Topic 3: Principles of Meteorological Doppler Radar 3 - 9 Topic 3: Principles of Meteorological...

Distance Learning Operations Course

Topic 3: Principles of Meteorological Doppler Radar

Presented by the

Warning Decision Training Branch

Version: 0609


This page intentionally left blank.

On purpose.Except for the header.

Oh, and the page number.But otherwise, it’s supposed to be blank.

So don’t worry.

3 - 2




Table of Contents

Topic 3, Lesson 1: WSR-88D Fundamentals ........................................... 3 - 7WSR-88D Fundamentals (self guided web module) ...........................................3 - 8Objectives...............................................................................................................3 - 8

Topic 3, Lesson 2: Signal Processing.................................................... 3 - 11Signal Processing (instructor guided web module).........................................3 - 12Objectives.............................................................................................................3 - 12Radial Velocity (Objective 1)...............................................................................3 - 12

Key Points About Radial Velocity ...................................................................................... 3 - 13Radial Speed Equation...................................................................................................... 3 - 13Examples........................................................................................................................... 3 - 16.......................................................................................................................................... 3 - 17

The Doppler Effect (Objective 2) ........................................................................3 - 17Sound Wave Example ....................................................................................................... 3 - 20WSR-88D Pulse Example ................................................................................................. 3 - 21WSR-88D Velocity Detection Method................................................................................ 3 - 21Phasors ............................................................................................................................. 3 - 22Phasors for Two Pulses..................................................................................................... 3 - 23

WSR-88D Radial Speed Computation (Objective 3) .........................................3 - 24Maximum Unambiguous Velocity ..................................................................................... 3 - 25Phase Shift-Radial Speed Relationship............................................................................. 3 - 26Phase Shift Depiction Using Phasors................................................................................ 3 - 26Phase Shift and Unambiguous Velocity............................................................................. 3 - 27

Obtaining I and Q Values (Objective 4).............................................................3 - 30I and Q Components ......................................................................................................... 3 - 30Both I and Q Values Needed ............................................................................................. 3 - 31Determining Target Direction............................................................................................. 3 - 31Calculations Using Phasors .............................................................................................. 3 - 34Actual Phase Shift Exceeds 180° ................................................................................................3 − 35Calculations Using Phasors .............................................................................................. 3 - 35Key Points ......................................................................................................................... 3 - 37Signal Processing Review Exercises ................................................................................ 3 - 38

Topic 3, Lesson 3: Base Data Generation.............................................. 3 - 41Base Data Generation (instructor guided web module)...................................3 - 42Objectives.............................................................................................................3 - 42Base Data Estimation Considerations (Objective 1) ........................................3 - 42

Base Reflectivity Data ....................................................................................................... 3 - 42Base Mean Radial Velocity Data ....................................................................................... 3 - 43Base Spectrum Width Data ............................................................................................... 3 - 45

Spectrum Width - Meteorological Factors (Objective 2) .................................3 - 47

Table of Contents 3 - 3


Spectrum Width - Nonmeteorological Factors (Objective 3) ..........................3 - 49Base Data Generation Review Exercises.......................................................................... 3 - 50

Topic 3, Lesson 4: Clutter Suppression................................................. 3 - 53Clutter Suppression (instructor guided web module)......................................3 - 54

A Note on Terminology ...................................................................................................... 3 - 54Objectives.............................................................................................................3 - 54Clutter Contamination on Base Products (Objective 1) ...................................3 - 54

Ground Clutter Contamination General Characteristics .................................................... 3 - 55Reflectivity Products .......................................................................................................... 3 - 55Mean Radial Velocity Products.......................................................................................... 3 - 56Spectrum Width Products .................................................................................................. 3 - 57

Anomalous Propagation (AP) on Base Products (Objective 1).......................3 - 58AP Clutter General Characteristics ................................................................................... 3 - 58Reflectivity Products .......................................................................................................... 3 - 59Mean Radial Velocity Products.......................................................................................... 3 - 60Spectrum Width Products .................................................................................................. 3 - 60

Clutter Suppression Technique: GMAP.............................................................3 - 61Reference.......................................................................................................................... 3 - 61Clutter vs. Meteorological Signal ....................................................................................... 3 - 62GMAP Performance Examples ......................................................................................... 3 - 63

