Radar Performance

Radar Performance
The actual performance of a weather system is a combination of many factors. Peak
power, receiver sensitivity, pulse rate, pulse width and antenna size to name a few. The
following pages describe the effect those factors have on radar performance.

As a practical matter, the primary factors limiting performance are typically the
transmitter’s maximum duty cycle, and the receiver’s noise figure. Both are the result of
the real world of physics applied to the transmitter and receiver. Other factors, such as
antenna size, are factors which can be solved by simply spending more money. The
physics of duty cycle and noise figure are not so easy.

The transmitter duty cycle limits both the maximum pulse rate and the maximum pulse
width. The duty cycle is dependent on the transmitter design and type (magnetron,
Klystron or solid state), the modulator and high voltage power supply and the physics
associated with each of these technologies.

Wider pulses improve the radar’s ability to detect weak precipitation at long ranges.
Pulse width is limited by the transmitter’s maximum duty cycle. Typically, many radars
limit the maximum pulse width to approximately 2 microseconds. This limits the
sensitivity at longer ranges.

Higher pulse rates are required to measure higher velocities. This is also limited by the
transmitter’s maximum duty cycle. Typically, many radars limit the maximum pulse rate
to approximately 1200 pulses per second. This limits the maximum velocity
measurement capability.

Pulse Width And Sensitivity

The radar system’s pulse width, minimum detectable signal (MDS), receiver bandwidth
and range resolution are all related.

Changing the radar transmitter’s pulse width changes the radar’s sensitivity and range
resolution. Unfortunately, those changes oppose each other. Wider pulses effectively
increase the radar’s sensitivity to weak atmospheric events, and increase the radar’s
ability to penetrate heavy precipitation. Narrower pulses improve the radar’s range
resolution.

The end result is that, in a given weather environment, there is one unique pulse width
that will produce the best data.

Many radars typically provide fixed pulse widths of about 0.8 µsec for velocity mode and
about 2.0 µsec for reflectivity mode. These fixed values are compromises which produce
useful results under many conditions, but restrict the radar’s ability to provide the best
data under a wide range of conditions.
 Radar Performance

The following series of images clearly indicates the improvement in sensitivity that
increased pulse width provides. All data for these images was processed using 12 bit
A/D conversion, 256 levels (8 bits) of reflectivity for processing, and 16 levels (4 bits) of
reflectivity for display.

1 µsec Pulse Width 2 µsec Pulse Width

4 µsec Pulse Width 8 µsec Pulse Width

Figure 1 - Same Storm Images Showing Improved Detection Of Weak
Precipitation With Wider Pulses

Using wider pulses improves the radar’s ability to detect weak precipitation in two ways.
First, by increasing the receiver’s sensitivity and second by increasing the amount of
signal power reflected by the precipitation.

Receiver Sensitivity

The term “Minimum Detectable Signal” (MDS) is worth a comment. The formal
definition is based on a statistical analysis of the probability of accurate detection of a
very weak signal (Ref: Skolnik, Radar Handbook - 2 ed., pg. 213-214, and IEEE Std.
686-1982). As an alternative that is much more clearly defined, many makers of weather
radar systems have adopted a definition of MDS as being a signal to noise ratio of 0 dB
for the noise level and bandwidth of the receiver. In other words, the minimum
detectable signal is equal to the receiver’s noise power level.
 Radar Performance

For C-band, that equation is:

NPo = -114dB/mHz + 10logBW(mHz) + Noise Figure(dB)
The best available receiver technology currently limits the receiver’s noise figure to
around 3dB (less is better). Applying this to the bandwidths and NF for a weather radar
produces the following MDS values:

I/F B/W 10 log NF MDS

(mHz) B/W (dB) (dB)
0.15 -114 -8.24 3 -119
0.5 -114 -3.01 3 -114
1 -114 0.00 3 -111
2 -114 3.01 3 -108
Table 1- MDS vs. Bandwidth At Specified Receiver Noise Figure (3 dB)

Radar theory and industry convention is to match receiver bandwidth to transmitter pulse
width according to the T = 1/τ relationship. The following table illustrates how the pulse
width and receiver bandwidth affect the MDS:

Pulse Width (µsec) I/F Bandwidth MDS

>5.0 150 kHz -119
1.9 - 5.0 500 kHz -114
0.6 - 1.9 1 MHz -111
<0.6 2 MHz -108
Table 2 - Bandwidth And MDS For Radar Pulse Width Ranges
The radar control software must automatically select the appropriate receiver filter
whenever the user selects a new pulse width.

Precipitation Reflections

The Probert-Jones equation is the basic equation which defines the operation of all
weather radar systems. It relates the radar’s operating parameters to the amount of power
reflected by the target precipitation.

