Short Course On Radar Meteorology

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A short course on radar meteorology
Tobias Otto

Delft
University of
Technology Remote Sensing of the Environment (RSE)
Tobias Otto: A short course on radar meteorology. 1

A
T Radar Meteorology
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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.

Radar Meteorology:
The study of the atmosphere and weather using radar as the
means of observation and measurement.

Meteorology:
The study of the physics, chemistry, and dynamics of the
Earth's atmosphere.

Reference: AMS Glossary
Delft
University of

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T Microwaves
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S HF 3 - 30 MHz
VHF 30 - 300 MHz
mobile
UHF 300 - 1000 MHz KNMI Windprofiler
phones
L 1 - 2 GHz
S 2 - 4 GHz
C 4 - 8 GHz
X 8 - 12 GHz PARSAX
Ku 12 - 18 GHz KNMI
WLAN Weather
K 18 - 27 GHz Radar

Ka 27 - 40 GHz
V 40 - 75 GHz IDRA

W 75 - 110 GHz
mm 110 - 300 GHz Cloud Radar

Reference: Radar-frequency band nomenclature (IEEE Std. 521-2002)
Delft
University of

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T Microwaves and Water
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scattering

electromagnetic waves
frequency ≈ 2.4 GHz
wavelength ≈ 12 cm
T. Otto

absorption

Delft
University of

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T Water and Radar
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radar received
power

PARSAX on top of EWI faculty time
T. Otto

Delft
University of

A
T Information in microwaves
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O
S Electromagnetic waves are transversal waves, i.e. their direction of
oscillation is orthogonal to their direction of propagation.

1. Amplitude
y
x can be related to the strength of
precipitation / rain rate

A
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z

Delft
University of

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1. Amplitude
y
2. Frequency
Doppler shift, relative radial velocity
of the precipitation
z

Delft
University of

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1. Amplitude
y
2. Frequency
z 3. Phase
can be used to measure refractive
index variations

Delft
University of

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1. Amplitude
y can be related to the strength of
x precipitation / rain rate
2. Frequency
3. Phase
z
can be used to measure refractive
index variations
4. Polarisation
hydrometeor / rain drop shape
Delft
University of

A
T Radar Meteorology
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S
radio energy.

Radar Meteorology:

Meteorology:
Earth's atmosphere.

Delft
University of

A
T Radar Equation for a Point Target
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S antennae range R
Pt
transmitter Gt
target
σ
Pr
receiver Gr

isotropic
backscattered power density
antenna
at receiving antenna

Pt .. transmitted power (W)
Gt .. antenna gain on transmit Pt 1 Gr 2
R .. range (m) Pr   Gt    
σ
Gr
.. radar cross section (m2)
.. antenna gain on receive
4R 2
4R 2
4
Pr .. received power (W)
power density incident effective area of
on the target the receiving antenna

Delft
University of

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T Radar Equation for a Point Target
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S antennae range R
Pt
transmitter Gt
target
σ
Pr
receiver Gr

radar constant target characteristics
Pt .. transmitted power (W)
Gt .. antenna gain on transmit
Pt Gt Gr    2
R .. range (m)
Pr 
4   R
σ .. radar cross section (m2) 3 4
Gr .. antenna gain on receive free-space
Pr .. received power (W) propagation

Delft
University of

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T From Point to Volume Targets
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- the radar equation for a point target needs to be customised and expanded
to 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 the
radar cross sections of all scatterers in the resolution volume V (range-bin):

 
range bin
i V 
unit volume
i

Delft
University of

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T Radar Resolution Volume
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antenna beam-width

θ

c
range R
radar resolution volume r 
(range-bin) 2B
c .. speed of light
B .. 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
Delft
University of

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T Range Resolution of a Pulse Radar
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Delft
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1 2 3

e.g. pulse duration 1 µs
300m 
c  (s )
 m

f0

Delft
University of

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1 2 3

c 
2
• each target 1 consists of the sum of the
sample
backscattered signals of a volume with
response
the length c·τ/2
target 2
• for a pulse radar, the optimum sampling rate of
response
the backscattered signal is 2/τ (Hz)
target 3
response

Now we sample
the backscattered signal.

Delft
University of

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T Radar Equation for Volume Targets
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S PGt Gr  2  R 2 2 c
Pr  t
  V    i  i
44 R 2 16 ln 2 B unit volume
 R
33 44
unit volume

c
V   r  2

2B
2
    c
r V     R tan  
θ/2   2  2 B
R tan(α) ≈ α (rad) for small α
 rad 
c
r  2
c 1
2B
V  R 2
 
4 2 B 2 ln 2
volume reduction factor due to
Gaussian antenna beam pattern
Delft
University of

A
T Radar Cross Section σ
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Pbackscattered 2
 (m )
Sincident
Pbackscattered .. backscattered power (W)
Sincident .. 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

Delft
University of

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M
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S Monostatic radar cross section of a conducting sphere:

a .. radius of the sphere
normalised radar cross section

 .. wavelength

Rayleigh region: a << 

Resonance / Mie region:

electrical size
Optical region: a >> 

Figure: D. Pozar, “Microwave Engineering”, 2nd edition, Wiley.
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 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:

