velocity of the precipitation
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 8
Information in microwaves
Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation.
xy
z
1. Amplitudecan be related to the strength of precipitation / rain rate
2. FrequencyDoppler shift, relative radial velocity of the precipitation
3. Phasecan be used to measure refractive index variations
y
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 9
Information in microwaves
Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation.
x
y
z
1. Amplitudecan be related to the strength of precipitation / rain rate
2. FrequencyDoppler shift, relative radial velocity of the precipitation
3. Phasecan be used to measure refractive index variations
4. Polarisationhydrometeor / rain drop shape
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 10
Radar Meteorology
Reference: AMS Glossary
Radar: Radio Detection And Ranging
An electronic instrument used for the detection and ranging of distant objects of such composition that they scatter or reflect radio energy.
Meteorology:
The study of the physics, chemistry, and dynamics of the Earth's atmosphere.
Radar Meteorology:
The study of the atmosphere and weather using radar as the means of observation and measurement.
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 11
Radar Equation for a Point Target
Pt
Pr
Gt
Gr
transmitter
receiver
antennae range R
targetσ
Pt .. transmitted power (W)Gt .. antenna gain on transmitR .. range (m)σ .. radar cross section (m2)Gr .. antenna gain on receivePr .. received power (W)
44
1
4
2
22r
tt
r
G
RG
R
PP
backscattered power densityat receiving antenna
isotropicantenna
power density incidenton the target
effective area ofthe receiving antenna
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 12
Radar Equation for a Point Target
Pt
Pr
Gt
Gr
transmitter
receiver
antennae range R
targetσ
Pt .. transmitted power (W)Gt .. antenna gain on transmitR .. range (m)σ .. radar cross section (m2)Gr .. antenna gain on receivePr .. received power (W)
43
2
4
R
GGPP rttr
radar constant target characteristics
free-spacepropagation
Remote Sensing of the Environment (RSE)
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DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 13
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)
- radar has a limited spatial resolution, it does not observe single targets (i.e. raindrops, ice crystals etc.), instead it always measures a volume filled| with a lot of targets
volume (distributed) target instead of a point target
- to account for this, the radar cross section is replaced with the sum of theradar cross sections of all scatterers in the resolution volume V (range-bin):
eunit volumbinrange
ii V
Remote Sensing of the Environment (RSE)
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DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 14
Radar Resolution Volume
range Rradar resolution volume
(range-bin) B
cr
2
c .. speed of lightB .. bandwidth of the transmitted signal
(the bandwith of a rectangular pulse is the inverse its duration B=1/τ)
Δr is typically between 3m - 300m,and the antenna beam-width is between 0.5° - 2° for weather radars
θ
antenna beam-width
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 15
Range Resolution of a Pulse Radar
Remote Sensing of the Environment (RSE)
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DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 16
Range Resolution of a Pulse Radar
e.g. pulse duration 1 µs300 m
1 2 3
mc )(s
f0
Remote Sensing of the Environment (RSE)
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DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 17
Range Resolution of a Pulse Radar
1 2 3
target 1response
target 2response
target 3response
Now we samplethe backscattered signal.
2
c
• each sample consists of the sum of the backscattered signals of a volume withthe length c·τ/2
• for a pulse radar, the optimum sampling rate of the backscattered signal is 2/τ (Hz)
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 18
Radar Equation for Volume Targets
2 2 2
3 4unit volume
16 ln 24t t r
r i
PGG R cP
BR
2
3 4unit volume
4t t r
r i
PGGP V
R
B
cr
2
R
θ/2
B
crV
22
r B
cRV
22tan
2
tan(α) ≈ α (rad) for small α
2ln2
1
24
rad 22
B
cRV
2
volume reduction factor due toGaussian antenna beam pattern
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 19
Radar Cross Section σ
)m( 2
incident
redbackscatte
S
P
Pbackscattered
Sincident
.. backscattered power (W)
.. incident power density (W/m2)
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
Remote Sensing of the Environment (RSE)
ATMOS
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DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 20
Radar Cross Section σ
Monostatic radar cross section of a conducting sphere:
a
.. radius of the sphere
.. wavelength
Rayleigh region: a <<
Resonance / Mie region:
Optical region: a >>
Figure: D. Pozar, “Microwave Engineering”, 2nd edition, Wiley.
