Distance Learning
Operations Course
Topic 3: Principles of
Meteorological
Doppler Radar
Presented by the
Warning Decision Training Branch
Version: 0609
Distance Learning Operations Course
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Topic 3: Principles of Meteorological Doppler Radar
Distance Learning Operations Course
Topic 3: Principles of Meteorological Doppler Radar
Table of Contents
Topic 3, Lesson 1: WSR-88D Fundamentals ........................................... 3 - 7
WSR-88D Fundamentals (self guided web module) ...........................................3 - 8
Objectives...............................................................................................................3 - 8
Topic 3, Lesson 2: Signal Processing.................................................... 3 - 11
Signal Processing (instructor guided web module).........................................3 - 12
Objectives............................................................................................................. 3 - 12
Radial Velocity (Objective 1)............................................................................... 3 - 12
Key Points About Radial Velocity ...................................................................................... 3 - 13
Radial Speed Equation ...................................................................................................... 3 - 13
Examples........................................................................................................................... 3 - 16
.......................................................................................................................................... 3 - 17
The Doppler Effect (Objective 2) ........................................................................ 3 - 17
Sound Wave Example ....................................................................................................... 3 - 20
WSR-88D Pulse Example ................................................................................................. 3 - 21
WSR-88D Velocity Detection Method................................................................................ 3 - 21
Phasors ............................................................................................................................. 3 - 22
Phasors for Two Pulses..................................................................................................... 3 - 23
WSR-88D Radial Speed Computation (Objective 3) .........................................3 - 24
Maximum Unambiguous Velocity ..................................................................................... 3 - 25
Phase Shift-Radial Speed Relationship............................................................................. 3 - 26
Phase Shift Depiction Using Phasors................................................................................ 3 - 26
Phase Shift and Unambiguous Velocity............................................................................. 3 - 27
Obtaining I and Q Values (Objective 4)............................................................. 3 - 30
I and Q Components ......................................................................................................... 3 - 30
Both I and Q Values Needed ............................................................................................. 3 - 31
Determining Target Direction ............................................................................................. 3 - 31
Calculations Using Phasors .............................................................................................. 3 - 34
Actual Phase Shift Exceeds 180° ................................................................................................3 − 35
Calculations Using Phasors .............................................................................................. 3 - 35
Key Points ......................................................................................................................... 3 - 37
Signal Processing Review Exercises ................................................................................ 3 - 38
Topic 3, Lesson 3: Base Data Generation.............................................. 3 - 41
Base Data Generation (instructor guided web module)................................... 3 - 42
Objectives............................................................................................................. 3 - 42
Base Data Estimation Considerations (Objective 1) ........................................ 3 - 42
Base Reflectivity Data ....................................................................................................... 3 - 42
Base Mean Radial Velocity Data ....................................................................................... 3 - 43
Base Spectrum Width Data ............................................................................................... 3 - 45
Spectrum Width - Meteorological Factors (Objective 2) ................................. 3 - 47
Table of Contents
3-3
Distance Learning Operations Course
Spectrum Width - Nonmeteorological Factors (Objective 3) .......................... 3 - 49
Base Data Generation Review Exercises.......................................................................... 3 - 50
Topic 3, Lesson 4: Clutter Suppression................................................. 3 - 53
Clutter Suppression (instructor guided web module)...................................... 3 - 54
A Note on Terminology ...................................................................................................... 3 - 54
Objectives............................................................................................................. 3 - 54
Clutter Contamination on Base Products (Objective 1) ................................... 3 - 54
Ground Clutter Contamination General Characteristics .................................................... 3 - 55
Reflectivity Products .......................................................................................................... 3 - 55
Mean Radial Velocity Products.......................................................................................... 3 - 56
Spectrum Width Products .................................................................................................. 3 - 57
Anomalous Propagation (AP) on Base Products (Objective 1)....................... 3 - 58
AP Clutter General Characteristics ................................................................................... 3 - 58
Reflectivity Products .......................................................................................................... 3 - 59
Mean Radial Velocity Products.......................................................................................... 3 - 60
Spectrum Width Products .................................................................................................. 3 - 60
Clutter Suppression Technique: GMAP............................................................. 3 - 61
Reference .......................................................................................................................... 3 - 61
Clutter vs. Meteorological Signal ....................................................................................... 3 - 62
GMAP Performance Examples ......................................................................................... 3 - 63
Application of Ground Clutter Suppression .................................................... 3 - 69
Filtering of Normal vs. Transient Clutter ............................................................................ 3 - 69
Clutter Filter Bypass Map(s) .............................................................................................. 3 - 69
Bypass Map Generation Process ...................................................................................... 3 - 70
Clutter Suppression Regions Files .................................................................................... 3 - 73
Clutter Regions Window .................................................................................................... 3 - 74
Clutter Regions Window .................................................................................................... 3 - 76
Editing/Creating Clutter Regions ....................................................................................... 3 - 78
Clutter Filter Control (CFC) Product .................................................................................. 3 - 80
Examples of Data With and Without Proper Clutter Filtering............................................. 3 - 83
Negative Effects When All Bins Inappropriately Applied ................................................... 3 - 86
Ground Clutter Suppression Limitations (Objective 3) ...................................................... 3 - 92
Appropriate Ground Clutter Suppression Strengths (Objective 3)..................................... 3 - 93
Clutter Suppression Review Exercises.............................................................................. 3 - 94
Topic 3, Lesson 5: Mitigation of Data Ambiguities ............................... 3 - 97
Mitigation of Data Ambiguities (teletraining) .................................................... 3 - 98
Objectives............................................................................................................. 3 - 98
PRF effects on Rmax and Vmax (Objective 1) ..................................................... 3 - 99
Rmax Definition .................................................................................................................. 3 - 99
Vmax Definition................................................................................................................... 3 - 99
Key Points ......................................................................................................................... 3 - 99
“Doppler Dilemma” .......................................................................................................... 3 - 100
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Table of Contents
Topic 3: Principles of Meteorological Doppler Radar
Data Recognition and Algorithms (Objectives 2 & 3)..................................... 3 - 101
Range Folding.................................................................................................... 3 - 101
Often on Velocity and Spectrum Width Products............................................................. 3 - 102
Rarely on Reflectivity Products........................................................................................ 3 - 102
