1. Radar Doppler Velocities
Fundamentals of Doppler Radar
Mesocyclone
WER
Hook
Echo
Radar Reflectivity
Radar Doppler Velocities
Atmospheric Instrumentation
M. D. Eastin

2. Outline Fundamentals of Doppler Radar Basic Concept Single Radar Pulse
Multiple Radar Pulses
Maximum Doppler Velocity Range
Doppler Dilemma
Doppler Spectra of Weather Targets
Basic Interpretation of Doppler Velocities
Dual-Doppler Radar Analysis
Airborne Doppler Radar Analysis
Atmospheric Instrumentation
M. D. Eastin

3. Basic Concept Doppler Effect: Generic Definition
A frequency shift (cycles per second → Hertz) of any electromagnetic wave pulse
due to the “target” moving toward or away from the observer
Atmospheric Instrumentation
M. D. Eastin

4. Basic Concept Doppler Effect: Sound Waves
The Doppler shift for sound waves is the change in sound that one hears as race cars
or airplanes approach and then recede from a stationary observer
Atmospheric Instrumentation
M. D. Eastin

5. Basic Concept Doppler Effect: Meteorology
A frequency shift between the transmitted radar pulse and the return echo pulse due
to hydrometeors moving either toward or away from the radar antenna
Atmospheric Instrumentation
M. D. Eastin

6. Doppler Frequency Shift
Single Radar Pulse
Doppler Effect: Frequency Shift
The relationship between the return echo frequency
to the transmitted pulse frequency is:
(1)
where: fR = return echo frequency (s-1)
fT = transmitted frequency (s-1)
vR = “along-beam” radial velocity (m s-1)
c = speed of light (m s-1)
The frequency difference between the return echo
and transmitted pulse (after a little algebra):
(2)
where: fDOP = Doppler frequency (s-1)
Stationary Target
Moving Away
Doppler Frequency Shift
Moving Toward
Atmospheric Instrumentation
M. D. Eastin

7. Single Radar Pulse Doppler Effect: Frequency Shift
Since the Doppler frequency shift is computed from the difference (or subtraction) between
the transmitted and return echo frequencies, a radar must “listen” long enough (Δt) to
observe a full waveform (0 → 2π) of the Doppler shift frequency
If we assume: fT = 3 × 109 s-1 (10-cm radar)
c = 3 × 108 m s-1
vR = 1 m s-1 (for minimum shift)
Minimum Required Listening Time: Δt = 1.0 × 10-1 s
Maximum Allowed Listening Time: TR = 1.0 × 10-3 s (pulse period of the WSR-88D)
PROBLEM: The radar would need to “listen” at least 100 times longer between each pulse
to observe the full waveform of the Doppler frequency shift
Longer listening times require slower antenna rotation rates
Single elevation: 30 minutes
Single VCP: hours
We must use
another method !!!
Not Practical
Atmospheric Instrumentation
M. D. Eastin

8. Single Radar Pulse Doppler Effect: Frequency Shift
Police officers are required to keep the radar “gun” focused on an individual vehicle
for several seconds in order to obtain a full waveform of the Doppler shift frequency
Atmospheric Instrumentation
M. D. Eastin

9. Single Radar Pulse Doppler Effect: Phase Shift
The frequency difference can also be expressed
as a phase shift (0 → 2π) between the return
echo and the transmitted pulse
(3)
where: fDOP = Doppler frequency (s-1)
fT = transmitted frequency (s-1)
Δφ = phase shift (radians)
Δt = elapsed time (s)
c = speed of light (m s-1)
If we use the relationship between transmitted frequency and wavelength, we can define
the fractional phase shift for a single return echo:
(4) π 2π
π/3
Time
Amplitude
Atmospheric Instrumentation
M. D. Eastin

