Radar works by sending out pulses of energy and measuring the return signal, or backscatter. The strength of the returned signal depends on characteristics of the targets such as size, shape, and concentration. Radar is used to estimate precipitation by relating the measured reflectivity to rainfall rate, though there are limitations since the actual drop size distribution is not known. Doppler radar additionally measures the radial velocity of targets by detecting changes in frequency of the returned signal from the Doppler effect. Managing the pulse repetition frequency allows tradeoffs between maximum unambiguous range and velocity but can cause ambiguities like range folding if not properly adjusted.

1. PRINCIPLES OF
METEOROLOCIAL RADAR

2. OUTLINE
• OVERVIEW
– Sampling
– Rmax
– Superrefraction, subrefraction, operational
impacts
– Sidelobes
– Beam Width
– Range Folding
– PRF’s (Pulse Repition Frequency)

3. • 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

4. SAMPLING
Radar 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)

5. SAMPLING (CONT’D)
2 main types of scattering…Rayleigh and
Non-Raylieigh
Rayleigh… occurs with targets whose diameter (D)
is small compared to the wavelength (L) of the
radar beam (D<L/10)
WSR-88D wavelength about 10 cm..so Rayleigh
scattering with target diameters less than or equal
to about 1 cm (.4in). Raindrops mostly less than 7 mm,
hailstones mostly non-Rayleigh…energy away from the
radar!

6. 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

7. 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.

8. Rmax
Rmax = 250nm
200 nm

9. Where will the data display?
Rmax=250 nm
300 nm

10. 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)

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

12. 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

13. Beam Width
Angular distance
between the half
power points define
the beam width..
For the 88D about 1
Degree
(Beam diameters in
NM)8.46.74240
6.353180
4.23.42120
2.11.7160
1.00.80.530
57S74C88DRange
(NM)

14. 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…

15. 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).

16. Precipitation Estimates
We’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!

17. 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.

18. Rainfall rate, R is dependent on the dropsize distribution..but also
the velocity of the drops.
R=(pi/6)N(D)D3
wt(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

19. 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.

20. 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

21. Rainfall Errors (cont’d)
• Below beam effects
– Strong horizontal winds
– Evaporation below the beam
– Coalescence below the beam

22. 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.

23. 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.

24. 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

25. 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

26. 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.

27. 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)

28. 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)

29. TutorialTutorial
• Go to www.atmos.uiuc.edu
• Weather World 2010
• Online Guides
• Remote Sensing
• Radars
• Start with the Basics