Application of Ground Clutter Suppression ....................................................3 - 69Filtering of Normal vs. Transient Clutter ............................................................................ 3 - 69Clutter Filter Bypass Map(s) .............................................................................................. 3 - 69Bypass Map Generation Process ...................................................................................... 3 - 70Clutter Suppression Regions Files .................................................................................... 3 - 73Clutter Regions Window.................................................................................................... 3 - 74Clutter Regions Window.................................................................................................... 3 - 76Editing/Creating Clutter Regions ....................................................................................... 3 - 78Clutter Filter Control (CFC) Product .................................................................................. 3 - 80Examples of Data With and Without Proper Clutter Filtering............................................. 3 - 83Negative Effects When All Bins Inappropriately Applied ................................................... 3 - 86Ground Clutter Suppression Limitations (Objective 3) ...................................................... 3 - 92Appropriate Ground Clutter Suppression Strengths (Objective 3)..................................... 3 - 93Clutter Suppression Review Exercises.............................................................................. 3 - 94

Topic 3, Lesson 5: Mitigation of Data Ambiguities ............................... 3 - 97Mitigation of Data Ambiguities (teletraining) ....................................................3 - 98Objectives.............................................................................................................3 - 98PRF effects on Rmax and Vmax (Objective 1) .....................................................3 - 99

Rmax Definition .................................................................................................................. 3 - 99Vmax Definition................................................................................................................... 3 - 99Key Points ......................................................................................................................... 3 - 99“Doppler Dilemma” .......................................................................................................... 3 - 100

3 - 4 Table of Contents


Data Recognition and Algorithms (Objectives 2 & 3).....................................3 - 101Range Folding....................................................................................................3 - 101

Often on Velocity and Spectrum Width Products............................................................. 3 - 102Rarely on Reflectivity Products........................................................................................ 3 - 102

Range Unfolding Algorithm..............................................................................3 - 104Non-overlaid Echoes Case.............................................................................................. 3 - 105Overlaid Echoes Case......................................................................................................3 - 110The Effects of TOVER ......................................................................................................3 - 113Range Unfolding Algorithm ..............................................................................................3 - 114Strengths ..........................................................................................................................3 - 114Limitations ........................................................................................................................3 - 114

Improperly Dealiased Velocities....................................................................... 3 - 115Velocity Dealiasing Algorithm .......................................................................... 3 - 119

Step 1: Radial Continuity Check...................................................................................... 3 - 120Step 2: Nine Point Average ............................................................................................. 3 - 121Step 3: Expanded Search................................................................................................ 3 - 122Step 4: Environmental Winds .......................................................................................... 3 - 122Error Checks ................................................................................................................... 3 - 124Velocity Dealiasing Algorithm .......................................................................................... 3 - 124Strengths ......................................................................................................................... 3 - 124Limitations ....................................................................................................................... 3 - 125Operational Considerations............................................................................................. 3 - 125

Multiple PRF Dealiasing Algorithm (MPDA) ....................................................3 - 126MPDA is an RPG-based Solution.................................................................................... 3 - 126Applying MPDA ............................................................................................................... 3 - 126VCP 121 Considerations ................................................................................................. 3 - 129MPDA Processing for a Single Range Bin ...................................................................... 3 - 130MPDA Adaptable Parameters ......................................................................................... 3 - 132Strengths of MPDA.......................................................................................................... 3 - 133Limitations of MPDA........................................................................................................ 3 - 133

Minimizing Range Folding (Objective 4)..........................................................3 - 134Minimizing Range Folding ............................................................................................... 3 - 134MPDA (VCP 121) and Auto PRF..................................................................................... 3 - 137Mitigation of Data Ambiguities Review Exercises............................................................ 3 - 139

Topic 3, Lesson 6: Precipitation Estimation........................................ 3 - 143Precipitation Estimation (instructor guided web module).............................3 - 144Objectives...........................................................................................................3 - 144Reflectivity, Z and Rainfall Rate, R (Objective 1) ............................................3 - 144

Reflectivity - Z.................................................................................................................. 3 - 144Sample Z computation..................................................................................................... 3 - 145Rainfall Rate - R .............................................................................................................. 3 - 146Sample R computation .................................................................................................... 3 - 147Same Z, Different R......................................................................................................... 3 - 147Same R, Different Z......................................................................................................... 3 - 148

Table of Contents 3 - 5


Interim Summary ............................................................................................................. 3 - 148WSR-88D Z-R Relationships........................................................................................... 3 - 149

Error Sources in Radar Estimated Rainfall (Objective 2)...............................3 - 150Types of errors ................................................................................................................ 3 - 150Z estimate errors ............................................................................................................. 3 - 150Z-R relationship errors..................................................................................................... 3 - 152Below beam effect errors................................................................................................. 3 - 153

