Lecture Session1

7/27/2019 Lecture Session1

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Course on

Dual Polarization Weather Radar

and Applications


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Instructor:

Professor V. ChandrasekarColorado State University and

University of Helsinki


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3 Dual Polarization Weather Radar and Appli cation s

Dual Polarization Weather Radarand Applications

V. Chandrasekar

Colorado State University and

University of Helsinki


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Overview of Dual Polarization WeatherRadar and Applications

Fundamentals of Weather Radar

Concept of Electromagnetic Polarization

Introduction to Dual Polarization Weather Radar

Doppler Weather Radar Theory

Dual Polarized Weather Radar Fundamentals

Rainfall

Precipitation Microphysics

Hydrometeor Classification

Attenuation and Attenuation Correction

Examples of Dual-Polarization Weather Radar Observations


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Fundamentals of weather radar

Radar equation for

Precipitation

Reflectivity factormeasurements Context for Dual

polarization


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The characteristics of a radar is essentially determined by theproperties of how electromagnetic waves interact with physicalobject such as airplanes or precipitation particles.

Radar

Radar a contraction of termsRadio detection and ranging
http://upload.wikimedia.org/wikipedia/commons/0/07/Radarops.gif


7/657 Dual Polarization Weather Radar and Appli cation s

Basic Principle of a Radar

The basic principle of a radar can be described by the followingdiagram.

The radar consists of a transmitter connected to the transmittingantenna, propagating electromagnetic wave outward from thetransmitter and a receiver connected to a receiving antenna forthe reception of any scattered wave.


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The portion scattered in the direction of the receiver travels at

the speed of light to the receiver located at a distance R2 awayand is received by the receiving antenna, which converts thewave to a received signal s(t).

The information about the scatterer is contained in the receivedwaveform.

Continued

The scatterer or target exists in the mediumbetween the transmitter and receiverlocations.

The transmitter waveform u(t)that is produced by thetransmitter is converted to radiating electromagnetic wave thattravels at the speed of light.

This wave encounters a scatter at a range R1.

The incident electromagnetic wave is scattered in all directions.


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Propagation Medium

The simplest propagation medium is free space.

However in the context of weather radar, the medium throughwhich the electromagnetic wave propagates can beprecipitation.


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Function of a Weather Radar

The detection function consists of detecting features of

weather/precipitation characteristics from the received

signal.

2) Measurement

1) Detection

Measurement of the scattering volume characteristicsinvolve measuring scatterer location in three dimensionalspace (range, azimuth, elevation), scatterer velocity as wellas the strength or type of scatterers.


11/65


Key Variables in Observation

Range: measure the distance of the target from radar

Direction: the angular position of the target

The radiation is directional,focused by the antenna.

Intensity: the size and dielectric properties of thetarget

Compare the power changes between the radiation and the echoes

Velocity: the relative movement of the target

Compare the frequency change between the radiationand the echoes

Doppler effect: where you get tickets for speeding

2

cr


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Radar As a System

Radar is a good example of a system composed of many types

of subsystems or elements. Specially weather radars aredesigned to observe what is termed as volume targets. Thefollowing shows a simple block diagram of a pulsed radar.

Antenna

IF Matched

Amp Filter

Second

demodulator

VideoAmp

MixerLow-noise

Amp

Duplexer

Local OSC

Output

PowerAmp

Pulse

Modulator

WaveformGenerator

Block diagram of pulsed radar


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In a Doppler radar the received signal is compared against a copyof the transmitted signal. In coherent systems where this is

done, the transmitter waveform is compared against receivewaveform. The transmitter waveform is a high frequency sinusoidmodulated by a train of pulses. The information carrying portion ofthe transmitter is the rectangular waveform. The high frequencysinusoid is called the carrier.

The transmitter waveform is generated by a combination of twooscillators, stable local oscillator (STALO) and coherent localoscillator (COHO)

Radar As a System (Continued)

The transmitted waveform is generated by the oscillators termedCOHO, STALO and amplified and fed to the antenna. The simplesttransmitter waveform is a train of pulses.