10. Transmitted Pulse Wavelength (λ)
Single Radar Pulse
Doppler Effect: Phase Shift Magnitude
Since we know the transmitted wavelength (λ), we can
estimate the maximum fractional phase shift (Δφ/2π)
of a single return echo using the pulse period (Δt = TR)
for a typical range of Doppler radial velocities (vR)
PROBLEM: As expected, the maximum fractional phase shift (Δφ/2π) returned by a single
pulse is much smaller than the full phase shift cycle required to reconstruct
the return echo “wave form” and determine the Doppler frequency
Phase Shift (Δφ/2π)
Transmitted Pulse Wavelength (λ)
[ for TR = 1×10-3 s ]
X-band
C-band
S-band
Radial Velocity (vR)
( 3-cm )
( 5-cm )
( 10-cm )
1 m/s
0.067
0.040
0.020
5 m/s
0.333
0.200
0.100
10 m/s
0.667
0.400
Atmospheric Instrumentation
M. D. Eastin

11. Full Doppler Frequency Cycle
Multiple Radar Pulses
Method to Overcome:
Transmit a rapid-fire “train” of multiple pulses → increase the pulse repetition frequency
Each pulse in the “train” will return a slightly different phase (φ1, φ2, φ3, φ4, … φN)
The multiple phase shifts are used to reconstruct (estimate) the full Doppler shift cycle
Doppler radial velocity (vR) is then computed from the mean phase shift along the train
Full Doppler Frequency Cycle
Time
Phase shift from
a single pulse
in a pulse train
Amplitude
Atmospheric Instrumentation
M. D. Eastin

12. Multiple Radar Pulses ANOTHER PROBLEM No unique solution
More than one Doppler frequency
(or waveform) will “fit” a finite
sample of phase shifts
Minimum Phase Criteria:
A minimum of two phase observations
are required to determine a waveform
of a Doppler frequency (N ≥ 2) OR
The phase change between any two
successive pulses must be less than
half a wavelength (Δφ ≤ π)
Other Criteria:
Since the maximum number of phase observations is set by the pulse repetition frequency
and the minimum number is set by the wavelength, there is a range of possible radial
velocities than can be unambiguously determined (next few slides…)
Time
Amplitude
Atmospheric Instrumentation
M. D. Eastin

13. Maximum Radial Velocity Range
Nyquist Velocity:
Starting with (4) and using the pulse period (TR) – or time between sequential pulses – for
the maximum elapsed time (Δt):
(5)
We next re-arrange and apply the “half wavelength criteria” (0 → π)
OR (6)
Solving (6) for radial velocity (vR) and using the relationship between pulse period (TR)
and pulse repetition frequency (F)
(7)
The Nyquist velocity represents the maximum (or minimum) radial velocity a Doppler radar
can measure unambiguously [ function of wavelength and pulse repetition frequency ]
Atmospheric Instrumentation
M. D. Eastin

14. Unambiguous Velocity Range Actual Radial Velocity
Maximum Radial Velocity Range
Nyquist Velocity:
The maximum (or minimum) radial velocity
a radar can measure unambiguously
Any actual radial velocities larger (or smaller)
than this value will be “aliased” back into another
unambiguous range → multiple aliases can occur
Example: Assume a radar with a Nyquist velocity
of ±10 m/s observes an area of rainfall
moving away from the radar at 15 m/s
[ Reported Actual ]
Aliased Velocities
-10 10 -5 5
Unambiguous Velocity Range
-20
-30 20 30
Actual Radial Velocity
Atmospheric Instrumentation
M. D. Eastin

15. Radar Reflectivity (DBZ)
Maximum Radial Velocity Range
Can you find the aliased velocities in this image?
Radar Reflectivity (DBZ)
Radial Velocity (VR)
Atmospheric Instrumentation
M. D. Eastin

16. They are inversely related
Doppler Dilemma
Maximizing the Nyquist Velocity:
This table shows that Doppler radars capable of measuring a large range of radial velocities
unambiguously have a longer wavelength (λ) and a large pulse repetition frequency (F)
Problem:
Recall that in order for radars to maximize their range, a small pulse repetition frequency
is required
Nyquist Velocity
Pulse Repetition Frequency (F)
Wavelength (λ)
200 s-1
500 s-1
1000 s-1
2000 s-1
3 cm
1.5
3.75
7.5
15.0
5 cm
2.5
6.25
12.5
25.0
10 cm
5.0
50.0
Which do we choose?
They are inversely related
Atmospheric Instrumentation
M. D. Eastin