Radar Estimates vs. Rain Gages (Objective 3) ...............................................3 - 154Scenarios ........................................................................................................................ 3 - 154Scenario 1 ....................................................................................................................... 3 - 155Scenario 2 ....................................................................................................................... 3 - 155Scenario 3 ....................................................................................................................... 3 - 156

Precipitation Processing Subsystem (PPS) (Objective 4) .............................3 - 156Overview ......................................................................................................................... 3 - 157Enhanced Precipitation Preprocessing (EPRE) .............................................................. 3 - 158Precipitation Rate Algorithm............................................................................................ 3 - 167Precipitation Accumulation Algorithm.............................................................................. 3 - 168Precipitation Adjustment Algorithm.................................................................................. 3 - 171Summary ......................................................................................................................... 3 - 174Precipitation Processing Subsystem - Strengths............................................................. 3 - 174Precipitation Processing Subsystem - Limitations........................................................... 3 - 174

Snow Accumulation Algorithm (SAA) (Objective 5).......................................3 - 175References ...................................................................................................................... 3 - 175SAA Design ..................................................................................................................... 3 - 175Begin and End of Snowfall Accumulations...................................................................... 3 - 176Reset (Begin) the Snow Accumulations .......................................................................... 3 - 177Converting Reflectivity to the Rate of Snow Water Equivalent ........................................ 3 - 177Range/Height Correction................................................................................................. 3 - 179Snow Ratio ...................................................................................................................... 3 - 180SAA Adaptable Parameters............................................................................................. 3 - 180SAA Products .................................................................................................................. 3 - 181

Snow Accumulation Algorithm - Strengths (Objective 5).............................3 - 182Snow Accumulation Algorithm - Limitations (Objective 5) ..........................3 - 182

Precipitation Estimation Review Exercises...................................................................... 3 - 182Review Exercises Answer Key.........................................................................3 - 185

Signal Processing............................................................................................................ 3 - 185Base Data Generation ..................................................................................................... 3 - 188Clutter Suppression......................................................................................................... 3 - 189Mitigation of Data Ambiguities ......................................................................................... 3 - 190 Precipitation Estimation .................................................................................................. 3 - 193

3 - 6 Table of Contents


Topic 3, Lesson 1: WSR-88D Fundamentals

Presented by the

Warning Decision Training BranchDistance Learning Operations Course


Version: 0609


WSR-88DFundamentals (self

guided webmodule)

This lesson will present information that is funda-mental to weather radars in general, such as beampropagation and the Probert-Jones radar equa-tion. It will also present information that is veryspecific to the WSR-88D, such as the characteris-tics 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. Theremaining web modules, Lessons 2, 3, 4, and 6,are instructor guided, a sequence of annotatedslides with accompanying audio for each slide.Lesson 1 has no audio, and it is designed as muchfor 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 1will vary depending on your experience with theWSR-88D. The average completion time is esti-mated to be 2 hours.

Objectives 1. Identify the range resolutions and correspond-ing display ranges for Base Reflectivity, BaseVelocity, and Base Spectrum Width.

2. Given dBZ values along a radial at .54 nm reso-lution, identify which dBZ values would be usedto build lower resolution Base Reflectivity prod-ucts.

3. Given Base Velocity and Spectrum Width val-ues along a radial at .13 nm resolution, identifywhich Base Velocity and Spectrum Width val-

3 - 8 WSR-88D Fundamentals (self guided web module)


ues would be used to build lower resolutionBase Velocity and Spectrum Width products.

4. Given Rmax and the actual target range, R,identify other ranges at which an echo from atarget could appear.

5. Identify the two situations where sidelobe con-tamination is likely to occur.

6. Identify meteorological conditions conducive tosuperrefraction and subrefraction of the radarbeam, and the resultant operational impacts.

Objectives 3 - 9


3 - 10 Objectives


Topic 3, Lesson 2: Signal Processing

Presented by the

Warning Decision Training BranchDistance Learning Operations Course


Version: 0609


Signal Processing(instructor guided

web module)

The WSR-88D provides three types of base data,Reflectivity, Velocity and Spectrum Width. Asthese data are the input for the generation of allradar products, it is important that the base databe of the highest possible quality. There are dataquality issues inherent in meteorological Dopplerweather radars. Proper interpretation of the WSR-88D products requires an understanding of dataquality, and this section lays the necessary foun-dation for this understanding.

Objectives 1. Compute the radial velocity of a target given theradar viewing angle, actual target velocity, andthe appropriate equation.

2. Identify how Doppler information is obtained bythe WSR-88D to determine atmosphericmotion.

3. Compute the speed a radar initially assigns arange bin, given a pulse-pair phase shift and amaximum unambiguous velocity (Vmax).

