Radar MeteorologyM. D. Eastin Doppler Radar From Josh Wurman.

Radar Meteorology M. D. Eastin

Doppler Radar

From Josh Wurman


Doppler Radar

Outline

• Basic Concepts• Doppler Radar Components• Phase Shifts and Pulse Trains• Maximum Range of Radial Velocity• Doppler Dilemma• Doppler Spectra of Weather Targets


Basic ConceptsDoppler Shift:

• A frequency shift in electromagnetic waves due to the motion of scatters toward or away from the observer

Analogy: The Doppler shift for sound waves is the change in frequency one detects as race cars or airplanes approach and then recede from

a stationary observer

Doppler Radar:

• A radar that can determine the frequency shift through measurement of the phase change that occurs in electromagnetic waves during a series of pulses


Doppler Shift from a Single Radar Pulse:

• Recall the electric field of a transmitted wave:

(1)

• The returned electric field at some later time:

(2)

• Time it took to travel to and from the object(s):

(3)

• Substituting:

(4)

Basic Concepts

00 2cos tfEtE tt

11 2cos ttfEtE tt

c

rt2

11

22cos

c

rtfEtE tt


Doppler Shift from a Single Radar Pulse:

(4)

• The received frequency can be determined by taking the time derivative of the quantity in parentheses and dividing by 2π:

where: vr = Radial velocity of targetfd = Doppler shift

(5)

(6)

Basic Concepts

11

22cos

c

rtfEtE tt

dtr fff

dt

dr

c

fff ttr

2

c

vfff rttr

2

rrt

d

v

c

vff

22


Sign Conventions:

• Doppler shift is negative (lower frequency, red shift) for objects moving away from the radar (positive vr)• Doppler shift is positive (higher frequency, blue shift) for objects moving toward the radar (negative vr)

• These “color” shift conventions are often translated to radar displays:

Basic Concepts

rrt

d

v

c

vff

22

Red: Moving away from radar

Blue/Green: Moving toward radar


Component of Motion:

• The observed radial velocity is the component of three-dimensional air motion that is along the radar beam

• In essence, the Doppler radar only measures one component of the full wind field

Basic Concepts


Magnitude of a Doppler Shift:

• These frequency shifts are very small: Thus Doppler radars must employ very stable transmitters and receivers in order to detect Doppler shifts with high accuracy (i.e. resolve vr to within 1 m/s or less)

Basic Concepts

Transmitted Frequency

X-band C-band S-band

Radial Velocity 9.37 GHz 5.62 GHz 3.0 GHz

1 m/s 62.5 Hz 37.5 Hz 20.0 Hz

10 m/s 625 Hz 375 Hz 200 Hz

50 m/s 3125 Hz 1875 Hz 1000 Hz


Block Diagram:

• STALO generates local frequency (fL)• COHO generates a known phase (fC)• Mixer combines fC with fL to get transmitted frequency (fT)• Klystron amplifies • Antenna transmits

• Frequency of received echo is the transmitted (fT) plus Doppler shift (fD)• Receiver uses STALO signal to remove local frequency• Signal amplified• Phase detector use COHO signal to estimate the Doppler shift from the original phase

Doppler Radar Components


Block Diagram:

Amplitude of Doppler signal:

Phase of the Doppler signal:

Doppler Radar Components

)cos(210 tAA

d

)sin(210 tAA

d

2210

2QI

AA

I

Qd

1tan


Why Emphasis is on Phase and not Frequency?

• Typical period of a Doppler shift cycle → 1/fD → 1 millisecond• Typical pulse duration → τ → 1 microsecond

Problem:

• Only a very small fraction of an entire Doppler shift cycle is contained in a single return

Method to Overcome:

• Transmit a “rapid-fire” train of pulses • Each pulse will return a slightly different phase (φ1, φ2, φ3, φ4, …)• The multiple phase shifts are then used to reconstruct, or estimate, the Doppler shift cycle (see next slide)• The Doppler frequency (i.e. radial velocity, vr) can then be estimated from the mean difference between successive phases returned by the train of pulses (see the slide after next)

Pulse Shifts and Pulse Trains


Reconstructing the Doppler shift cycle from multiple phase shifts:

Dots correspond to the measured samples of phase φfrom a “train” composed of 16 pulse returns



Relating Phase Shifts to Radial Velocity:

• Consider a single target moving radially along the radar beam

• Distance target moves in one pulse period (Tr):

(7)

• Corresponding phase shift between two successive pulses is equal to the the fraction of a wavelength traversed between two consecutive pulses:

(8)

• Solving for radial velocity:

(9)

• In practice, the radial velocity must be determined from the mean phase shift from all successive pulses in the train


rrvTd

rrvT2

212

2212

rr Tv


Problem: No Unique Solution

• More than one Doppler frequency (i.e. radial velocity) will fit a finite sample of phase values

• In essence a determined radial velocity is not unique• However, the possible radial velocities are multiples of a common value determined by the radar transmission characterisiics (see next slide…)



Maximum Range of Radial Velocity

2212

rr Tv

rrTv4

44max

F

Tv

rr


Nyquist velocity (vr-max):

• Represents the maximum (or minimum) radial velocity a Doppler radar can measure unambiguously• True radial velocities larger (or smaller) than this value will be “folded” back into the unambiguous range → multiple folds can occur

44max

F

Tv

rr

0-10 10-5 5 0-10 10-5 50-10 10-5 5

Unambiguous Velocity Range

0-10-20-30 10 20 30

Actual Radial Velocity



Folded Radial Velocities:


Folded Velocities


Can you find the folded velocities in this image?



Maximizing your Nyquist Velocity :

• Table shows that Doppler radars capable of measuring a large range of radial velocities unambiguously have long wavelengths and large PRFs

Problem:

• Recall that in order for radars to maximize their range, a small PRF is required

Doppler Dilemma

Wavelength Radar PRF (s-1)

(cm) 200 500 1000 2000

3 1.5 3.75 7.5 15.0

5 2.5 6.25 12.5 25.0

10 5.0 12.5 25.0 50.0

F

cr

2max 4max

Fv

8maxmax

crv Which do we choose?

They are inversely related


Maximizing your Nyquist Velocity :

Doppler Dilemma


How to Circumvent the Dilemma: Alternating PRFs

• Radar transmits burst of pulses at alternating low and high frequencies• Lower PRF for reflectivity with higher PRF for radial velocities

• This technique is regularly used by the NEXRAD radars

• The result → Doppler winds are determined out to 120 km range → Reflectivity determined out to 240 km range

Doppler Dilemma

Measure reflectivity Measure velocity


Variability in Vr:

• Despite small time periods between each pulse in a train, changes in air motions and the drop size distribution within the contributing volume will occur• As before, we need to account for this variability

Reasons for Variability:

1. Wind shear (especially in the vertical)

2. Turbulence

3. Differential fall velocity (more relevant at large elevation angles)

4. Antenna rotation

5. Curvature of microwave wave fronts (e.g. Gaussian main lobe)

Doppler Spectra of Weather Targets


Variability in Vr: Result

• A series of pulses will measure a spectrum of velocities (or Doppler frequencies)



Variability in Vr: First Three Moments

Zero Order

• Average returned power from pulse train• Area under the curve (see previous slide)• Related to equivalent radar reflectivity factor Ze


dvvSdffSPv

v

rdr

max

max



First Order

• Mean radial velocity• Associated with peak in the power spectrum (see previous slide)• Reflectivity weighted (i.e. large drops have greater influence on mean radial velocity)


r

v

v

r

v

v

r

v

v

r

r P

dvvvS

dvvS

dvvvS

v

max

max

max

max

max

max



Second Order

• Spectral width• Associated with the variation in observed radial velocities (see previous slide)• Influenced by turbulence and wind shear


r

v

v

rr

v

v

r

v

v

rr

v P

dvvSvv

dvvS

dvvSvv

max

max

max

max

max

max

22

2


Example:

• Vertically pointing Doppler radar with a large beam width (8 degs) during a spring storm


Small Raindrops

Ground Clutter

Freezing Level

Snowflakes

Radar MeteorologyM. D. Eastin Doppler Radar From Josh Wurman.

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Transcript of Radar MeteorologyM. D. Eastin Doppler Radar From Josh Wurman.