Range Unfolding Algorithm .............................................................................. 3 - 104
Non-overlaid Echoes Case.............................................................................................. 3 - 105
Overlaid Echoes Case......................................................................................................3 - 110
The Effects of TOVER ......................................................................................................3 - 113
Range Unfolding Algorithm ..............................................................................................3 - 114
Strengths ..........................................................................................................................3 - 114
Limitations ........................................................................................................................3 - 114
Improperly Dealiased Velocities....................................................................... 3 - 115
Velocity Dealiasing Algorithm .......................................................................... 3 - 119
Step 1: Radial Continuity Check ...................................................................................... 3 - 120
Step 2: Nine Point Average ............................................................................................. 3 - 121
Step 3: Expanded Search................................................................................................ 3 - 122
Step 4: Environmental Winds .......................................................................................... 3 - 122
Error Checks ................................................................................................................... 3 - 124
Velocity Dealiasing Algorithm .......................................................................................... 3 - 124
Strengths ......................................................................................................................... 3 - 124
Limitations ....................................................................................................................... 3 - 125
Operational Considerations ............................................................................................. 3 - 125
Multiple PRF Dealiasing Algorithm (MPDA) .................................................... 3 - 126
MPDA is an RPG-based Solution.................................................................................... 3 - 126
Applying MPDA ............................................................................................................... 3 - 126
VCP 121 Considerations ................................................................................................. 3 - 129
MPDA Processing for a Single Range Bin ...................................................................... 3 - 130
MPDA Adaptable Parameters ......................................................................................... 3 - 132
Strengths of MPDA .......................................................................................................... 3 - 133
Limitations of MPDA ........................................................................................................ 3 - 133
Minimizing Range Folding (Objective 4).......................................................... 3 - 134
Minimizing Range Folding ............................................................................................... 3 - 134
MPDA (VCP 121) and Auto PRF..................................................................................... 3 - 137
Mitigation of Data Ambiguities Review Exercises............................................................ 3 - 139
Topic 3, Lesson 6: Precipitation Estimation ........................................ 3 - 143
Precipitation Estimation (instructor guided web module) ............................. 3 - 144
Objectives........................................................................................................... 3 - 144
Reflectivity, Z and Rainfall Rate, R (Objective 1) ............................................ 3 - 144
Reflectivity - Z.................................................................................................................. 3 - 144
Sample Z computation..................................................................................................... 3 - 145
Rainfall Rate - R .............................................................................................................. 3 - 146
Sample R computation .................................................................................................... 3 - 147
Same Z, Different R......................................................................................................... 3 - 147
Same R, Different Z......................................................................................................... 3 - 148
Table of Contents
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Distance Learning Operations Course
Interim Summary ............................................................................................................. 3 - 148
WSR-88D Z-R Relationships........................................................................................... 3 - 149
Error Sources in Radar Estimated Rainfall (Objective 2)............................... 3 - 150
Types of errors ................................................................................................................ 3 - 150
Z estimate errors ............................................................................................................. 3 - 150
Z-R relationship errors..................................................................................................... 3 - 152
Below beam effect errors................................................................................................. 3 - 153
Radar Estimates vs. Rain Gages (Objective 3) ............................................... 3 - 154
Scenarios ........................................................................................................................ 3 - 154
Scenario 1 ....................................................................................................................... 3 - 155
Scenario 2 ....................................................................................................................... 3 - 155
Scenario 3 ....................................................................................................................... 3 - 156
Precipitation Processing Subsystem (PPS) (Objective 4) ............................. 3 - 156
Overview ......................................................................................................................... 3 - 157
Enhanced Precipitation Preprocessing (EPRE) .............................................................. 3 - 158
Precipitation Rate Algorithm ............................................................................................ 3 - 167
Precipitation Accumulation Algorithm .............................................................................. 3 - 168
Precipitation Adjustment Algorithm.................................................................................. 3 - 171
Summary ......................................................................................................................... 3 - 174
Precipitation Processing Subsystem - Strengths............................................................. 3 - 174
Precipitation Processing Subsystem - Limitations........................................................... 3 - 174
Snow Accumulation Algorithm (SAA) (Objective 5).......................................3 - 175
References ...................................................................................................................... 3 - 175
SAA Design ..................................................................................................................... 3 - 175
Begin and End of Snowfall Accumulations ...................................................................... 3 - 176
Reset (Begin) the Snow Accumulations .......................................................................... 3 - 177
Converting Reflectivity to the Rate of Snow Water Equivalent ........................................ 3 - 177
Range/Height Correction ................................................................................................. 3 - 179
Snow Ratio ...................................................................................................................... 3 - 180
SAA Adaptable Parameters............................................................................................. 3 - 180
SAA Products .................................................................................................................. 3 - 181
Snow Accumulation Algorithm - Strengths (Objective 5)............................. 3 - 182
Snow Accumulation Algorithm - Limitations (Objective 5) .......................... 3 - 182
Precipitation Estimation Review Exercises...................................................................... 3 - 182
Review Exercises Answer Key ......................................................................... 3 - 185
Signal Processing............................................................................................................ 3 - 185
Base Data Generation ..................................................................................................... 3 - 188
Clutter Suppression ......................................................................................................... 3 - 189
Mitigation of Data Ambiguities ......................................................................................... 3 - 190
Precipitation Estimation .................................................................................................. 3 - 193
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Table of Contents
Distance Learning
Operations Course
Topic 3, Lesson 1: WSR-88D
Fundamentals
Presented by the
Warning Decision Training Branch
Distance Learning Operations Course
Topic 3: Principles of Meteorological Doppler Radar
Version: 0609
Distance Learning Operations Course
WSR-88D
Fundamentals (self
guided web
module)
This lesson will present information that is fundamental to weather radars in general, such as beam
propagation and the Probert-Jones radar equation. It will also present information that is very
specific to the WSR-88D, such as the characteristics of a particular Volume Coverage Pattern
(VCP).