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DigitalModulator

GPSReference

PowerAmplifierMixer

STALO

sT

0T

Low NoiseAmplifier (LNA)

From STALO

ADCDigital Quadrature COHO

Low PassFilter

Low PassFilter

I

Q

IF Amplifier

Duplexer

Transmitter

Receiver


CSU-CHILL Radar System


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The scattered signal will be a replica of the transmitted signalexcept for a range time delay and Doppler frequency shift.

The STALO is used to bring down the carrier frequency toproduce the intermediate frequency signal. Subsequently these

are demodulated to obtain the information carrying part of thesignal for analysis.

In the process of describing the block diagram of the radar manyterms are introduced.

Waveforms: In a pulsed radar the transmitted waveform isdescribed as a train of rectangular pulses denoted by u(t).However this pulse modulates a high frequency sinusoid requiredfor radiation.



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The mathematical form of such a waveform is

is the carrier frequency.

)](2cos[)()( ttftuts o of

Radar transmitted signalshown as a sinusoid offrequency (f0) modulatedby a rectangular pulse ofduration T0

Magnitude ofthe spectrum ofthe transmittedsignal


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The location of precipitation to be measured by radar needs

definition of coordinate system.

Radar Coordinates

The natural coordinatesystem for a radar is

spherical polar coordinatesystem. The angles usedare azimuth angle,elevation angleand thedistance reference is

range. The azimuth angleis measured with respectto north.The elevationangle is measured withrespect to horizontal.


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Radar signal return intensities (or powers) are expressedin 2D image plots called Plan Position Indicator (PPI) or

Range Height Indicator (RHI).

Radar Coordinates (Continued)

PPI

RHI


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Range to a Target

The common radar waveform is a train of rectangular

pulses modulating a sine wave carrier. The range to

the target is determined by the time tR.

Electromagnetic waves travel at speed of light C.

The time for the signal to travel to range R andreturn is

C

R2


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Therefore, the range to the target is

IfR is in micro sec then

}{)(081.0)(15.0

)(150

2

1)(103

2

10)( 86

milesNauticalnmiskms

ms

ssmm

sCR

R

R

R

RR

2RCR


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Maximum Unambiguous Range

Once a signal is radiated into space by a radar,

sufficient time must elapse to allow for all the echo

signals to return to radar before the next pulse is

transmitted.

This elapsed time is determined by the largest range at

which targets are expected. If the time between the

pulses or sampling time TS is too short, then the echofrom this pulse arriving after the next pulse

transmission will be associated with that pulse.


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sT

oT sT sT2 sT2 sT3

)( tVr

)( sr TtV

)2( sr TtV


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PRF

CCTR S

22max

Echoes that arrive after the transmission ofnext pulse are called second trip echoes.

PRF = Pulse Repetition

Frequency


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1000

100

10 1000100PRF

104

10000

unR

nauticalmiles


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Radar Frequencies

Radars in the past have been built from 100 MHz to 36GHz. These are not hard limits.

Over the horizon radars operate at several MHzwhereas mm wave radars have been built at 240 GHz.

During world war II codes such as S, X and L were

used to designate frequency bands.


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IEEE standard radar-frequency

letter-band nomenclature

BandDesignation

NominalFrequency

Range

Specific Frequency Ranges forRadar based on ITU Assignments in

Region 2

HF

VHF

UHF

L

S

C

X

3-30 MHz

30-300 MHz

300-1000 MHz

1-2 GHz

2-4 GHz

4-8 GHz

8-12 GHz

138-144 MHz216-225 MHz

420-450 MHz

850-942 MHz

1215-1400 MHz

2300-2500 MHz;2700-3700 MHz

5250-5925 MHz

8500-10,680 MHz


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BandDesignation

NominalFrequency Range

Specific Frequency Ranges forRadar based on ITU

Assignments in Region 2

Ku

K

KaV

W

mm

12-18 GHz

18-27 GHz

27-40 GHz

40-75 GHz

75-110 GHz

110-300 GHz

13.4-14 GHz

15.7-17.7 GHz24.05-24.25 GHz

33.4-36 GHz

59-64 GHz

76-81 GHz

92-100 GHz

126-142 GHz ;144-149 GHz

231-235 GHz ;238-248 GHz


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Applications of Radars

Military : Radar is an important part of air-defense

systems as well as operation of offensive

missiles.