17. Doppler Dilemma Maximizing the Nyquist Velocity:
Atmospheric Instrumentation
M. D. Eastin

18. Measure radial velocity
Doppler Dilemma
How to Circumvent the Dilemma:
Radar transmits pulses at alternating low and high pulse repetition frequencies
Lower frequencies are used for surveillance (reflectivity)
Higher frequencies are used for velocities (radial winds)
A version of this technique has been used regularly by the WSR-88D radars
1992–2008 → Alternating pulse repetition frequencies (lower two elevations scans)
→ Doppler winds determined out to 120 km range
→ Reflectivity determined out to 240 km range
2008–now → Separate lower elevation scans (different pulse repetition frequencies)
→ Doppler winds determined out to 300 km range
→ Reflectivity determined out to 360 km range
Measure reflectivity
Measure radial velocity
Pulse
Time
Atmospheric Instrumentation
M. D. Eastin

19. Doppler Dilemma Impact of the Dilemma:
The impact of determining radial velocities at a closer range than the radar reflectivity is
the “purple haze” (or range folding) often seen at far ranges on Doppler radar imagery
This results from echoes returning after the next pulse is transmitted (i.e., r > rMAX)
Atmospheric Instrumentation
M. D. Eastin

20. Doppler Spectra of Weather Targets
Variations in Radial Velocity:
A series of rapid-fire pulses in a pulse train will measure a “spectrum” of Doppler frequencies
(or radial velocities) from a which a “mean” and “standard deviation” can be computed
Radial velocity (vR) = mean value of the spectrum
Spectral width (σ) = standard deviation of the spectrum
= measure of the “spread” in velocities observed
within the sampling volume
–VMAX
+VMAX VR σ
spectrum
Atmospheric Instrumentation
M. D. Eastin

21. Doppler Spectra of Weather Targets
Variations in Radial Velocity:
Despite short time periods between each pulse of a rapid-fire pulse train, variations in the
computed mean radial velocities exist due to (1) changes in air motions, and (2) variability
in the drop size distribution within the contributing volume
Reasons for Variability:
1. Wind shear
2. Turbulence
3. Differential fall velocity
4. Antenna rotation
5. Curvature in the main lobe
Atmospheric Instrumentation
M. D. Eastin

22. Doppler Spectra of Weather Targets
Variations in Radial Velocity:
Doppler spectra observed by a vertically
pointing radar during passage of a winter
storm with mixed-phase precipitation
Notice how the spectra at individual heights vary by 1-2 m/s as a result
of variable drop diameters and their
associated fall speeds
Archived Spectra:
Full spectra observed by the WSR-88D
radars are not archived due to the large
amount of storage space required
However, the spectral width is archived and used by forecasters to help identify:
1. Small tornadoes at far ranges
2. Intense turbulence that may
impact aircraft operations
Atmospheric Instrumentation
M. D. Eastin

23. Basic Interpretation of Doppler Velocities
Radial Velocity: Along-Beam Motion
The measured radial velocity is that portion of the actual 3-D wind vector oriented along
the radar beam [ most radial velocities contain horizontal and vertical motions ]
Any single radar only measures one component of the three dimensional wind vector,
so to obtain a more practical estimate of two or three-dimensional flow:
1. Users must learn how to interpret single radar Doppler imagery (next lecture…)
2. Multiple Doppler radars can be used to “re-construct” the 3-D flow (next topic…)
Actual
Wind
Radial
component
seen by radar
RADAR
Atmospheric Instrumentation
M. D. Eastin

24. Basic Interpretation of Doppler Velocities
Doppler Effect: Meteorology
The sign [ + / – ] of the frequency shift is used to
determine the color of the radial velocity data
plotted on Doppler velocity displays
A negative shift (called a “red shift” in optics)
occurs as targets move away from the radar
Lower frequency = Positive radial velocity
= Outbound flow
A positive shift (called a “green shift” in optics)
occurs as targets move toward the radar
Higher frequency = Negative radial velocity
= Inbound flow
These “color” shift conventions are then translated
to radar displays:
Red: Moving away from radar
Green: Moving toward radar
Atmospheric Instrumentation
M. D. Eastin