Lesson 1 is unlike any other part of Topic 3,
because it is a self guided web module. The
remaining web modules, Lessons 2, 3, 4, and 6,
are instructor guided, a sequence of annotated
slides with accompanying audio for each slide.
Lesson 1 has no audio, and it is designed as much
for future reference as it is for initial learning.
Lesson 1 is accessed from the DLOC Main Page,
http://wdtb.noaa.gov/courses/dloc/index.html
Under Web Modules, you will find a link to Topic 3,
Lesson 1, WSR-88D Fundamentals.
The amount of time needed to complete Lesson 1
will vary depending on your experience with the
WSR-88D. The average completion time is estimated to be 2 hours.
Objectives
1. Identify the range resolutions and corresponding display ranges for Base Reflectivity, Base
Velocity, and Base Spectrum Width.
2. Given dBZ values along a radial at .54 nm resolution, identify which dBZ values would be used
to build lower resolution Base Reflectivity products.
3. Given Base Velocity and Spectrum Width values along a radial at .13 nm resolution, identify
which Base Velocity and Spectrum Width val-
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WSR-88D Fundamentals (self guided web module)
Topic 3: Principles of Meteorological Doppler Radar
ues would be used to build lower resolution
Base Velocity and Spectrum Width products.
4. Given Rmax and the actual target range, R,
identify other ranges at which an echo from a
target could appear.
5. Identify the two situations where sidelobe contamination is likely to occur.
6. Identify meteorological conditions conducive to
superrefraction and subrefraction of the radar
beam, and the resultant operational impacts.
Objectives
3-9
Distance Learning Operations Course
3 - 10
Objectives
Distance Learning
Operations Course
Topic 3, Lesson 2: Signal
Processing
Presented by the
Warning Decision Training Branch
Distance Learning Operations Course
Topic 3: Principles of Meteorological Doppler Radar
Version: 0609
Distance Learning Operations Course
Signal Processing
(instructor guided
web module)
The WSR-88D provides three types of base data,
Reflectivity, Velocity and Spectrum Width. As
these data are the input for the generation of all
radar products, it is important that the base data
be of the highest possible quality. There are data
quality issues inherent in meteorological Doppler
weather radars. Proper interpretation of the WSR88D products requires an understanding of data
quality, and this section lays the necessary foundation for this understanding.
Objectives
1. Compute the radial velocity of a target given the
radar viewing angle, actual target velocity, and
the appropriate equation.
2. Identify how Doppler information is obtained by
the WSR-88D to determine atmospheric
motion.
3. Compute the speed a radar initially assigns a
range bin, given a pulse-pair phase shift and a
maximum unambiguous velocity (Vmax).
4. Determine whether apparent target motion is
toward or away from the radar, given I and Q
values from two successive returned pulses.
Radial Velocity
(Objective 1)
3 - 12
Radial velocity (Vr) is defined as the component
of target motion parallel to the radar radial (azimuth). It is that component of a target's actual
velocity (V) that is either toward or away from the
radar site along the radial.
Signal Processing (instructor guided web module)
Topic 3: Principles of Meteorological Doppler Radar
Some important principles to remember about Key Points About Radial
Velocity
Doppler radial velocity are:
1. Radial velocities will always be less than or
equal to actual target velocities.
2. Radial velocity equals actual velocity only
where target motion is directly toward or away
from the radar.
3. Zero velocity is measured where target motion
is perpendicular to a radial or where the target
is stationary.
When sampling large-scale atmospheric flow, The Relation of Actual
most of what is depicted will be less than the Velocity to Radial Velocity
actual environmental flow. The same holds true
even for storm-scale rotational flows since only
that component of a circulation either directly
toward or away from the radar will have its actual
velocity detected.