Remote sensing :1) Atmospheric observations.

2) Planetary observation.

3) Below ground probing.

4) Sea ice mapping.

Air traffic control (ATC) :

ASR(Air Surveillance Radar)-TDWR(Terminal DopplerWeather Radar)


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Law Enforcement / Highway safety :

- Police radar, collision avoidance systems.

- Aircraft safety/ Navigation/ Radar altimeter.

Space:

- Space vehicles use radar for rendezvous anddocking, Radio astronomy.

History :

- Basic concept of electromagnetic radiation shown

by Heinrich Hertz during 1885-1888.- He experimentally demonstrated James clerkMaxwells theory (published in 1864).


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- Early development , Hulsmeyer in early 1900sdeveloped to sell ship collision avoidance system.

- Marconi promoted the usage and presented tothe Institute of Radio Engineers (now the IEEE).

- Then came the heavy military bomber aircraft in1930s, which suddenly needed a device.

USA :

- The Naval Research Laboratory developedhundreds of radars by 1940.


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UK :

- Deployed radars by 1938.- The radars primarily were credited for turningthe momentum in the war.

- The invention of the magnetron revolutionizedthe development of high frequency radar.

- The cavity magnetron was delivered to MITRadiation Lab to accelerate the development.

Magnetron :

- Invented in Birmingham, UK.- Allowed development of small radars to becarried on ships and aircraft.


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After WW-II

- Doppler radars.

- High power amplifiers, Klystron, travelingwave tubes solid state transmitters.

- Monopulse radar.

- Pulse compression.


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Summary of Weather Radar Principles

Weather radar consists of a transmitter, the propagationmedium, precipitation scatters, and receiver.

TransmitterPropagation

Medium

Scatterer

ReceiverPropagation

Medium

Transmitter determines the frequency and radiated power andthe antenna determines the direction of transmission andpolarization.


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The receiver/processor determines how weak a signalcan be measured, and processed.

The receiver/processor module also generates userdefined products.

The transmitter receiver and processor are designed tomake the desired observation about the scatterers(which for weather radars is precipitation)

Summary (Continued)


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Fundamentals of weather radar

Radar equation for

Precipitation

Reflectivitymeasurements Context for Dual

polarization


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Weather Radar Equation for a Single Raindrop

Consider a pulsed Doppler radar transmitting a pulse of high frequencysinusoid (most weather radars)

Radar equation relates the range of a radar to the characteristics ofthe transmitter, receiver, antenna, target, and environment. It serves

as a means for understanding the factors affecting radar performance.

If the transmitter power Pt is radiated by an isotropic antenna, thenthe power density at a distance R from the radar is given by,

Power density

where 4R2is the surface area of a sphere

)(4

2

2mw

R

Pt

24 R

Pt

Raindrop


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Weather Radar Equation for a Single Raindrop (Continued)

Radars use directive antennas to concentrate the radiated

power, Pt in a particular direction. The gain of the antenna is ameasure of the increased power density radiated in somedirection as compared to that of an isotropic antenna.

Power density of a directive antenna =

antennaisotropicanbyradiateddensitypower

antennadirectiveabyradiateddensitypowerG

24 R

GPt

The scatterer intercepts a portion of the incident energy and scatters

it in various directions.

Only the power radiated in the direction of the radar is of interest.

The radar cross section () of a scatterer determines the amount of

scattered power.


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Concept of Radar Cross Section

When the object is large compared to the wavelength of theincident electromagnetic wave (such as large metal sphere)the scattering cross section of the radar is the same as thegeometric cross section.

2

D Whenever an electric field is incident on a dielectric sphere

such as a raindrop, then the dipoles in the water moleculesget aligned parallel to the electric field, and the net effect isan electric field with in the sphere. This dipole radiates

back, whose strength is proportional to the volume of thedrop.

Therefore the scattered field is proportional to volume of thesphere or V and the power is proportional to or

3D 6D2V



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The factor comes from the fact that the electric fieldwithin the sphere is less than what is applied due to depolarizingfactor. The factor comes from plane wave scattering. Scatteringfor such objects is called Rayleigh scattering.