4. Determine whether apparent target motion istoward or away from the radar, given I and Qvalues from two successive returned pulses.

Radial Velocity(Objective 1)

Radial velocity (Vr) is defined as the componentof target motion parallel to the radar radial (azi-muth). It is that component of a target's actualvelocity (V) that is either toward or away from theradar site along the radial.

3 - 12 Signal Processing (instructor guided web module)


Key Points About Radial Velocity

Some important principles to remember aboutDoppler radial velocity are:

1. Radial velocities will always be less than orequal to actual target velocities.

2. Radial velocity equals actual velocity onlywhere target motion is directly toward or awayfrom the radar.

3. Zero velocity is measured where target motionis perpendicular to a radial or where the targetis stationary.

The Relation of Actual Velocity to Radial Velocity

When sampling large-scale atmospheric flow,most of what is depicted will be less than theactual environmental flow. The same holds trueeven for storm-scale rotational flows since onlythat component of a circulation either directlytoward or away from the radar will have its actualvelocity detected.

Radial Speed EquationThe relationship between a target's actual velocityand the WSR-88D depicted radial velocity can bedescribed mathematically by using the RadialSpeed Equation

(1)

where:• Vr = radial velocity• V = actual velocity• β = smaller angle between V

and the radar radial• cos = cosine

The Angle βThe angle β (beta) is always the smaller of thetwo angles between the radar viewing angle (i.e.radar radial or azimuth) and the actual targetvelocity vector (V).

Vr V βcos⋅=

Radial Velocity (Objective 1) 3 - 13


β is Equal to 0° When β is equal to 0°, target motion is parallel tothe radar beam and cos β is 1. The target radialspeed (|Vr|) is equal to the actual target speed(|V|).

β is Equal to 90° When β is equal to 90°, target motion is perpendic-ular to the radar beam and cos β is zero. Theradial speed (|Vr|) is zero, and there is no compo-nent of target motion toward or away from theradar.

Radial Speed ComputationExample

Assume that the actual wind is uniform from adirection of 300° at 30 knots through the loweratmosphere (Figure 2).

As the antenna is pointed due west (along the270° radial), a radial wind speed of 26 knots wouldbe measured. This answer is obtained by usingequation (1) and β= 30°.

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.

Figure 2. Radial speed computation example.

3 - 14 Radial Velocity (Objective 1)


| Vr | = | V | cos β| Vr | = (30 kt) cos (30°)| Vr | = (30 kt) (.866)| Vr | = 25.98 kt ≈ 26 kt

Target DirectionOnce the speed is calculated from equation (1),the direction, inbound or outbound, must be deter-mined. This is simply the direction of the compo-nent of the actual wind that lies along the radial. InFigure 2, the radial component, Vr, would beinbound toward the RDA. Thus the radial velocityis -26 knots.

Figure 3 shows how equation (1) comes from trig-onometry, where the actual wind vector and thecomponents along and perpendicular to the radarradial form a right triangle. Also in Figure 3, theactual wind is southerly over the display. A radarazimuth has been selected in each quadrant andthe actual wind vector has been decomposed intocomponents along and perpendicular to the radial.Although the magnitudes differ, note that the radialvelocities in the two southern quadrants areinbound and in the two northern quadrants are out-bound.

Figure 3. Determining the direction of the radial component of the actual velocity.

Radial Velocity (Objective 1) 3 - 15


Relationship Between βand Percentage of Actual

Velocity

The greater the angle between the target's veloc-ity vector and the radar azimuth, the smaller thepercentage of the target's actual velocity that willbe measured and depicted on the velocity prod-ucts. Table 3 shows the relationship between βand the percentage of actual target speed that isdirectly measured. The relationship between theactual speed and the radial speed is based on thecosine function. Therefore it is not a linear relation-ship. For example, a β of 45° (halfway between 0°and 90°) results in a radial speed that is about70% of the actual speed, not 50%

Examples In each of the following examples, draw the radarazimuth and the actual velocity vector. Then drawthe components of the velocity parallel to and per-pendicular to the radar radial. Determine β anduse Equation (1) to calculate the radial speed.

Table 3: Percentage of Target Speed Measuredβ

degreesCosine

βPercent

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

3 - 16 Radial Velocity (Objective 1)


1. V = 40 kts from 270°, radar azimuth is 315°.



The Doppler Effect (Objective 2)

The Doppler Effect is defined as “the change infrequency with which energy reaches a receiverwhen the receiver and the energy source are inmotion relative to each other” (from the Glossaryof Meteorology). Determining the Doppler Effect orshift is straightforward when the energy transmis-sion source is stationary and the target being sam-pled is moving (or stationary). Any frequency shifts

The Doppler Effect (Objective 2) 3 - 17


would be solely the result of the target movingtoward or away from the energy transmissionsource.