The relationship between a target's actual velocity Radial Speed Equation
and the WSR-88D depicted radial velocity can be
described mathematically by using the Radial
Speed Equation
V r = V ⋅ cos β
(1)
where:
• Vr = radial velocity
• V = actual velocity
• β = smaller angle between V
and the radar radial
• cos = cosine
The angle β (beta) is always the smaller of the The Angle β
two angles between the radar viewing angle (i.e.
radar radial or azimuth) and the actual target
velocity vector (V).
Radial Velocity (Objective 1)
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Distance Learning Operations Course
Figure 1.
As target motion becomes more (less) perpendicular to the radar beam, β
increases (decreases). When the target motion is exactly perpendicular to
the radar beam β is 90° and the radial velocity is zero.
β is Equal to 0° When β is equal to 0°, target motion is parallel to
the radar beam and cos β is 1. The target radial
speed (|Vr|) is equal to the actual target speed
(|V|).
β is Equal to 90° When β is equal to 90°, target motion is perpendicular to the radar beam and cos β is zero. The
radial speed (|Vr|) is zero, and there is no component of target motion toward or away from the
radar.
Radial Speed Computation Assume that the actual wind is uniform from a
Example direction of 300° at 30 knots through the lower
atmosphere (Figure 2).
Figure 2.
Radial speed computation example.
As the antenna is pointed due west (along the
270° radial), a radial wind speed of 26 knots would
be measured. This answer is obtained by using
equation (1) and β= 30°.
3 - 14
Radial Velocity (Objective 1)
Topic 3: Principles of Meteorological Doppler Radar
| Vr | = | V | cos β
| Vr | = (30 kt) cos (30°)
| Vr | = (30 kt) (.866)
| Vr | = 25.98 kt ≈ 26 kt
Once the speed is calculated from equation (1), Target Direction
the direction, inbound or outbound, must be determined. This is simply the direction of the component of the actual wind that lies along the radial. In
Figure 2, the radial component, Vr, would be
inbound toward the RDA. Thus the radial velocity
is -26 knots.
Figure 3 shows how equation (1) comes from trigonometry, where the actual wind vector and the
components along and perpendicular to the radar
radial form a right triangle. Also in Figure 3, the
actual wind is southerly over the display. A radar
azimuth has been selected in each quadrant and
the actual wind vector has been decomposed into
components along and perpendicular to the radial.
Although the magnitudes differ, note that the radial
velocities in the two southern quadrants are
inbound and in the two northern quadrants are outbound.
Figure 3.
Determining the direction of the radial component of the actual velocity.
Radial Velocity (Objective 1)
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Distance Learning Operations Course
Relationship Between β The greater the angle between the target's velocand Percentage of Actual ity vector and the radar azimuth, the smaller the
Velocity percentage of the target's actual velocity that will
be measured and depicted on the velocity products. Table 3 shows the relationship between β
and the percentage of actual target speed that is
directly measured. The relationship between the
actual speed and the radial speed is based on the
cosine function. Therefore it is not a linear relationship. For example, a β of 45° (halfway between 0°
and 90°) results in a radial speed that is about
70% of the actual speed, not 50%
Table 3: Percentage of Target Speed Measured
β
degrees
Cosine
β
Percent
Measured
0
1
100
5
.996
99.6
10
.985
98.5
15
.966
96.6
30
.866
86.6
45
.707
70.7
60
.500
50.0
75
.259
25.9
90
0
0
Examples In each of the following examples, draw the radar
azimuth and the actual velocity vector. Then draw
the components of the velocity parallel to and perpendicular to the radar radial. Determine β and
use Equation (1) to calculate the radial speed.
3 - 16
Radial Velocity (Objective 1)
Topic 3: Principles of Meteorological Doppler Radar
1. V = 40 kts from 270°, radar azimuth is 315°.
2. V = 40 kts from 270°, radar azimuth is 60°.
3. V = 50 kts from 360°, radar azimuth is 165°.
The Doppler Effect is defined as “the change in
frequency with which energy reaches a receiver
when the receiver and the energy source are in
motion relative to each other” (from the Glossary
of Meteorology). Determining the Doppler Effect or
shift is straightforward when the energy transmission source is stationary and the target being sampled is moving (or stationary). Any frequency shifts
The Doppler Effect
(Objective 2)
The Doppler Effect (Objective 2)
3 - 17
Distance Learning Operations Course
would be solely the result of the target moving
toward or away from the energy transmission
source.
From basic physics, there is a relationship
between the speed of transmitted electromagnetic
(E-M) energy and the frequency and wavelength
of that energy. This relationship is expressed as
c = fλ
(2)
where c is the speed of light (assumed to be constant), f is the frequency and λ is the wavelength
of the energy. If the wavelength (λ) is increased,
the frequency (f) must decrease since the speed
(c) is constant and vice versa.
If equation (2) is allowed to represent the Doppler
motion of a target sampled by a weather radar,
one might expect it to become
V
V r = f dop λ or f dop = ------r
λ
(3)
where Vr is the target's radial velocity, fdop is the
Doppler frequency shift due to target motion either
toward or away from the radar, and λ is the wavelength of the transmitted energy. For a stationary
target, there will be no wavelength or frequency
change (Figure 4).
For a moving target, the amount of frequency shift
due to motion toward or away from the radar will
be the same, except that the sign will be different
(Figure 5):
• shift is positive if the target is moving toward
the radar (along the positive x axis, λ has
decreased while fdop has increased)
3 - 18
The Doppler Effect (Objective 2)
Topic 3: Principles of Meteorological Doppler Radar
Figure 4.