)2/()1(3 rr

4

0k

Concept of Radar Cross Section (Continued)

If the scatterer is small compared to the wavelength , then forobjects such as raindrops (that are dielectric objects) the radar cross

section is given by

where Vis the volume of the raindrop.

2

24

0

)2(

)1(3

4V

k

r

r

Substituting and3

6DV

20 k

;62

4

5

DK

2

2

2

1

r

rK


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The total RCS is given by,

RCS of simple objects(i) Sphere

2

0 0

sin),(4

1

S S

SSSSSt dd

Direction to receiving

radar

x

y

z


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Due to symmetry waves scattered from a perfectlyconducting sphere are co-polarized with incident waves.

The normalized cross section for a perfectly conductingsphere in a Mie series is given by,

where, is the radius of the sphere.

is spherical Bessel function of the first kind of ordern.

1

2)12()1(

n

n n

kr

j

r

)(

)(

)()(

)()()1()1()1(

1

1

krH

krJ

krnHkrkrH

krnJkrkrJ

n

n

nn

nn

;2

k

r

nJ


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is the Hankel function of ordern

Given by,is the spherical Bessel function of 2nd kind.

)1(

nH

)()()()1( krjYkrJkrHnnn

nY


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For optical region

Rayleigh region (small sphere)

r2r

42 )(9 krr r


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The back scatter matrix for a dielectric sphere is,

where,

i

v

i

h

FSA

ssss

ss

ss

rik

s

v

s

h

E

E

Sk

iSk

i

Sk

iS

k

i

r

e

E

E

)(cos

)(sin

)(sin

)(cos

2

0

2

0

1

0

1

00

S

Snne

S

Snno

n

S

P

d

dP

nn

nS

sin

)(cos)(cos

)1(

12)(

1

1

1

1

1

1

S

Snne

S

Snno

n

Sd

dPP

nn

nS

)(cos

sin

)(cos

)1(

12)(

1

1

1

1

1

2

Radar cross section of a dielectric sphere


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)()()()(

)()()()(

0)2(00)2(0

0000

1

nnnnr

nnrnn

no

hjjh

jjjj

)()()()(

)()()()(

)2()2(1

nonoononr

ononrnono

ne

jhhj

jjjj

ak00 ; r 0

arChandrasekandBringiofaeqasSameno )(104.2.1

arChandrasekandBringiofbeqasSameno )(104.2.1


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Extending and computing the radar scattering cross

section

where,

2

),(4),( iifiib

2

1

112

0))(12()1(

nneno

n

nk

2

12

0

))(12()1(

n

S

n

S

n

n bank

;1neSna no

S

nb 1


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The total scattering cross section,

The extinction cross section

Fast numerical methods are available in, Barber and

Hill 1990.

The number of terms in series summations you need

is,

1

22

2

0

)12(2

n

S

n

S

nS bank

1

2

0

Re)12(2

n

S

n

S

next bank

2)(05.4 3/1max akakn oo


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The radar cross section is defined as the area , such that the

incident power density intercepted by this area , radiating as

an isotropic radiator yields the same power density as received

by the radar.

The cross section is dependent

on target shape and size.

2244 RR

GPt

Power density backscattered towards the radar

W th R d E ti f Si l R i d (C ti d )


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The radar antenna receives the energy incident on it. The Powerreceived by the radar is the product of the incident power density and

the effective area.


Effective area (Ae) of the receiving antenna is related to the physical

area by the aperture efficiency .a

e

tt

r ARR

GP

wattsP 22 44)(

42)4( R

AGP ett

,AAae

43

22

)4( R

GPt

The term comes from a two-way propagating wave, becausethe roundtrip distance is 2r.

kRje 2

kRjt e

GP2

234

The corresponding voltage signal is

Weather Radar Equation for Volume Targets


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If there is a large continuum ofprecipitation particles in range such as

raindrops and ice particles Then the backscattered signals from

all the hydrometeors in the range

to arrive at the same

time such that

is the range resolution

R RR

oT

c

RR

c

R

22

2

ocTR

mR 150 For a of 1 microsec. (typical)

o

T

The phase term of the received voltage

runs through several cycles of360o over 150m (because it cycles 360o

over one wavelength typical 10 cm)

Rkj oe2

oT

c

r2

R

RR

time

Weather Radar Equation for Volume Targets

W th R d E ti f V l T t (C ti d )


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Thus if we observe the received signal at time t, it comes froma volume of scatters between the ranges to . Because

of the random phase, the average power received is sum ofthe powers from individual precipitation particle (calledincoherent addition). Thus in radial extent, the contribution islimited to , but in angular extent (azimuth or elevation)the contribution is limited by the narrow antenna beam.