From basic physics, there is a relationshipbetween the speed of transmitted electromagnetic(E-M) energy and the frequency and wavelengthof that energy. This relationship is expressed as

(2)

where c is the speed of light (assumed to be con-stant), f is the frequency and λ is the wavelengthof 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 Dopplermotion of a target sampled by a weather radar,one might expect it to become

or (3)

where Vr is the target's radial velocity, fdop is theDoppler frequency shift due to target motion eithertoward or away from the radar, and λ is the wave-length of the transmitted energy. For a stationarytarget, there will be no wavelength or frequencychange (Figure 4).

For a moving target, the amount of frequency shiftdue to motion toward or away from the radar willbe the same, except that the sign will be different(Figure 5):

• shift is positive if the target is moving towardthe radar (along the positive x axis, λ hasdecreased while fdop has increased)

c fλ=

Vr fdopλ= fdopVrλ------=

3 - 18 The Doppler Effect (Objective 2)


• shift is negative if the target is moving awayfrom the radar (along the negative x axis, λhas increased while fdop has decreased)

Figure 4. A stationary target has no frequency shift.

Figure 5. A moving target has a frequency shift.



However, equation (3) will not yield the true veloc-ity of a target. In the case of meteorological Dop-pler radar, the equation is

(4)

The physical explanation for doubling the fre-quency is due to two factors: (1) the target's elec-tric vibrational frequency increases by an amountequal to Vr/λ and (2) the frequency of the target'sradiation field in the direction of the radar receiveris also increased by the amount Vr/λ (DopplerRadar and Weather Observations, Doviak andZrnic, 1984). The negative sign is included toaccount for target motion toward or away from theradar (i.e. a negative Vr produces a positive fdopand vice versa).

Since λ is constant for a given radar, equation (4)illustrates the direct relationship between the Dop-pler frequency shift and the radial velocity.

Sound Wave Example The Doppler Effect is usually demonstrated usingsound waves. An example would be when anemergency vehicle with its siren blaring is travel-ling toward you at a fairly high rate of speed. Theincrease in the sound pitch (frequency) is due tothe compression (shorter wavelength) of thewaves. As the vehicle moves away from you, thesound pitch (frequency) is decreased due to theexpansion (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 ismoving at 50 knots toward or away from thereceiver, a Doppler frequency shift of ~800 Hzwould occur. That amount of frequency shift is

fdop2Vr–λ

------------=



~8% of the original transmitted frequency. Thiscan be easily measured, even by the human ear!

WSR-88D Pulse ExampleE-M waves transmitted by the WSR-88D are of amuch higher frequency than sound waves andtravel at the speed of light. For a Doppler radarusing a wavelength of ~10.5 cm, the transmissionfrequency is ~2.85 X 109 Hz (2.85 billion Hz). Atarget radial motion of 50 knots would produce aDoppler frequency shift of 487 Hz which is only ~2X 10-5% (.00002%) of the original transmitted fre-quency! This is too small a frequency shift to bemeasured directly.

(Note: The Doppler frequency shift equations arenot the same for sound and E-M energy. Themedium through which waves travel is importantfor sound but not for E-M energy. This is the rea-son for the different frequency shifts obtained inthe previous examples, even though the targetvelocity was the same.)

WSR-88D Velocity Detection Method

The WSR-88D does not measure frequency shiftsdirectly to determine target radial velocity butinstead uses the pulse-to-pulse phase changebetween successive returned pulses which is eas-ily and more accurately measured. This techniqueis called “Pulse-Pair Processing”.

For any type of periodic motion, the phase of awave is “a point or 'stage' in the period to which themotion has advanced with respect to a given initialpoint” (Glossary of Meteorology). A complete wave(Figure 6) consists of a 360° cycle. If a wave wasto intercept a target at a position equal to one-fourth its wavelength, it would do so at a phaseangle of 90°. For the WSR-88D to be able toextract Doppler motion from targets, the initialphase information about each transmitted pulse is



known. The phase of each returned pulse is alsoknown and then compared to subsequent returnedpulses.

Coherency The WSR-88D is a coherent radar, which meansthat phase information for each pulse is known.The frequency of each transmitted pulse is con-stant and the phase is identical to that of an inter-nal reference signal. When the pulse returns, acomparison to this reference signal is used todetermine the phase. Any pulse to pulse phasechanges can then be computed, which are relateddirectly to target motion.

