1. Doppler Radar
From Josh Wurman
Radar Meteorology
M. D. Eastin

2. 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

3. Basic Concepts Doppler 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

4. Basic Concepts 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)
Radar Meteorology
M. D. Eastin

5. Basic Concepts 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 target
fd = Doppler shift
(5)
(6)
Radar Meteorology
M. D. Eastin

6. Basic Concepts 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:
Red: Moving away from radar
Blue/Green: Moving toward radar
Radar Meteorology
M. D. Eastin

7. Basic Concepts 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
Radar Meteorology
M. D. Eastin

8. Transmitted Frequency
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)
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

9. Doppler Radar Components
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
Radar Meteorology
M. D. Eastin

10. Doppler Radar Components
Block Diagram:
Amplitude of Doppler signal:
Phase of the Doppler signal:
Radar Meteorology
M. D. Eastin

11. Pulse Shifts and Pulse Trains
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)
Radar Meteorology
M. D. Eastin

12. Pulse Shifts and Pulse Trains
Reconstructing the Doppler shift cycle from multiple phase shifts:
Dots correspond to the measured samples of phase φ
from a “train” composed of 16 pulse returns
Radar Meteorology
M. D. Eastin

13. Pulse Shifts and Pulse Trains
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
Radar Meteorology
M. D. Eastin

14. Pulse Shifts and Pulse Trains
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…)
Radar Meteorology
M. D. Eastin

15. Maximum Range of Radial Velocity
What is the maximum possible radial velocity before ambiguity occurs?
We need at least two measurements per wavelength to determine phase
Thus, the phase change between successive pulses must be less than half a wavelength:
Starting with (9):
Re-arranging and applying the criteria above:
(10)
Solving for radial velocity in the extreme case [right side of (10)]:
(11)
where: F = sampling rate (or the PRF for the pulse period)
Radar Meteorology
M. D. Eastin

16. Unambiguous Velocity Range Actual Radial Velocity
Maximum Range of Radial Velocity
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
-10 10 -5 5
Unambiguous Velocity Range
-20
-30 20 30
Actual Radial Velocity
Radar Meteorology
M. D. Eastin

17. Maximum Range of Radial Velocity
Folded Radial Velocities:
Folded Velocities
Radar Meteorology
M. D. Eastin

18. Maximum Range of Radial Velocity
Can you find the folded velocities in this image?
Radar Meteorology
M. D. Eastin

19. They are inversely related
Doppler Dilemma
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
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
50.0
Which do we choose?
They are inversely related
Radar Meteorology
M. D. Eastin

20. Doppler Dilemma Maximizing your Nyquist Velocity : Radar Meteorology
M. D. Eastin

21. 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
Measure reflectivity
Measure velocity
Radar Meteorology
M. D. Eastin

22. Doppler Spectra of Weather Targets
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)
Radar Meteorology
M. D. Eastin

23. Doppler Spectra of Weather Targets
Variability in Vr: Result
A series of pulses will measure a spectrum of velocities (or Doppler frequencies)
Radar Meteorology
M. D. Eastin

24. Doppler Spectra of Weather Targets
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
Radar Meteorology
M. D. Eastin

25. Doppler Spectra of Weather Targets
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)
Radar Meteorology
M. D. Eastin

26. Doppler Spectra of Weather Targets
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
Radar Meteorology
M. D. Eastin

27. Doppler Spectra of Weather Targets
Example:
Vertically pointing Doppler radar
with a large beam width (8 degs)
during a spring storm
Snowflakes
Freezing Level
Ground Clutter
Small Raindrops
Radar Meteorology
M. D. Eastin