PRINCIPLES OF METEOROLOCIAL RADAR

OUTLINE

• OVERVIEW– Sampling– Rmax

– Superrefraction, subrefraction, operational impacts

– Sidelobes– Beam Width– Range Folding– PRF’s (Pulse Repition Frequency)

• PRECIPITATION ESTIMATES– Identify how reflectivity Z and rainfall R depend on drop

size distribution and discuss limitations– Potential Errors

• SIGNAL PROCESSING– Doppler Effect– Radial Velocity– Spectrum Width

• MITIGATION OF DATA AMBIGUITIES– Impact PRF changes have on Rmax and Vmax

– BRIEF discussion on minimizing velocity aliasing and range folding

SAMPLINGRadar send energy in a beam…as the beam

encounters a target…some of the energy will be

scattered by the target in all directions…the

portion received by the radar receiver is

Called “backscatter.

The degree of backscatter depends on..

-size

-shape

-state (liquid freezing, mixed, dry, etc)

-concentration (# per unit volume)

SAMPLING (CONT’D)

2 main types of scattering…Rayleigh andNon-Raylieigh

Rayleigh… occurs with targets whose diameter (D)is small compared to the wavelength (L) of theradar beam (D<L/10)

WSR-88D wavelength about 10 cm..so Rayleighscattering with target diameters less than or equalto about 1 cm (.4in). Raindrops mostly less than 7 mm,hailstones mostly non-Rayleigh…energy away from theradar!

Z and dBZ

Ze=the concentration of uniformaly distributed small water drops which would return the amount of power received by the radar (Z from now on)

Z=N(D)D6

Z=reflectivity factor

D-drop diameter

N(D)=number of drops of given diameter per cubic meter

Suppose a one meter cube with 4000 one millimeter drops

Z=4000mm6/m3

Z can range over 10 orders of magnitude..so we use Decibels of Z or dBZ

dBZ=10 x log Z 10(log 4000)=10 x 3.6 = 36 dBZ

Z could range from 0.0006 to over 3,000,000,000, dBZ over this same range would reach from -32 to 95.

Rmax

Rmax = 250nm

200 nm

Where will the data display?

Rmax=250 nm

300 nm

Superrefraction, Subrefraction, and Operational Impacts

Normally the height of the radar beam center line assumes a standard atmosphere and the beam is assumed to refract a certain amount…but

Superrefraction…beam refracts more than standard and is lower then calculated (often with temp inversion)

Subrefraction…beam refracts less than normal and the beam is higher than calculated (temp lapse rates approach dry adiabatic)

Storms are to your east…rain cooled air caused an inversion..are under, over or right on measuring storm tops?

Subrefraction

Standard refraction

Superrefraction

Sidelobe contamination

The result of returned power from the lobes off the main beam (much weaker than the main beam)

Most significant contamination if convection at close range

Beam Width

Angular distancebetween the halfpower points definethe beam width.. For the 88D about 1Degree

(Beam diameters in NM)

8.46.74240

6.353180

4.23.42120

2.11.7160

1.00.80.530

57S74C88DRange

(NM)

Range Folding

Range folding is the placement by the radar of an echo in a location whose azimuth is correct but whose range is erroneous. This occurs when a target lies beyond the maximum unambiguous range of the radar.

How do we correct? By using different Pulse Repetition Frequencies…

PRF’s (Pulse Repetition Frequency)

PRF…number of pulses transmitted per second PRT (Pulse Repetition Time) is the elapsed time from the beginning of one pulse to the beginning of the next.

The 88D scanning strategy uses two sweeps for the 2 lowest angles…one sweep uses short pulses (5.7 sec/hr transmitting…longer listening..larger Rmax) the other long pulses (17.1 sec/hr transmitting..shorter listening.. smaller Rmax but better velocity).

Precipitation EstimatesWe’ve looked at Z for a uniform distribution of droplets… suppose we sample a cubic meter with 729 one millimeter drops and one 3 millimeter drop…

Z=(729 drop/m3)(1mm)6 + (1 drop/m3)(3mm)6

=729mm6/m3 + 729mm6/m3

=1458mm6/m3

=32 dBZ

The contribution to total reflectivity from the single three millimeter drop equals that of the 729 one millimeter drops!

Limitations…radars do not measure dropsize distributions…only returned power!

Once returned power is measured, Z can be estimated using

Z=PrR2/C Pr=returned power

R=target range

C=radar constant (unique by radar)

Z is dependent on the dropsize distribution, in particular the sixth power of the drop diameter. R is proportional to the third power of drop diamter. So for a given R…many Z values are possible.

Rainfall rate, R is dependent on the dropsize distribution..but also the velocity of the drops.

R=(pi/6)N(D)D3wt(D)

R=Rainfall Rate

D=Drop Diameter

N(D)=number of drops for a given diamter per cubic meter

Wt(D)=fall velocity for a given diameter

Z-R relationship

Through considerable research…for the 88D…

Z=300 R1.4 … or

R=e[ln(Z/300)]/1.4 substitute a value for Z and solve for R

This has been found to be the best all round relationship..results in less overestimation of light precipitation and less underestimation of heavy precipitation than conventional radars.

Rainfall Errors• Z estimate errors

– Ground clutter– Anamoulous Propagation (AP)– Partial beam filling– Wet radome– Incorrect hardwar calibration– Chaff

• Z-R relationship errors– Variations in drop size distribution– Mixed precipitation

Rainfall Errors (cont’d)

• Below beam effects– Strong horizontal winds– Evaporation below the beam– Coalescence below the beam

Signal Processing

Doppler Effect…the change in frequency with which energy reaches a receiver when the receiver and energy source are in motion relative to each other..

Radial Velocity…the component of target motion parallel to the radar radial. It is that component of a target’s motion that is either toward or away from the radar site along the radial..

Key points…1) radial velocities will always be less than or equal to actual target velocities..2) actual velocity is measured by Doppler radars 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…of where the target is stationary.

Coherency

Most radars now are coherent radars..

Phase information for each pulse is known. Ths 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 determines the phase.

Relationship between a target’s actual velocity and radar depicted velocity…

|Vr| = |V|.cos B Where:

Vr = radial velocity

V = actual velocity

B = smallest angle between V and radar radial

ASSUME…

The actual wind is uniform from a direction of 300 degree at 30 knots through the lower atmosphere across the entire observational range of the radar. As the antenna is pointed due west (along the 270 degree) a radial wind speed of 26 knots would be measured…

|Vr| =(30 kt) cos (30)

=30 kt (.866)

= 25.98 kt

Spectrum Width

…actually “velocity” spectrum width…and is a measure of the amount of velocity dispersion within a range bin. It is proportional to the variation of speed and direction…the reliability of velocity estimates decreases as spectrum width estimates increase.

Useful for…Boundaries..thunderstorms..shear regions…turbulence..wind shear..different fall speeds for different sized hydrometers.

Mitigation of Data Ambiguities

We’ve discussed Rmax…what about Vmax??

Vmax is the maximum mean radial velocity that the radar can measure unambiguosly.

Vmax= L.PRF/4 and

Rmax =c/(2)(PRF) c=speed of light

So…as PRF increases Rmax decreases and Vmax increases (and vice-versa)

What’s ahead??What’s ahead??

• Dual Polarization(1-3 years)Dual Polarization(1-3 years)• Phased array radars (10 years?)Phased array radars (10 years?)• Small radar networks (10+ years)Small radar networks (10+ years)

TutorialTutorial

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