25. Basic Interpretation of Doppler Velocities
Doppler Effect: Meteorology
The magnitude of the frequency shift is used to
determine the brightness of the radial velocity
data plotted on Doppler velocity displays
Much lower frequency = Strong outbound flow
Slightly lower frequency = Weak outbound flow
Much higher frequency = Strong inbound flow
Slightly higher frequency = Weak inbound flow
Atmospheric Instrumentation
M. D. Eastin

26. Basic Interpretation of Doppler Velocities
Examples of Data from a Single Doppler Radar:
GR2Analyst Demonstration
Atmospheric Instrumentation
M. D. Eastin

27. Dual-Doppler Radar Analysis
Using Two Doppler Radars:
One of the key limitations of Doppler radar data is that it only measures one component
of the three-dimensional (3-D) wind field
However, if a second unique component of the same wind field can be measured, then the
the third component can be derived (computed) using “boundary conditions”
The second component should be observed at an angle 30°-90° different
Requires the two radars to be “carefully spaced relative to one another”
Atmospheric Instrumentation
M. D. Eastin

28. Dual-Doppler Radar Analysis
Using Two Doppler Radars:
The baseline distance between the two radars must be “small” in order to provide sufficient
horizontal resolution (< 2 km) and coverage of the low-level (< 1 km) winds to observe the
critical flow fields associated with any convective feature of interest
[ Remember: Radar pulses expand in size and increase altitude far from the radar ]
Baseline distances: Less than 100 km [ too far apart for WSR-88Ds ]
[ easy for mobile DOWs ]
Atmospheric Instrumentation
M. D. Eastin

29. Dual-Doppler Radar Analysis
Doppler on Wheels (DOWs):
Must be deployed (and leveled)
within 10 km of the target storm
Scans at multiple elevation angles
or uses pre-programmed volume
coverage patterns
Alternates staggered pulse repetition
frequencies for reflectivity and radial
velocity measurements
Can now operate in single or dual
polarization modes
Parameter
DOW-1
DOW-2
Frequency
9.37 GHz
9.38 GHz
Wavelength
3.2 cm (X-band)
Radial resolution
12 m (minimum)
Maximum PRF
3200 s-1
5000 s-1
Transmitted power
250 kW
Pulse duration
2.0 μs
Beam width
0.93°
Gain
35 dB
Rotation period
12 s
9 s
Maximum Range
45 km
30 km
Atmospheric Instrumentation
M. D. Eastin

30. Dual-Doppler Radar Analysis
Doppler on Wheels (DOWs):
During tornado chase field experiments, the DOW radars will carefully place themselves near
a “promising” storm in order to collect dual-Doppler winds of the supercell and any tornado
DOW-2
DOW-1
Atmospheric Instrumentation
M. D. Eastin

31. Dual-Doppler Radar Analysis
Reconstructing 3-D Wind Fields:
The two radars obtain two unique (nearly simultaneous) measurements of radar-relative “radial winds” across the dual-Doppler domain
1. The radial winds (vR1 and vR2) are used to derive the east-west (U) and north-south (V)
horizontal wind components via → the radial winds are largely horizontal
where: θ1 = elevation angle (degrees) of radar #1
θ2 = elevation angle (degrees) of radar #2
β1 = azimuth (degrees) of radar #1
β2 = azimuth (degrees) of radar #2
Details are provided in Wurman (1994) and Jorgensen et al. (1996)
Atmospheric Instrumentation
M. D. Eastin

32. Dual-Doppler Radar Analysis
Reconstructing 3-D Wind Fields:
The two radars obtain two unique (nearly simultaneous) measurements of radar-relative “radial winds” across the dual-Doppler domain
2. The horizontal winds (U, V) are then used to compute the vertical wind (W) using a
density-weighted version of the continuity equation (below), assuming the vertical
motion a the ground is zero (W = 0 at z = 0), and subtracting an estimate of the mean
hydrometeor fall speed (WF) – derived from the mean radar reflectivity – from the
total vertical velocity (WT)
where: ρ = atmospheric density (kg m-3)
WT = total vertical velocity (m s-1)
WF = hydrometeor fall speed (m s-1)
Details are provided in Wurman (1994) and Jorgensen et al. (1996)
Atmospheric Instrumentation
M. D. Eastin