A stationary target has no frequency shift.
• shift is negative if the target is moving away
from the radar (along the negative x axis, λ
has increased while fdop has decreased)
Figure 5.
A moving target has a frequency shift.
The Doppler Effect (Objective 2)
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Distance Learning Operations Course
However, equation (3) will not yield the true velocity of a target. In the case of meteorological Doppler radar, the equation is
– 2V
f dop = ------------r
λ
(4)
The physical explanation for doubling the frequency is due to two factors: (1) the target's electric vibrational frequency increases by an amount
equal to Vr/λ and (2) the frequency of the target's
radiation field in the direction of the radar receiver
is also increased by the amount Vr/λ (Doppler
Radar and Weather Observations, Doviak and
Zrnic, 1984). The negative sign is included to
account for target motion toward or away from the
radar (i.e. a negative Vr produces a positive fdop
and vice versa).
Since λ is constant for a given radar, equation (4)
illustrates the direct relationship between the Doppler frequency shift and the radial velocity.
Sound Wave Example The Doppler Effect is usually demonstrated using
sound waves. An example would be when an
emergency vehicle with its siren blaring is travelling toward you at a fairly high rate of speed. The
increase in the sound pitch (frequency) is due to
the compression (shorter wavelength) of the
waves. As the vehicle moves away from you, the
sound pitch (frequency) is decreased due to the
expansion (longer wavelength) of the waves.
The frequency of a typical sound wave is 1 X 104
Hz (10,000 Hz). In a case where the source is
moving at 50 knots toward or away from the
receiver, a Doppler frequency shift of ~800 Hz
would occur. That amount of frequency shift is
3 - 20
The Doppler Effect (Objective 2)
Topic 3: Principles of Meteorological Doppler Radar
~8% of the original transmitted frequency. This
can be easily measured, even by the human ear!
E-M waves transmitted by the WSR-88D are of a WSR-88D Pulse Example
much higher frequency than sound waves and
travel at the speed of light. For a Doppler radar
using a wavelength of ~10.5 cm, the transmission
frequency is ~2.85 X 109 Hz (2.85 billion Hz). A
target radial motion of 50 knots would produce a
Doppler frequency shift of 487 Hz which is only ~2
X 10-5% (.00002%) of the original transmitted frequency! This is too small a frequency shift to be
measured directly.
(Note: The Doppler frequency shift equations are
not the same for sound and E-M energy. The
medium through which waves travel is important
for sound but not for E-M energy. This is the reason for the different frequency shifts obtained in
the previous examples, even though the target
velocity was the same.)
The WSR-88D does not measure frequency shifts WSR-88D Velocity
directly to determine target radial velocity but Detection Method
instead uses the pulse-to-pulse phase change
between successive returned pulses which is easily and more accurately measured. This technique
is called “Pulse-Pair Processing”.
For any type of periodic motion, the phase of a
wave is “a point or 'stage' in the period to which the
motion has advanced with respect to a given initial
point” (Glossary of Meteorology). A complete wave
(Figure 6) consists of a 360° cycle. If a wave was
to intercept a target at a position equal to onefourth its wavelength, it would do so at a phase
angle of 90°. For the WSR-88D to be able to
extract Doppler motion from targets, the initial
phase information about each transmitted pulse is
The Doppler Effect (Objective 2)
3 - 21
Distance Learning Operations Course
known. The phase of each returned pulse is also
known and then compared to subsequent returned
pulses.
Figure 6.
Radar wave characteristics.
Coherency The WSR-88D is a coherent radar, which means
that phase information for each pulse is known.
The frequency of each transmitted pulse is constant and the phase is identical to that of an internal reference signal. When the pulse returns, a
comparison to this reference signal is used to
determine the phase. Any pulse to pulse phase
changes can then be computed, which are related
directly to target motion.
Phasors One way to graphically illustrate the concept of a
pulse-pair phase shift is to use phasors. A phasor
is a rotating vector used to represent an alternating current signal. Applied to the WSR-88D, a phasor represents the phase and amplitude (power) of
each returned pulse. The phase of each returned
pulse is the angle that the phasor sweeps out from
the positive x axis. A phasor represents a snapshot of the phase and amplitude of the returned
signal. In Figure 7, the phase for pulse 1 would be
30°.
3 - 22
The Doppler Effect (Objective 2)
Topic 3: Principles of Meteorological Doppler Radar
Figure 7.
Pulse 1 phasor with amplitude and phase.
As a target changes radial position between two Phasors for Two Pulses
successive pulses (Figure 8), the phase of the
returned signal will change from pulse to pulse.
This occurs because a moving target intercepts
each transmitted wave at a different phase position along the wave. The angle between the two
phasors is 90° and it is called the pulse pair phase
shift. For any pulse pair, the phase shift is some
portion of the wavelength (10 cm), so target
change in distance from pulse to pulse is known.
Since the time between pulses is also known,
each pulse-pair phase shift has an associated
velocity (distance divided by time!).
Figure 8.
Pulse 1 and Pulse 2 phasors with amplitude and phase.
The Doppler Effect (Objective 2)
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Distance Learning Operations Course
Phasors for two successive pulses represent two
snapshots of the returned signal. Assumptions
must be made about the target’s behavior between
pulses.