Phasors One way to graphically illustrate the concept of apulse-pair phase shift is to use phasors. A phasoris a rotating vector used to represent an alternat-ing current signal. Applied to the WSR-88D, a pha-sor represents the phase and amplitude (power) ofeach returned pulse. The phase of each returnedpulse is the angle that the phasor sweeps out fromthe positive x axis. A phasor represents a snap-shot of the phase and amplitude of the returnedsignal. In Figure 7, the phase for pulse 1 would be30°.

Figure 6. Radar wave characteristics.



Phasors for Two PulsesAs a target changes radial position between twosuccessive pulses (Figure 8), the phase of thereturned signal will change from pulse to pulse.This occurs because a moving target interceptseach transmitted wave at a different phase posi-tion along the wave. The angle between the twophasors is 90° and it is called the pulse pair phaseshift. For any pulse pair, the phase shift is someportion of the wavelength (10 cm), so targetchange in distance from pulse to pulse is known.Since the time between pulses is also known,each pulse-pair phase shift has an associatedvelocity (distance divided by time!).

Figure 7. Pulse 1 phasor with amplitude and phase.

Figure 8. Pulse 1 and Pulse 2 phasors with amplitude and phase.



Phasors for two successive pulses represent twosnapshots of the returned signal. Assumptionsmust be made about the target’s behavior betweenpulses.

Frequency Shift vs. PhaseShift

Recall that Doppler frequency shifts are occurringas a result of a target’s radial motion, but are notdirectly measured. Pulse-to-pulse phase shifts andDoppler frequency shifts are both dependent on atarget’s radial motion. Doppler frequency shifts areinherent within the pulse-to-pulse phase shiftssince the time rate of phase change equals fdop.Since the time between pulses is constant for agiven range bin, there is a direct (linear) relation-ship between the amount of phase shift from pulseto pulse and the target’s radial velocity.

For any particular pulse pair, there are two possi-ble angles between the individual pulse phasors(Figure 9). The angle <180° is the one that isalways used. The next objective will explain whythis is the case.

WSR-88D RadialSpeed

Computation(Objective 3)

The speed the WSR-88D will initially assign to arange bin is directly related to the amount ofphase shift between successive returned pulses.However, there is a maximum amount of phaseshift, 180°, that the WSR-88D can measure from

Figure 9. Two possible angles between the two phasors.

3 - 24 WSR-88D Radial Speed Computation (Objective 3)


one pulse to the next. If a target moves too farbetween pulses such that its true phase shiftexceeds 180°, an apparent phase shift of less than180° would still be assigned. A true phase shift of≥180° introduces ambiguity (Figure 10).

The radial velocity that is initially assigned isbased on a pulse pair phase shift of <180°. If thetrue pulse pair phase shift is <180°, the first guessvelocity will be correct.

Maximum Unambiguous Velocity

Since 180° is the maximum phase shift that theWSR-88D can recognize, there is then a maxi-mum velocity that the radar can measure unam-biguously. It is the maximum unambiguousvelocity, Vmax, and it corresponds to a maximumpulse-pair phase shift of 180°.

The process of determining target speed is rela-tively simple once the phase angles of two succes-sive returned pulses have been determined.

1. The phase of the first returned pulse and thephase of the second returned pulse areobtained and the difference (pulse-pair phaseshift) is computed.

Figure 10. A phase shift of ≥ 180° introduces ambiguity.

WSR-88D Radial Speed Computation (Objective 3) 3 - 25


2. The pulse-pair phase shift is then compared tothe maximum measurable phase shift of 180°and the phase shift percentage is then multi-plied by Vmax.

Phase Shift-Radial SpeedRelationship

This is simply the ratio

(5)

where P.S. is the amount of pulse-pair phase shift,|Vr| is the target radial speed, and |Vmax| is themaximum unambiguous speed (magnitude ofVmax). For any given Vmax, target speed is directlyrelated to the amount of pulse-pair phase shift thatoccurs.

Phase Shift DepictionUsing Phasors

The angle between two phasors represents thepulse pair phase shift and, hence, the target'sspeed. Given the limit of using phase shifts lessthan 180°, the WSR-88D always uses the smallerangle between the two phasors to determine thepulse pair phase shift.