33. Dual-Doppler Radar Analysis
An Example:
From Wurman et al. (2007)
Atmospheric Instrumentation
M. D. Eastin

34. Dual-Doppler Radar Analysis
An Example:
From Wurman et al. (2007)
Atmospheric Instrumentation
M. D. Eastin

35. Dual-Doppler Radar Analysis
An Example:
From Wurman et al. (2007)
Atmospheric Instrumentation
M. D. Eastin

36. Airborne Doppler Radar Analysis
Airborne Radars: NOAA WP-3D and NCAR Electra
NOAA Tail Doppler radar
Single antenna with adjustable tilt
Scans in “vertical” plane normal
to the aircraft track
NCAR Tail Doppler radars
Two antenna fixed at 18.5° fore/aft
Scans in “vertical” plane normal to
the aircraft track
Parameter
NOAA
(one antenna)
NCAR
(both antenna)
Frequency
9.32 GHz
9.40 GHz
Wavelength
3.2 cm (X-band)
Radial resolution
125 m
150 m
Maximum PRF
1600 s-1
2000 s-1
Transmitted power
60 kW
50 kW
Pulse duration
0.5 μs
1.0 μs
Beam width
1.5°
1.8°
Gain
40.0 dB
38.7 dB
Rotation period
6.0 s
5.5 s
Maximum Range
93 km
70 km
Atmospheric Instrumentation
M. D. Eastin

37. Airborne Doppler Radar Analysis
Airborne Doppler Radars:
Similar to ground-based Doppler radars, if at least two unique “views” of the same wind field
can be obtained in a short period of time (simultaneously) by airborne Doppler radars, then
the three-dimensional wind field can be derived
The two views should be observed at different angles (30°-90° apart)
Requires the aircraft to complete a specific flight path
Single Aircraft – Vertical Plane Scanning
Antenna rotates through plane at 90° to the flight track
Aircraft must “box-off” target
convection by flying adjacent
leg over a short period, and
then turn 90° and fly a second
leg of similar length
Two views within 15 minutes
at typical aircraft speeds
Permits a “pseudo” dual
Doppler analysis
Aircraft track
Atmospheric Instrumentation
M. D. Eastin

38. Airborne Doppler Radar Analysis
Airborne Doppler Radars:
Similar to ground-based Doppler radars, if at least two unique “views” of the same wind field
can be obtained in a short period of time (simultaneously) by airborne Doppler radars, then
the three-dimensional wind field can be derived
The two views should be observed at different angles (30°-90° apart)
Requires the aircraft to complete a specific flight path
Single Aircraft – Fore-Aft (FAST) Scanning
Antenna alternates between a tilt of ~20° fore
and ~20° aft in subsequent rotations
Two views within 1-2 minutes at typical aircraft speeds
Does not require aircraft to box-off convection
Permits a “pseudo” dual-Doppler analysis with
less concern for storm steadiness
Atmospheric Instrumentation
M. D. Eastin

39. Airborne Doppler Radar Analysis
Airborne Doppler Radars:
Similar to ground-based Doppler radars, if at least two unique “views” of the same wind field
can be obtained in a short period of time (simultaneously) by airborne Doppler radars, then
the three-dimensional wind field can be derived
The two views should be observed at different angles (30°-90° apart)
Requires the aircraft to complete a specific flight path
Single Aircraft – Fore-Aft (FAST) Scanning
Antenna alternates between a tilt of ~20° fore
and ~20° aft in subsequent rotations
Two views within 1-2 minutes at typical aircraft speeds
Does not require aircraft to box-off convection
Permits a “pseudo” dual-Doppler analysis with
less concern for storm steadiness
Atmospheric Instrumentation
M. D. Eastin

40. Airborne Doppler Radar Analysis
Removing Navigation and Return Echo Errors:
The aircraft motion and orientation must
be accounted for and removed
Drift angle ± 20°
Pitch angle ± 10°
Roll angle ± 45°
Vertical motion ± 20 m/s
Horizontal motion m/s
Return echo considerations that must
be accounted for or removed
Low-power noise
Sea clutter
Second-trip echoes
Side-lobe contamination
De-aliasing radial velocities
Drift
Atmospheric Instrumentation
M. D. Eastin