Frequency Shift vs. Phase Recall that Doppler frequency shifts are occurring
Shift as a result of a target’s radial motion, but are not
directly measured. Pulse-to-pulse phase shifts and
Doppler frequency shifts are both dependent on a
target’s radial motion. Doppler frequency shifts are
inherent within the pulse-to-pulse phase shifts
since the time rate of phase change equals fdop.
Since the time between pulses is constant for a
given range bin, there is a direct (linear) relationship between the amount of phase shift from pulse
to pulse and the target’s radial velocity.
Figure 9.
Two possible angles between the two phasors.
For any particular pulse pair, there are two possible angles between the individual pulse phasors
(Figure 9). The angle <180° is the one that is
always used. The next objective will explain why
this is the case.
WSR-88D Radial
Speed
Computation
(Objective 3)
3 - 24
The speed the WSR-88D will initially assign to a
range bin is directly related to the amount of
phase shift between successive returned pulses.
However, there is a maximum amount of phase
shift, 180°, that the WSR-88D can measure from
WSR-88D Radial Speed Computation (Objective 3)
Topic 3: Principles of Meteorological Doppler Radar
one pulse to the next. If a target moves too far
between pulses such that its true phase shift
exceeds 180°, an apparent phase shift of less than
180° would still be assigned. A true phase shift of
≥180° introduces ambiguity (Figure 10).
Figure 10. A phase shift of ≥ 180° introduces ambiguity.
The radial velocity that is initially assigned is
based on a pulse pair phase shift of <180°. If the
true pulse pair phase shift is <180°, the first guess
velocity will be correct.
Since 180° is the maximum phase shift that the Maximum Unambiguous
WSR-88D can recognize, there is then a maxi- Velocity
mum velocity that the radar can measure unambiguously. It is the maximum unambiguous
velocity, Vmax, and it corresponds to a maximum
pulse-pair phase shift of 180°.
The process of determining target speed is relatively simple once the phase angles of two successive returned pulses have been determined.
1. The phase of the first returned pulse and the
phase of the second returned pulse are
obtained and the difference (pulse-pair phase
shift) is computed.
WSR-88D Radial Speed Computation (Objective 3)
3 - 25
Distance Learning Operations Course
2. The pulse-pair phase shift is then compared to
the maximum measurable phase shift of 180°
and the phase shift percentage is then multiplied by Vmax.
Phase Shift-Radial Speed This is simply the ratio
Relationship
Vr
P.S.
------------ = ----------------V max
180°
(5)
where P.S. is the amount of pulse-pair phase shift,
|Vr| is the target radial speed, and |Vmax| is the
maximum unambiguous speed (magnitude of
Vmax). For any given Vmax, target speed is directly
related to the amount of pulse-pair phase shift that
occurs.
Phase Shift Depiction The angle between two phasors represents the
Using Phasors pulse pair phase shift and, hence, the target's
speed. Given the limit of using phase shifts less
than 180°, the WSR-88D always uses the smaller
angle between the two phasors to determine the
pulse pair phase shift.
Figure 11. Phasors are used to identify the pulse-pair phase shift.
Example In Figure 11, the phase for pulse 1, α1, is 30°, and
the phase for pulse 2, α2, is 120°. The pulse-pair
phase shift is then 90° (one half of 180°). If Vmax is
60 knots, the target's speed will be 30 knots (one
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WSR-88D Radial Speed Computation (Objective 3)
Topic 3: Principles of Meteorological Doppler Radar
half of 60 kts). This answer is obtained by using
equation (5), P.S. = 90°, and |Vmax| = 60 kts such
that
90°/180° = |Vr| / 60 kts
1/2 = |Vr| / 60 kts
60 kt (.5) = |Vr| = 30 kts
Notice that in this example, we have only obtained
the target's speed, not its direction of motion
(inbound or outbound). Also, if Vmax had been 40
knots instead of 60 knots, the same amount of
pulse-pair phase shift would have produced a
lesser target speed of 20 knots. Therefore, there
is no unique target speed for every pulse-pair
phase shift due to its dependence on Vmax.
Phase Shift and
Unambiguous Velocity
If the actual pulse-pair phase shift is less than Pulse-Pair Phase Shift
180° (Figure 12), then the target speed and direc- Less Than 180°
tion can be unambiguously measured and the
“first guess” velocity measurement is correct.
Figure 12. Phase shift of < 180°.
If the actual pulse-pair phase shift is equal to 180° Pulse-Pair Phase Shift
(Figure 13), then the speed will be correct and Equal to 180°
WSR-88D Radial Speed Computation (Objective 3)
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Distance Learning Operations Course
equal to Vmax, but the target's direction (inbound
or outbound) will be unknown.
Figure 13. Phase shift of 180°. The speed is correct but the direction unknown.
Pulse-Pair Phase Shift If the actual pulse-pair phase shift is greater than
Greater Than 180° 180° (Figure 14), velocity detection is ambiguous.
By using the smaller of the two angles between
phasors, the radar will assign an improper velocity
(both speed and direction) to the target. Each Vmax
defines an interval of first guess velocities. For
example, if Vmax = 50 kts, the first guess velocities
will range from -50 kts to +50 kts. Though this first
guess velocity measurement will be incorrect,
there are other possible velocities, sometimes
called “aliases”.