 K Di6 5 2
D .. hydrometeor diameter
i   .. wavelength
 4 |K|2 .. dielectric factor depending on the
material of the scatterer

Delft
University of

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T Radar Equation for Weather Radar
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Pt Gt Gr   R  c  K 2 2 2 5 2

Pr      i   Di6
4  R
3 4
4
16 ln 2 B unit volume unit volume

 Pt Gt Gr  c3
1 2
Pr  K  Dei  R 2
2 6

1024 ln 2 B 2
unit volum

radar constant radar reflectivity factor z, purely a
property of the observed precipitation

Delft
University of

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T Radar Reflectivity Factor z
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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: z  Pr CR2
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

Delft
University of

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T Summary of the assumptions made so far
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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 approximated
by a Gaussian function
• far-field of the radar antenna, using linear polarisation
• so far, we neglected the propagation term (attenuation)

Delft
University of

A
T Radar Meteorology
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S
radio energy.

Radar Meteorology:

Meteorology:
Earth's atmosphere.

Delft
University of

A
T Radar Reflectivity Factor z
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S  mm6 
z  D  m3 
 i
6

 spans over a large range; to compress it into a smaller
range of numbers, a logarithmic scale is preferred

unit volume 

1 m3
 
dBZ 
z one raindrop equivalent to
Z  10 log10  3  D = 1mm 1mm6m-3 = 0 dBZ
 1mm / m 
6

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.

Delft
University of

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T Raindrop-Size Distribution N(D)
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O 
N0
S z  D   D N ( D)dD  7  6!
unit volume
i
6 6

0
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:

N D   N 0 exp  D 
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)

Delft
University of

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T Reflectivity – Rainfall Rate Relations
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reflectivity (mm6m-3) z   D 6 N ( D)dD
D


liquid water content (mm3m-3) LWC 
6 
D
D 3 N ( D)dD
raindrop volume

rainfall rate (mm h-1) R
6 
D
D 3v( D ) N ( D )dD
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 z  aRb
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
Delft
University of

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T Summing-up
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- 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 power
which is related to the amplitude of an electromagnetic wave,
what about frequency, phase and polarisation?
… more after a short break …

Delft
University of

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T 2nd Part - Outline
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 radar geometry and displays

 Doppler effect

 polarisation in weather radars

Delft
University of

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 Doppler effect


Delft
University of

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T Radar Display
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PPI (plan-position indicator):

RHI (range-height indicator):

Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra
Delft
University of

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 Doppler effect


Delft
University of

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T Doppler Effect
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http://en.wikipedia.org/wiki/File:Dopplerfrequenz.gif

2vr 
fd  vr ,m ax  
target  4Ts

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

Delft
University of

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T Weather Radar Measurement Example (PPI)
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Reflectivity (dBZ) Doppler velocity (ms-1)

Data: IDRA (TU Delft), Jordi Figueras i Ventura
Delft
University of

A
T Combining Reflectivity and Doppler Velocity
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Doppler Processing (Power Spectrum):

Mapping the backscattered power of
one radar resolution volume into the
Doppler velocity domain.

Power
Doppler Width

Mean Doppler Doppler
Velocity Velocity

Figures: Christine Unal
Delft
University of

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 Doppler effect


Delft
University of

A
T Can Polarimetry add Information
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 yes, because hydrometeors are not spheres

- ice particles

- hail

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
- raindrops 1987. http://commons.wikimedia.org/wiki/Category:Hail

Delft
University of

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T Measurement Principle
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S transmit

Zhh (dBZ) Zhv (dBZ)
receive

Zvh (dBZ) Zvv (dBZ)

Delft
University of

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S transmit

Zhh (dBZ) Zhv (dBZ)
receive

-
Zvh (dBZ) Zvv (dBZ)

= Zdr
differential
reflectivity

Delft
University of

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T Hydrometeor Classification
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rain
aggregateslayer
ice crystals
melting (snow)

Reflectivity Differential Reflectivity

Z hh  10 log CR Phh dBZ  dB
Phh
2
Z dr  10 log
Pvv
Delft
University of

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S transmit

Zhh (dBZ) Zhv (dBZ)
receive

-
Zvh (dBZ) Zvv (dBZ)

= LDR (dB)
linear depolar-
isation ratio

Delft
University of

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T Linear Depolarisation Ratio
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melting clutter
ground layer

Reflectivity Linear Depolarisation Ratio

Z hh  10 log CR Phh dBZ  dB
Phv
2
LDR  10 log
Pvv
Delft
University of

A
T Estimation of raindrop-size distribution
M
N D   N 0 exp  D 
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S

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
Delft
University of

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T Summing-up
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- 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,
- …

Delft
University of

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A short course on radar meteorology
Tobias Otto

e-mail t.otto@tudelft.nl

web http://atmos.weblog.tudelft.nl
http://rse.ewi.tudelft.nl
http://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.

Delft
University of

Short Course On Radar Meteorology

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