Example In Figure 11, the phase for pulse 1, α1, is 30°, andthe phase for pulse 2, α2, is 120°. The pulse-pairphase shift is then 90° (one half of 180°). If Vmax is60 knots, the target's speed will be 30 knots (one

P.S.180°------------

VrVmax------------------=

Figure 11. Phasors are used to identify the pulse-pair phase shift.



half of 60 kts). This answer is obtained by usingequation (5), P.S. = 90°, and |Vmax| = 60 kts suchthat

90°/180° = |Vr| / 60 kts1/2 = |Vr| / 60 kts60 kt (.5) = |Vr| = 30 kts

Notice that in this example, we have only obtainedthe target's speed, not its direction of motion(inbound or outbound). Also, if Vmax had been 40knots instead of 60 knots, the same amount ofpulse-pair phase shift would have produced alesser target speed of 20 knots. Therefore, thereis no unique target speed for every pulse-pairphase shift due to its dependence on Vmax.

Phase Shift and Unambiguous Velocity

Pulse-Pair Phase Shift Less Than 180°

If the actual pulse-pair phase shift is less than180° (Figure 12), then the target speed and direc-tion can be unambiguously measured and the“first guess” velocity measurement is correct.

Pulse-Pair Phase Shift Equal to 180°

If the actual pulse-pair phase shift is equal to 180°(Figure 13), then the speed will be correct and

Figure 12. Phase shift of < 180°.



equal to Vmax, but the target's direction (inboundor outbound) will be unknown.

Pulse-Pair Phase ShiftGreater Than 180°

If the actual pulse-pair phase shift is greater than180° (Figure 14), velocity detection is ambiguous.By using the smaller of the two angles betweenphasors, the radar will assign an improper velocity(both speed and direction) to the target. Each Vmaxdefines an interval of first guess velocities. Forexample, if Vmax = 50 kts, the first guess velocitieswill range from -50 kts to +50 kts. Though this firstguess velocity measurement will be incorrect,there are other possible velocities, sometimescalled “aliases”.

Figure 13. Phase shift of 180°. The speed is correct but the direction unknown.

Figure 14. Phase shift of > 180°. First guess speed and direction are incorrect.



Pulse-Pair Phase Shift of 0°, 360°, etc.

If no pulse-pair phase shift is measured (0°, 360°,etc.), then the target is stationary or, in mostcases, moving perpendicular to the radar beam.

High PRFs Needed for Velocity

When the true radial velocity equals or exceedsVmax, the radar's first guess velocity will be incor-rect. Each first guess velocity has a group of mete-orologically plausible aliases, which are used bythe Velocity Dealiasing Algorithm (discussed inTopic 3 Lesson 5). To reduce the likelihood of anincorrect first guess velocity, a target should besampled frequently so that the target location doesnot change much between successive pulses.Therefore, the best velocity estimates areobtained by using high PRFs.

ExamplesDetermine the first guess radial speed given theVmax and the pulse-pair phase shift.

#1: Vmax = 60 kts, Phase Shift = 90°





Obtaining I and QValues

(Objective 4)

Recall that Doppler frequency changes are notmeasured by the WSR-88D system. Instead,mean radial velocity is determined from the aver-age rate of change of phase between a series ofpulse pairs. The amount of pulse-pair phase shiftis caused by a change in target position from pulseto pulse.

I and Q Components A target detected by a single pulse will return asignal represented by the phasor in Figure 15.Since a phasor is a vector, it has both magnitude(amplitude) and direction (phase angle) and hascomponents in the x and y directions. ConcerningWSR-88D signal processing, the component of aphasor in the x direction is called the In-Phasecomponent (or I component) and the component inthe y direction is called the Quadrature component(or Q-component).

The I and Q components contain all the necessaryinformation to generate the base reflectivity, radialvelocity, and spectrum width data. The amplitudeof the signal, which is ultimately reflectivity, is com-puted from the I and Q values. Pulse pair phaseshifts are also computed from the I and Q values,which are then used to generate radial velocityand spectrum width.

Figure 15. A phasor and its components.

3 - 30 Obtaining I and Q Values (Objective 4)


The I component (In-Phase) is essentially thereturned raw signal. The Q component is thereturned 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.

Both I and Q Values Needed

The I and Q values together provide both targetspeed and direction. This is illustrated in Figure 17where the I and Q components are known forpulse 1 (I1 = 5 and Q1 = 2). For pulse 2, only the Iinformation is shown. The Q component would benecessary to determine if the pulse 2 phasor lies inthe 2nd or 3rd quadrant (inbound or outboundmotion), as well as the pulse 2 amplitude.

Determining Target Direction

Once the I and Q values for two successivereturned pulses have been determined, therespective phasors can be plotted. The rotationfrom Phasor #1 to Phasor #2 determines thedirection of the target’s radial motion.

Figure 18 illustrates the result of the two possiblerotations. When trying to find the resultant vector

Volta

ge

Figure 16. Example of the relationship between I and Q values.