Figure 14. Phase shift of > 180°. First guess speed and direction are incorrect.
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WSR-88D Radial Speed Computation (Objective 3)
Topic 3: Principles of Meteorological Doppler Radar
If no pulse-pair phase shift is measured (0°, 360°, Pulse-Pair Phase Shift of
etc.), then the target is stationary or, in most 0°, 360°, etc.
cases, moving perpendicular to the radar beam.
When the true radial velocity equals or exceeds High PRFs Needed for
Vmax, the radar's first guess velocity will be incor- Velocity
rect. Each first guess velocity has a group of meteorologically plausible aliases, which are used by
the Velocity Dealiasing Algorithm (discussed in
Topic 3 Lesson 5). To reduce the likelihood of an
incorrect first guess velocity, a target should be
sampled frequently so that the target location does
not change much between successive pulses.
Therefore, the best velocity estimates are
obtained by using high PRFs.
Determine the first guess radial speed given the Examples
Vmax and the pulse-pair phase shift.
#1: Vmax = 60 kts, Phase Shift = 90°
#2: Vmax = 60 kts, Phase Shift = 45°
#3: Vmax = 60 kts, Phase Shift = 30°
WSR-88D Radial Speed Computation (Objective 3)
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Distance Learning Operations Course
Obtaining I and Q
Values
(Objective 4)
Recall that Doppler frequency changes are not
measured by the WSR-88D system. Instead,
mean radial velocity is determined from the average rate of change of phase between a series of
pulse pairs. The amount of pulse-pair phase shift
is caused by a change in target position from pulse
to pulse.
I and Q Components A target detected by a single pulse will return a
signal represented by the phasor in Figure 15.
Since a phasor is a vector, it has both magnitude
(amplitude) and direction (phase angle) and has
components in the x and y directions. Concerning
WSR-88D signal processing, the component of a
phasor in the x direction is called the In-Phase
component (or I component) and the component in
the y direction is called the Quadrature component
(or Q-component).
Figure 15. A phasor and its components.
The I and Q components contain all the necessary
information to generate the base reflectivity, radial
velocity, and spectrum width data. The amplitude
of the signal, which is ultimately reflectivity, is computed from the I and Q values. Pulse pair phase
shifts are also computed from the I and Q values,
which are then used to generate radial velocity
and spectrum width.
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Obtaining I and Q Values (Objective 4)
Topic 3: Principles of Meteorological Doppler Radar
Voltage
The I component (In-Phase) is essentially the
returned raw signal. The Q component is the
returned raw signal that has been phase shifted
+90° (hence, the term Quadrature or 1/4th of 360°)
by the WSR-88D signal processor. See Figure 16.
Figure 16. Example of the relationship between I and Q values.
The I and Q values together provide both target Both I and Q Values
speed and direction. This is illustrated in Figure 17 Needed
where the I and Q components are known for
pulse 1 (I1 = 5 and Q1 = 2). For pulse 2, only the I
information is shown. The Q component would be
necessary to determine if the pulse 2 phasor lies in
the 2nd or 3rd quadrant (inbound or outbound
motion), as well as the pulse 2 amplitude.
Once the I and Q values for two successive Determining Target
returned pulses have been determined, the Direction
respective phasors can be plotted. The rotation
from Phasor #1 to Phasor #2 determines the
direction of the target’s radial motion.
Figure 18 illustrates the result of the two possible
rotations. When trying to find the resultant vector
Obtaining I and Q Values (Objective 4)
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Distance Learning Operations Course
Figure 17. With only the I component, the pulse 2 phasor angle and magnitude is unknown.
Figure 18. Phasor rotation and target direction.
from the cross-product of two vectors, we can use
the “right hand thumb rule” to determine whether
target motion is inbound or outbound. Place your
right hand along phasor #1 such that the fingers
point in the same direction as the phasor. From
this position, curl your fingers toward phasor #2. In
order to do this, your thumb will be pointing either
toward you or away from you. If your thumb points
away from you, then the apparent target motion is
outbound from the radar. If your thumb points
toward you, then the apparent target motion is
inbound to the radar.
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Obtaining I and Q Values (Objective 4)
Topic 3: Principles of Meteorological Doppler Radar
Another way of remembering the relationship
between phasor rotation and apparent target
motion is:
• counterclockwise rotation means target
motion is toward the radar and is denoted by
a negative velocity
• clockwise rotation means target motion is
away from the radar and is denoted by a positive velocity
Figure 19. The phasor rotation from pulse 1 to pulse 2 is counterclockwise, thus target
motion is toward the radar.
Figure 19 shows the phasors used to demonstrate
a pulse-pair phase shift. Note that the phase shift
from pulse 1 to pulse 2 sweeps out an angle in the
counterclockwise direction. Thus the target is moving toward the radar, and the velocity will be
denoted by a negative sign.
Note: Objective 4 only requires that you be able to
determine target direction (inbound or outbound)
and not speed from the plotting of phasors.
Obtaining I and Q Values (Objective 4)
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Distance Learning Operations Course
Calculations Using
Phasors
Example #1 Given:
Vmax = 60 KT (180° Phase Shift)
Phasor #1: I1 = +4 AND Q1 = +4
Phasor #2: I2 = -4 AND Q2 = 0
Q
I
The pulse-pair phase shift from #1 to #2 is _____o
and phasor rotation is (clockwise / counterclockwise) indicating that the apparent target motion is
(inbound to / outbound from) the radar at _____
knots. The first guess velocity would be _____.