That reflected power is received by the radar. All other things being equal, doubling the
pulse width doubles the power reflected by precipitation. Thus, increasing the pulse
width provides additional power to penetrate heavy precipitation.
 Radar Performance

The Probert-Jones equation:

PG θ Hπ 3 K 2 LZ
2 2
Pr = t
1024(ln 2 )λ2 R 2
Pr Reflected signal power received at the radar antenna
Pt Transmitted power- fixed by transmitter design
G Antenna gain- fixed by antenna design
θ Antenna beamwidth- fixed by antenna design
H Pulse width- most radars limit this to a choice of 2 values
K2 Physical constant - typically 0.93 for rain or 0.197 for ice
L Loss factor- determined by radar installation and atmospheric factors
Z Target reflectivity- determined by the type and intensity of precipitation
λ Transmitter wavelength- fixed by transmitter design
R Range- distance from radar antenna to target

With all other things equal, doubling the pulse width (H) doubles the reflected power.
The effect this has on the detection of weak precipitation is clearly shown in the previous
series of images. This is subject to the Probert-Jones assumption that the precipitation
area must be large enough to fill the entire pulse volume.

The maximum pulse width that is available is limited by the transmitter’s duty cycle.
Many radars have a duty cycle rating that limits the maximum pulse width to about 2.0
microseconds at the pulse rates that are required for long range (400 km) weather
detection. Longer pulses, if they are available, can provide better detection of weak
precipitation.

Sensitivity Data

The following graph compares the dBZ sensitivity versus range between a typical
magnetron radar at 2 µsec pulse width, a WSR88-D (NEXRAD) radar at 4.5 µsec pulse
width, and a Klystron radar at 10 µsec pulse width.

Please note that on this graph, lower is better (more sensitive).

 Radar Performance

Sensitivity versus Range

10.00 Typical Magnetron
250 kW C-band
0.00 2 µsec P/W
4.3 m Ant.
0 50 100 150 200 250 300
-10.00
WSR88-D
-20.00 750 kW S-band
4.5 µsec P/W
dBZ

-30.00 8.5 m Ant.

-40.00 Klystron
250 kW C-band
-50.00 10 µsec P/W
4.3 m Ant.
-60.00

-70.00
Range (km)

Graph 1 – Sensitivity At Range Curves For Typically Weather Radar Systems

This graph indicates the compares sensitivity at range for typical weather radar systems.

The table on the following page indicates the parameters used to calculate these
sensitivity curves.
 Radar Performance

Typical WSR88-D Klystron

Magnetron 750 kW 250 kW
250 kW S-band C-band
C-band 4.5 µsec P/W 10 µsec P/W
2 µsec P/W 8.5 m Ant. 4.3 m Ant.
4.3 m Ant.

Transmitter 250000 750000 250000 Watts

Power:
Transmit 5.60 2.75 5.60 GHz
Frequency:
Antenna 44.0 45.0 44.0 dB
Gain:
Beam Width: 0.95 0.95 0.95 Degrees
Minimum -113 -113 -119 dB
Discernible
Signal:
Losses: 1.0 1.0 1.0 dB
Pulse 2.0 4.5 10.0 µsec
Width:
X Constant: 24.615 24.615 24.615 (Probert-
Jones
17.756 or
24.615)

Range: dBz min dBz min dBz min

200km: -1.64 -5.76 -14.63
100km: -7.67 -11.78 -20.65
50km: -13.69 -17.80 -26.68
1km: -47.67 -51.78 -60.65

Table 3 - Radar Characteristics Used To Calculate

Typical Sensitivity Curves On Previous Page

Pulse Width And Range Resolution

Range resolution is defined as the smallest visible distance between two separate storm
cells along the radar beam’s centerline, i.e., in the radial direction. Storm cells that are
closer than that minimum distance will be displayed on the radar as a single cell. Note
that azimuth resolution is the distance between storm cells in the azimuth direction.
Azimuth resolution is determined by the antenna’s beam width.

The maximum range resolution is one-half the pulse length. This value can be calculated
from simple geometric relationships. An example is shown in the following diagram:
 Radar Performance
Radar Resolution vs. Beam Width, Range and Pulse Length

Top View

Radome 1° Radar Beam Width 3 km 3.5 km

3 km
10 µs
P/W 300 m
172 km 1 µs
P/W
200 km

Pulse Width, Range Resolution and Azimuth Resolution

This diagram shows the pulse volume for a 10 µsec pulse, and for a 1 µsec pulse. In the
radial direction, the 10 µsec pulse has a length of 3 km, and the 1 µsec has a pulse length
of 300 m. Thus the maximum radial resolution is 1.5 km for a 10 µsec pulse, and 150 m
for a 1 µsec pulse. This is the maximum resolution set by the basic physics of radar.
Other practical factors may reduce the actual resolution. For example, if the radar’s
signal processor does not have the capacity to process range bins rapidly enough,
resolution will be lost, even though the radar may use very narrow pulses.
For many operational meteorological purposes, such as providing public warnings of
approaching severe weather, heavy rains that could produce flash floods, etc.,
atmospheric events 3 km and larger are of primary interest.
Therefore, pulse widths up to 10 µsec can meet the Probert-Jones equation assumption of
precipitation filling the entire pulse volume and provide accurate data for events 3 km
and larger in size. Pulse widths of 10 µsec provide 1.5 km range resolution.
For large severe storms, such as in the tropics, pulse widths up the 20 µsec can provide
superior storm penetration and still provide 3 km range resolution.
The following images provide a visual comparison of data captured at 2 µsec and 16 µsec
pulse width.