RR R

RR R

R

43

22

4 R

GP iit

The total power received from all the precipitation particles asseen by a single power sample is given by

Weather Radar Equation for Volume Targets (Continued)


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62

4

5

DKb

It was shown earlier that for a single precipitation particle isb

2

c

1

1

Weather Radar Equation for Volume Targets (Continued)

If is the volumetric reflectivity per unit volume, then the term

can be written as

where the integral for a Gaussian beam is reduced

to

432

4 R

Gii

dV

R

fGo

43

22

4

,

2

11

3

22

22ln84 R

rcTGP ooot

,2f2ln8

11

),(

),(

f

GGo where


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In radar meteorology it is conventional to express in terms of

equivalent reflectivity as

where is computed for water

25

4

w

e

kZ

2

wk 93.0

The equivalent reflectivity factor is in the radar volumeexpressed as reflectivity in units of mm6/m3. The above equationis called meteorological radar equation.

6

iD

2

25

11

32

2

2ln842 r

rZkGPcTrP

ewotor

Therefore when the receiver sees power Prat a time tafter thepulse transmission, r is obtained as , and the aboveequation is used to compute reflectivity. 2

tcr

Reflectivity measurements

Sensitivity/Minimum Detectable Signal


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The equivalent reflectivity factor iscomputed from the received power

as r

t

e PrGPcTK

Z 22

1120

3

025

2ln8421

For correct detection, the Signal-to-Noise Ratio (SNR) needs to exceed

some threshold. The noise power canbe expressed through system noisefigure:

Assuming SNR=1, the minimumdetectable reflectivity at range r0 is

kTBr

GPcTKZ

t

e2

02

1120

3

025

min 2ln8421

Sensitivity/Minimum Detectable Signal

kTBPn

System Sensitivity of the CSU-CHILL Radar

Frequency = 2.725 GHz

Peak Transmit Power = 800 kW

Antenna Gain = 42

Receiver Noise Level = -113 dBm

Pulse Width = 1 us

Beamwidth = 1 deg

Receiver Loss = 1.5 dB

The sensitivity of CSU-CHILL is -8 dBZ at 50 km

(-7.5 dB at 50 km for NEXRAD)

Resolution


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Resolution

Resolution is another figure of merits for a radar system. Highresolution observations can reveal fine weather features andimprove the accuracy of quantitative retrievals.

The sensitivity implies a preference of long pulse and wide antenna

beam, in addition to higher transmit power and larger antenna gain.

However, short pulse and narrow antenna beam are essential to

obtain high resolution measurement.

kTBr

GPcTKZ

t

e2

02

1120

3

025

min 2ln8421

Resolution (continued)


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Resolution (continued)

The measured reflectivity is the mean value for the 3-D resolutionvolume.

dVr

R

fGo ),,(

4

,43

22

- The range resolution depends on the pulse width

-The cross-beam resolution depends on the beamwidth and range

- Resolution becomes poorer at far ranges

- Sidelobe can couple in unwanted echoesin other direction

2

ocTR

Sidelobe

Reason for Dual-polarization


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Reason for Dual polarization

Up to now, the particle is assumed as spheres.

The radar reflectivity is an equivalent factor by assumingspherical particles.

Not always true!