Example #2 Given:
Vmax = 60 KT (180° Phase Shift)
Phasor #1: I1 = +4 AND Q1 = -4
Phasor #2: I2 = -4 AND Q2 = 0
Q
I
The pulse-pair phase shift from #1 to #2 is _____o
and phasor rotation is (clockwise / counterclockwise) indicating that the apparent target motion is
3 - 34
Obtaining I and Q Values (Objective 4)
Topic 3: Principles of Meteorological Doppler Radar
(inbound to / outbound from) the radar at _____
knots. The first guess velocity would be ______.
Recall that the WSR-88D always assumes the Actual Phase Shift
phase shift due to target motion is the smaller Exceeds 180°
angle between phasors #1 and #2. What happens
when the actual phase shift is greater than 180°?
The apparent, or first guess, target motion will be
incorrect. The radial speed will be less than what it
actually is and the target direction will be opposite
the true direction.
Figure 20. When the actual phase shift exceeds 180°, the WSR-88D will still use an angle
smaller than 180° to compute a first guess velocity.
Calculations Using
Phasors
Given:
Example #3:
Vmax = 60 KT (180° Phase Shift)
Phasor #1: I1 = +4 AND Q1 = 0
Phasor #2: I2 = 0 AND Q2 = -4
Obtaining I and Q Values (Objective 4)
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Distance Learning Operations Course
Actual pulse-pair phase shift is 270° and phasor rotation is CCW
Q
I
The actual target motion is (inbound to / outbound
from) the radar at ____ knots. However, the
WSR-88D's first guess at target motion will
assume a phase shift of ______o and phasor rotation that is (clockwise/counterclockwise) indicating that the apparent target motion is (toward/away
from) the radar at ______ knots.
Table 20-1 depicts the relationship between true
velocities, first guess and aliased velocities. All of
these values are based on a Vmax = 60 kts. Thus
-60 kts to +60 kts defines the interval of first guess
velocities. When the true velocities fall within this
interval, the first guess velocity is correct.
A first guess velocity of +30 kts may be the correct
radial velocity or may be associated with a true
velocity of -90 kts. For a first guess velocity of +30
kts, the Velocity Dealiasing Algorithm (discussed
in Topic 3, Lesson 5) compares +30 kts, -90 kts
and other possible velocities to surrounding values. This is to determine if the first guess (+30 kts)
or one of its aliases (-90 kts) is appropriate for that
range bin.
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Obtaining I and Q Values (Objective 4)
Topic 3: Principles of Meteorological Doppler Radar
Table 20-1: True Radial Velocities vs. First Guess
and Aliased Velocities
First Guess (colored) and
Aliased Velocities (kts)
True Radial Velocities
(kts)
+15
-105
+30
-90
+45
-75
-60
-60
-45
-45
-30
-30
-15
-15
0
0
+15
+15
+30
+30
+45
+45
+60
+60
-45
+75
-30
+90
-15
+105
• The WSR-88D always uses phase shifts are Key Points
< 180°.
• Actual phase shifts ≥ 180° will result in first
guess velocities that are incorrect or ambiguous.
• Vmax defines an interval for first guess velocities. For the example of Vmax = 60 kts, all first
guess velocities will be from -60 kts to +60 kts.
• For every first guess velocity, there is a set of
meteorologically plausible velocities, or
aliases.
Obtaining I and Q Values (Objective 4)
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Distance Learning Operations Course
Signal Processing 1. The WSR-88D is a "coherent" system. What does
this mean?
Review Exercises
2. The Doppler Effect is defined as the change in frequency with which energy reaches a receiver when
the receiver and energy source are in motion relative
to each other.
a. Does the WSR-88D directly measure a frequency
shift? Why or why not?
b. What other characteristic of wave energy changes
due to target motion? Can the WSR-88D measure
this?
3. A target is moving due south at 40 knots. It is situated 20 nm to the west-southwest of the RDA
(240°/20 nm). What velocity will the radar detect?
4. For a given range bin, compute the speed the WSR88D will initially assign if:
a. Vmax = 40 knots, pulse pair phase shift is 45°.
b. Vmax = 60 knots, pulse pair phase shift is 135°.
c. Vmax = 60 knots, pulse pair phase shift is 225°.
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Obtaining I and Q Values (Objective 4)
Topic 3: Principles of Meteorological Doppler Radar
5. Select the degree of phase shift such that a smaller
shift is unambiguous and an equal or greater shift is
ambiguous.
a. 90°
b. 180°
c. 270°
d. 360°
6. If Vmax = 40 knots, identify a set of possible radial
velocities (knots) if the pulse pair phase shift is 90°
counter-clockwise. Hint: Use a technique similar to
the one you used in 4c above.
a. -20, -100, +60, +140
b. -20, -60, +20, +60
c. -10, -50, +30, +70
d. -10, -90, +70, +150
7. If I = 3 and Q = 3, graphically generate a phasor and
identify its amplitude and phase (relative to the positive x axis.)
8. In a range bin, assume I = 3 and Q = 3 from the first
pulse, while I = 0 and Q = 5 from the second pulse. If
the radar's first guess is correct, is the mean target
motion toward or away from the radar?
Obtaining I and Q Values (Objective 4)
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