41. Airborne Doppler Radar Analysis
Removing Navigation and Return Echo Errors:
Raw Data
Low-Power Noise
Notice aircraft’s tilt
Sea Clutter
Second Trip Echo
Radar Reflectivity
Radial Velocity
Atmospheric Instrumentation
M. D. Eastin

42. Airborne Doppler Radar Analysis
Removing Navigation and Return Echo Errors:
“Cleaned” Data
Radar Reflectivity
Radial Velocity
Atmospheric Instrumentation
M. D. Eastin

43. Airborne Doppler Radar Analysis
Reconstructing 3-D Wind Fields:
Similar to ground based-Doppler radars, the two radar views obtain two unique (nearly simultaneous) measurements of radar-relative “radial winds” within / near a given target
1. The radial winds (vR1 and vR2) are used to derive the east-west (U) and north-south (V)
horizontal wind components
where: θ1 = elevation angle (degrees) of radar #1
θ2 = elevation angle (degrees) of radar #2
β1 = azimuth (degrees) of radar #1
β2 = azimuth (degrees) of radar #2
Details are provided in Wurman (1994) and Jorgensen et al. (1996)
Atmospheric Instrumentation
M. D. Eastin

44. Airborne Doppler Radar Analysis
Reconstructing 3-D Wind Fields:
Similar to ground based-Doppler radars, the two radar views obtain two unique (nearly simultaneous) measurements of radar-relative “radial winds” within / near a given target
2. The horizontal winds (U, V) are then used to compute the vertical wind (W) using a
density-weighted version of the continuity equation (below), assuming the vertical
motion a the ground is zero (W = 0 at z = 0), and subtracting an estimate of the mean
hydrometeor fall speed (WF) – derived from the mean radar reflectivity – from the
observed total vertical velocity (WT)
where: ρ = atmospheric density (kg m-3)
WT = total vertical velocity (m s-1)
WF = hydrometeor fall speed (m s-1)
Details are provided in Wurman (1994) and Jorgensen et al. (1996)
Atmospheric Instrumentation
M. D. Eastin

45. Dual-Doppler Analysis
Airborne Doppler Radar Analysis
An Example:
Aircraft
Pass #2
Pass #1
“Pseudo”
Dual-Doppler Analysis A B
Winds
Reflectivity
z = 3.5 km
Atmospheric Instrumentation
M. D. Eastin

46. Airborne Doppler Radar Analysis
An Example: A B
Atmospheric Instrumentation
M. D. Eastin

47. Summary Fundamentals of Doppler Radar Basic Concept Single Radar Pulse
Multiple Radar Pulses
Maximum Doppler Velocity Range
Doppler Dilemma
Doppler Spectra of Weather Targets
Basic Interpretation of Doppler Velocities
Dual-Doppler Radar Analysis
Airborne Doppler Radar Analysis
Atmospheric Instrumentation
M. D. Eastin

48. References Atmospheric Instrumentation M. D. Eastin
Atlas , D., 1990: Radar in Meteorology, American Meteorological Society, 806 pp.
Crum, T. D., R. L. Alberty, and D. W. Burgess, 1993: Recording, archiving, and using WSR-88D data. Bulletin of the American Meteorological Society, 74,
Doviak, R. J., and D. S. Zrnic, 1993: Doppler Radar and Weather Observations, Academic Press, 320 pp.
Fabry, F., 2015: Radar Meteorology Principles and Practice, Cambridge University Press, 256 pp.
Joregensen, D. P., T. Matejka, and J. D. DuGranrut, 1996: Multi-beam techniques for deriving wind fields from airborne Doppler radars. Meteorology and Atmospheric Physics, 59,
Lee, W. C., F. D. Marks, and C. Walther, 2003: Airborne Doppler radar analysis workshop. Bulletin of the American Meteorological Society, 84,
Reinhart, R. E., 2004: Radar for Meteorologists, Wiley- Blackwell Publishing, 250 pp.
Wurman, J. 1994: vector winds from a single-transmitter bistatic dual-Doppler radar network. Bulletin of the American Meteorological Society, 75,
Wurman, J, Y. Richardson, C. Alexander, S. Weygandt, and P. F Zhang, 2007: Dual-Doppler analysis of winds and vorticity budget terms near a tornado. Monthly Weather Review, 135,
Atmospheric Instrumentation
M. D. Eastin