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Radar Meteorology M. D. Eastin
Doppler Radar
From Josh Wurman
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
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
Pulse Shifts and Pulse Trains
Radar Meteorology M. D. Eastin
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
Pulse Shifts and Pulse Trains
rrvTd
rrvT2
212
2212
rr Tv
Radar Meteorology M. D. Eastin
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…)
Pulse Shifts and Pulse Trains
Radar Meteorology M. D. Eastin
Maximum Range of Radial Velocity
2212
rr Tv
rrTv4
44max
F
Tv
rr
Radar Meteorology M. D. Eastin
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
Maximum Range of Radial Velocity
Radar Meteorology M. D. Eastin
Folded Radial Velocities:
Maximum Range of Radial Velocity
Folded Velocities
Radar Meteorology M. D. Eastin
Can you find the folded velocities in this image?
Maximum Range of Radial Velocity
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
Maximizing your Nyquist Velocity :
Doppler Dilemma
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
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
Radar Meteorology M. D. Eastin
Variability in Vr: Result
• A series of pulses will measure a spectrum of velocities (or Doppler frequencies)
Doppler Spectra of Weather Targets
Radar Meteorology M. D. Eastin
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
Doppler Spectra of Weather Targets
dvvSdffSPv
v
rdr
max
max
Radar Meteorology M. D. Eastin
Variability in Vr: First Three Moments
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)
Doppler Spectra of Weather Targets
r
v
v
r
v
v
r
v
v
r
r P
dvvvS
dvvS
dvvvS
v
max
max
max
max
max
max
Radar Meteorology M. D. Eastin
Variability in Vr: First Three Moments
Second Order
• Spectral width• Associated with the variation in observed radial velocities (see previous slide)• Influenced by turbulence and wind shear
Doppler Spectra of Weather Targets
r
v
v
rr
v
v
r
v
v
rr
v P
dvvSvv
dvvS
dvvSvv
max
max
max
max
max
max
22
2
Radar Meteorology M. D. Eastin
Example:
• Vertically pointing Doppler radar with a large beam width (8 degs) during a spring storm
Doppler Spectra of Weather Targets
Small Raindrops
Ground Clutter
Freezing Level
Snowflakes