Dual Polarization Measurements
http://images.google.com/imgres?imgurl=http://blog.spokanetogo.com/blogs/kris/snowflake.jpg&imgrefurl=http://blog.spokanetogo.com/blogs/kris/2007/11/&h=342&w=485&sz=70&hl=en&start=77&um=1&tbnid=_0hvFT7nx2Jo2M:&tbnh=91&tbnw=129&prev=/images?q=melting+snow+flake&start=60&ndsp=20&um=1&hl=en&rls=com.microsoft:en-US&sa=Nhttp://images.google.com/imgres?imgurl=http://images.aad.gov.au/img.py/153a.jpg&imgrefurl=http://www.classroom.antarctica.gov.au/the-big-white/1-11-snowflakes&h=425&w=640&sz=43&hl=en&start=21&um=1&tbnid=UV3tAErDZUiS1M:&tbnh=91&tbnw=137&prev=/images?q=ice+crystal&start=20&ndsp=20&um=1&hl=en&rls=com.microsoft:en-US&sa=Nhttp://images.google.com/imgres?imgurl=http://www.norcalblogs.com/watts/images/snowflakes.jpg&imgrefurl=http://jalmzpix.blogspot.com/2007/09/snowflakes.html&h=320&w=300&sz=62&hl=en&start=2&um=1&tbnid=1j2Kq1qEGDUfJM:&tbnh=118&tbnw=111&prev=/images?q=ice+crystal&um=1&hl=en&rls=com.microsoft:en-UShttp://images.google.com/imgres?imgurl=http://www.learner.org/jnorth/images/graphics/t/ice_crystal_Greg_Rob.jpg&imgrefurl=http://www.learner.org/jnorth/tm/tulips/ColdExper_IceCrystal.html&h=405&w=467&sz=24&hl=en&start=4&um=1&tbnid=jQuZM2oc-xeEMM:&tbnh=111&tbnw=128&prev=/images?q=ice+crystal&um=1&hl=en&rls=com.microsoft:en-UShttp://images.google.com/imgres?imgurl=http://www.markcassino.com/b2evolution/media/IMGP0219.jpg&imgrefurl=http://www.markcassino.com/b2evolution/index.php?m=200701&h=405&w=400&sz=75&hl=en&start=3&um=1&tbnid=sAdhJTXDbBmJ-M:&tbnh=124&tbnw=122&prev=/images?q=snow+flake&um=1&hl=en&rls=com.microsoft:en-UShttp://images.google.com/imgres?imgurl=http://www.theweatherprediction.com/severe/gianthail/hail1.jpg&imgrefurl=http://www.theweatherprediction.com/severe/gianthail/&h=400&w=600&sz=33&hl=en&start=27&um=1&tbnid=WcRK0u_ZlKNpbM:&tbnh=90&tbnw=135&prev=/images?q=hail&start=20&ndsp=20&um=1&hl=en&rls=com.microsoft:en-US&sa=Nhttp://www.crh.noaa.gov/gid/Web_Stories/2001/weather/04-06/1hail.jpghttp://images.google.com/imgres?imgurl=http://www.theweatherprediction.com/severe/gianthail/hail3.jpg&imgrefurl=http://www.theweatherprediction.com/severe/gianthail/&h=404&w=600&sz=35&hl=en&start=10&um=1&tbnid=RIupdim8kUhUCM:&tbnh=91&tbnw=135&prev=/images?q=hail&um=1&hl=en&rls=com.microsoft:en-US&sa=Nhttp://images.google.com/imgres?imgurl=http://www.tornadochaser.net/images/hail.jpg&imgrefurl=http://www.tornadochaser.net/hail.html&h=426&w=700&sz=39&hl=en&start=2&um=1&tbnid=BBIBtGcRIX1CyM:&tbnh=85&tbnw=140&prev=/images?q=hail&um=1&hl=en&rls=com.microsoft:en-US&sa=N


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Solution: observe the target using two orthogoanl polarizations(normally orthogonal).

V

H



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Polarimetric Capability


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p y

Raindrops are nonspherical and the nonspherical shape isincreased more pronounced with size.

Therefore different reflectivities are seen at horizontal andvertical polarizations.

We can measure other parameters to characterize the raindrop

in more details shape, size, orientation.

v

h

Plane containingthe electric field

Direction ofpropagation


65/65

Summary: Weather radar fundamentals

Scattering of electromagnetic wave by precipitationparticles

Range, direction, intensity, velocity

Radar as a system

Radar coordination: azimuth, elevation, range Radar equation for a single raindrop

Weather radar equation

Concept of reflectivity

Sensitivity

Resolution

Why dual polarization?

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