norm
alis
ed r
adar
cro
ss s
ectio
n
electrical size
Remote Sensing of the Environment (RSE)
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DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 21
Radar Cross Section σ
hydrometeors are small compared to the wavelengths used in weather radar
observations: weather radar wavelength 9cm max. 6mm raindrop diameter
Rayleigh scattering approximation can be applied;
radar cross section for dielectric spheres:
4
625
ii
DK
D|K|2
.. hydrometeor diameter
.. wavelength
.. dielectric factor depending on the material of the scatterer
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 22
Radar Equation for Weather Radar
eunit volum
64
2522
43
2
2ln16
4 i
rttr D
K
B
cR
R
GGPP
eunit volumi
2eunit volum
62
2
23 1
2ln1024
RDK
B
cGGPP i
rttr
radar constant radar reflectivity factor z, purely a property of the observed precipitation
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 23
Radar Reflectivity Factor z
2rz PCR
To measure the reflectivity by weather radars, we need to:
- precisely know the radar constant C (radar calibration),
- measure the mean received power Pr,
- measure the range R,
- and apply the radar equation for weather radars:
Summary:
Radar observations of the atmosphere mainly contain contributions from hydrometeors which are Rayleigh scatterers at radar frequencies.
This allowed us to introduce the radar reflectivity factor z, a parameter that
- only depends on the hydrometeor microphysics and is independent on radar parameters such as the radar frequency,
- i.e. the reflectivity within the same radar resolution volume measured by different radars should be equal
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 24
Summary of the assumptions made so far
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 propagation term (attenuation)
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 25
Radar Meteorology
Reference: AMS Glossary
Radar: Radio Detection And Ranging
An electronic instrument used for the detection and ranging of distant objects of such composition that they scatter or reflect radio energy.
Meteorology:
The study of the physics, chemistry, and dynamics of the Earth's atmosphere.
Radar Meteorology:
The study of the atmosphere and weather using radar as the means of observation and measurement.
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 26
Radar Reflectivity Factor z
dBZm/mm1
log103610
zZ
3
6
eunit volum
6
m
mmiDz
spans over a large range; to compress it into a smaller range of numbers, a logarithmic scale is preferred
1 m3
one raindropD = 1mm
equivalent to 1mm6m-3 = 0 dBZ
raindrop diameter #/m3 Z water volumeper 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.
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 27
Raindrop-Size Distribution N(D)
!6)(70
0
6
eunit volum
6
N
dDDNDDz i
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:
DNDN exp0
concentration (m-3mm-1) slope parameter (mm-1)
Marshall and Palmer (1948):
N0 = 8000 m-3mm-1
Λ = 4.1·R-0.21
with the rainfall rate R (mm/h)
Remote Sensing of the Environment (RSE)
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ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 28
Reflectivity – Rainfall Rate Relations
D
dDDNDz )(6reflectivity (mm6m-3)
D
dDDND )(6
LWC 3liquid water content (mm3m-3)
D
dDDNDvDR )()(6
3rainfall rate (mm h-1)
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
terminal fall velocity
baRz
raindrop volume
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 29
Summing-up
- electromagnetic waves and their interaction with precipitation
- radar principle
- radar equation for a point target
- extension of this radar equation to be applicable for volume targets and for weather radars
- the reflectivity was introduced, how it is determined from weather radar measurements, and its relation to rainfall rate (Z-R relations)
But, so far we only considered the backscattered received powerwhich is related to the amplitude of an electromagnetic wave,
what about frequency, phase and polarisation?