Obtaining I and Q Values (Objective 4) 3 - 31


from the cross-product of two vectors, we can usethe “right hand thumb rule” to determine whethertarget motion is inbound or outbound. Place yourright hand along phasor #1 such that the fingerspoint in the same direction as the phasor. Fromthis position, curl your fingers toward phasor #2. Inorder to do this, your thumb will be pointing eithertoward you or away from you. If your thumb pointsaway from you, then the apparent target motion isoutbound from the radar. If your thumb pointstoward you, then the apparent target motion isinbound to the radar.

Figure 17. With only the I component, the pulse 2 phasor angle and magnitude is unknown.

Figure 18. Phasor rotation and target direction.



Another way of remembering the relationshipbetween phasor rotation and apparent targetmotion is:

• counterclockwise rotation means targetmotion is toward the radar and is denoted bya negative velocity

• clockwise rotation means target motion isaway from the radar and is denoted by a posi-tive velocity

Figure 19 shows the phasors used to demonstratea pulse-pair phase shift. Note that the phase shiftfrom pulse 1 to pulse 2 sweeps out an angle in thecounterclockwise direction. Thus the target is mov-ing toward the radar, and the velocity will bedenoted by a negative sign.

Note: Objective 4 only requires that you be able todetermine target direction (inbound or outbound)and not speed from the plotting of phasors.

Figure 19. The phasor rotation from pulse 1 to pulse 2 is counterclockwise, thus target motion is toward the radar.



Calculations UsingPhasors

Example #1 Given:Vmax = 60 KT (180° Phase Shift)Phasor #1: I1 = +4 AND Q1 = +4Phasor #2: I2 = -4 AND Q2 = 0

The pulse-pair phase shift from #1 to #2 is _____o

and phasor rotation is (clockwise / counterclock-wise) 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 = -4Phasor #2: I2 = -4 AND Q2 = 0

The pulse-pair phase shift from #1 to #2 is _____o

and phasor rotation is (clockwise / counterclock-wise) indicating that the apparent target motion is

I

Q

I

Q



(inbound to / outbound from) the radar at _____knots. The first guess velocity would be ______.

Actual Phase Shift Exceeds 180°

Recall that the WSR-88D always assumes thephase shift due to target motion is the smallerangle between phasors #1 and #2. What happenswhen the actual phase shift is greater than 180°?The apparent, or first guess, target motion will beincorrect. The radial speed will be less than what itactually is and the target direction will be oppositethe true direction.

Calculations Using Phasors

Example #3: Given:Vmax = 60 KT (180° Phase Shift)Phasor #1: I1 = +4 AND Q1 = 0Phasor #2: I2 = 0 AND Q2 = -4

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.



Actual pulse-pair phase shift is 270° and pha-sor rotation is CCW

The actual target motion is (inbound to / outboundfrom) the radar at ____ knots. However, theWSR-88D's first guess at target motion willassume a phase shift of ______o and phasor rota-tion that is (clockwise/counterclockwise) indicat-ing that the apparent target motion is (toward/awayfrom) the radar at ______ knots.

Table 20-1 depicts the relationship between truevelocities, first guess and aliased velocities. All ofthese values are based on a Vmax = 60 kts. Thus-60 kts to +60 kts defines the interval of first guessvelocities. When the true velocities fall within thisinterval, the first guess velocity is correct.

A first guess velocity of +30 kts may be the correctradial velocity or may be associated with a truevelocity of -90 kts. For a first guess velocity of +30kts, the Velocity Dealiasing Algorithm (discussedin Topic 3, Lesson 5) compares +30 kts, -90 ktsand other possible velocities to surrounding val-ues. This is to determine if the first guess (+30 kts)or one of its aliases (-90 kts) is appropriate for thatrange bin.

Q

I



Key Points• The WSR-88D always uses phase shifts are< 180°.

• Actual phase shifts ≥ 180° will result in first guess velocities that are incorrect or ambigu-ous.

• Vmax defines an interval for first guess veloci-ties. 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.

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



Signal ProcessingReview Exercises

1. The WSR-88D is a "coherent" system. What does this mean?

2. The Doppler Effect is defined as the change in fre-quency 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 situ-ated 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 WSR-88D 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°.



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, +140b. -20, -60, +20, +60c. -10, -50, +30, +70d. -10, -90, +70, +150

7. If I = 3 and Q = 3, graphically generate a phasor and identify its amplitude and phase (relative to the posi-tive 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?


Date post:	07-May-2018
Category:	Documents
Upload:	vuongphuc
View:	219 times
Download:	0 times

Topic 3: Principles of Meteorological Doppler Radar 3 - 9 Topic 3: Principles of Meteorological...

Documents