… more after a short break …
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 30
2nd Part - Outline
radar geometry and displays
Doppler effect
polarisation in weather radars
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 31
2nd Part - Outline
radar geometry and displays
Doppler effect
polarisation in weather radars
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 32
Radar Display
Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra
PPI (plan-position indicator):
RHI (range-height indicator):
Remote Sensing of the Environment (RSE)
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ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 33
2nd Part - Outline
radar geometry and displays
Doppler effect
polarisation in weather radars
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 34
Doppler Effect
http://en.wikipedia.org/wiki/File:Dopplerfrequenz.gif
target r
d
vf
2
fd .. frequency shift caused by the moving target
vr .. relative radial velocity of the target with respect to the radar
λ .. radar wavelength
Ts .. sweep time
sr Tv
4max,
Remote Sensing of the Environment (RSE)
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DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 35
Weather Radar Measurement Example (PPI)
Data: IDRA (TU Delft), Jordi Figueras i Ventura
Reflectivity (dBZ) Doppler velocity (ms-1)
Remote Sensing of the Environment (RSE)
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DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 36
Combining Reflectivity and Doppler Velocity
Doppler Velocity
Power
Mean Doppler Velocity
Doppler Width
Figures: Christine Unal
Doppler Processing (Power Spectrum):
Mapping the backscattered power of one radar resolution volume into the Doppler velocity domain.
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 37
2nd Part - Outline
radar geometry and displays
Doppler effect
polarisation in weather radars
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 38
Can Polarimetry add Information
yes, because hydrometeors are not spheres
- ice particles
- hail
- raindrops
Beard, K.V. and C. Chuang: A New Model for the Equilibrium Shape of Raindrops, Journal of the Atmospheric Sciences, vol. 44, pp. 1509 – 1524, June 1987. http://commons.wikimedia.org/wiki/Category:Hail
Remote Sensing of the Environment (RSE)
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DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 39
Measurement Principle
Zhh (dBZ)
Zvh (dBZ)
Zhv (dBZ)
Zvv (dBZ)
Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra
transmit
rece
ive
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 40
Measurement Principle
Zhh (dBZ)
Zvh (dBZ)
Zhv (dBZ)
Zvv (dBZ)
Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra
transmit
rece
ive
-
= Zdrdifferentialreflectivity
Remote Sensing of the Environment (RSE)
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ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 41
Hydrometeor Classification
dBZlog10 2hhhh PCRZ dBlog10
vv
hhdr P
PZ
Differential ReflectivityReflectivity
Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra
rainmelting layeraggregates (snow)ice crystals
Remote Sensing of the Environment (RSE)
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ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 42
Measurement Principle
Zhh (dBZ)
Zvh (dBZ)
Zhv (dBZ)
Zvv (dBZ)
Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra
transmit
rece
ive
-
= LDR (dB)linear depolar-
isation ratio
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 43
Linear Depolarisation Ratio
dBZlog10 2hhhh PCRZ dBlog10
vv
hv
P
PLDR
Linear Depolarisation RatioReflectivity
Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra
melting layerground clutter
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 44
Estimation of raindrop-size distribution
DNDN exp0
concentration (m-3mm-1) slope parameter (mm-1)
1. the differential reflectivity Zdr depends only on the slope parameter Λ,so Λ can be directly estimated from Zdr
2. once that the slope parameter is known, the concentration N0 can be estimated in a second step from the reflectivity Zhh
Data: IDRA (TU Delft), Jordi Figueras i Ventura
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 45
Summing-up
- Doppler capabilities allow an insight into the dynamics and turbulence of precipitation
- Polarisation can be successfully applied for weather observation because hydrometeors are not spherical, main applications are:
- discrimination of different hydrometeor types,
- suppression of unwanted radar echoes, i.e. clutter,
- improving rainfall rate estimation,
- estimation of raindrop-size distribution,
- attenuation correction,
- …
Remote Sensing of the Environment (RSE)
ATMOS
ATMOS
DelftUniversity ofTechnology
Tobias Otto: A short course on radar meteorology. 46
e-mail [email protected]
web http://atmos.weblog.tudelft.nlhttp://rse.ewi.tudelft.nlhttp://radar.ewi.tudelft.nl (for information on PARSAX)
references R. E. Rinehart, “Radar for Meteorologists”,Rinehart Publications, 5th edition, 2010.
R. J. Doviak and D. S. Zrnić, “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.
A short course on radar meteorology
Tobias Otto