2 µsec Pulse Width 16 µsec Pulse Width

Figure 2 – Same Storm Images Showing Minimal Loss Of Visible Resolution
At Very Wide Pulse Widths
 Radar Performance

For many operational meteorological purposes, the loss of resolution caused by going to
the greater pulse width is not significant, because of the relatively large size of the
meteorological targets. In fact, it is likely that the decreased resolution is more than
offset by the increased visibility of weak precipitation at the greater pulse width.

The following table indicates the pulse length and corresponding range resolution for
various pulse widths.
P/W Pulse Range Comments
(µsec) Length Resolution(m)
(m)
0.5 150 75
0.8 240 120 Typical magnetron radar pulse width in velocity mode
1 300 150
2 600 300 Typical magnetron radar pulse width in reflectivity
mode
4.5 1349 675 WSR-88D (NEXRAD) pulse width
10 2998 1499 Provides maximum sensitivity/penetration consistent
with 3 km storm cell size
Table 4 - Pulse Width, Length And Resolution
For meteorological research purposes, it is often desirable to have the highest resolution
possible. Thus, a narrow beam and a narrow pulse width is usually specified for research
purposes.

The ideal situation would be to have a radar that can provide both wide and narrow
pulses that could be selected as the situation required. In addition, the ability to adjust
pulse rates over a wide range permits obtaining the best available Doppler velocity data
at a given range.

Pulse Rate And Velocity Measurement

In a pulsed Doppler radar system, the maximum unambiguous range, maximum

unambiguous velocity and Pulse Repetition Frequency (PRF) are interrelated. This is
sometimes referred to as the “Doppler Dilemma”. It is due to the basic laws of physics of
pulsed radar (the Nyquist theorem applied to the Doppler principle), and applies to all
pulsed Doppler radar systems.

Higher PRF’s are required to measure higher velocities, and lower PRF’s are required
for longer ranges.

The end result is that for a given range, there is one unique PRF that will permit
measurement of the maximum unambiguous velocity.

Most Doppler radar systems typically provide a choice of fixed PRF’s; one for velocity
mode (typically about 1200) and one for reflectivity mode (typically about 250).
 Radar Performance

The ability to adjust the PRF over a wide range permits selecting the optimum PRF such
that the maximum unambiguous velocity can be measured for the range in use. This is
illustrated in the following images.

Velocity At 200 km Range Velocity At 200 km Range

PRF 250 (with 3X unfolding) PRF 750 (with 3X unfolding)
Velocities are nearly impossible to read Velocities are clearly readable
Figure 3 – Same Storm Images Showing Higher PRF’s Ability To Measure Higher
Velocities Correctly and Intelligibly
The following graph illustrates relationship between PRF, maximum unambiguous
velocity and maximum unambiguous range for a C-band radar. Note that the values on
this chart are valid only for C-band.
Maximum Unambiguous Velocity/Range vs. PRF
C-Band Pulsed Doppler Radar
90 00
0
00
10

00
80

00
70

100.00
00
60

00
50

00
40

00
30

40
00
20

00

PR
15

20
00
12

00

16.00
10

0
90

0
Vmax (m/s)

80
70750
0

10.00
0
60

8
0
50

37 00
5
4

5
0
30

0
25

3.3
0
20

0
16

0
10

1.00

10 25 50 100 200 250 400 1000

Rmax (km)

Chart 2 - Maximum Unambiguous Range/Velocity vs. Pulse Rate

The red lines show the typical operating values for many weather radars: a PRF of 1200
for velocity mode, and a PRF of 250 for reflectivity mode.
 Radar Performance

The relationship between velocity and PRF expressed by the following formula:
PRFλ
V =
max
4
Where: Vmax = maximum unambiguous velocity
PRF = pulse repetition frequency (pulses per second)
λ = transmitted wavelength (0.0535 m for C-band, 5600 MHz)

The relationship between range and PRF is expressed by the following formula:
c
R =max

2( PRF )
Where: Rmax = Maximum unambiguous range
c = Speed of light (approx. 300,000 km/sec)
PRF = Pulse repetition frequency (pulses per second)

While these equations are relatively simple, there is some fairly complex physics behind
them. Going through that physics is beyond the scope of this presentation. However, the
end result is that, at any given range, the is one unique PRF that will provide the
maximum velocity measurement capability.

Again, the radar transmitter’s duty cycle limits the performance. The maximum PRF,
and thus the maximum velocity, is limited by the duty cycle in velocity mode.

Bibliography

Rinehart, R.E., 1997: Radar For Meteorologists 3rd Edition. Rinehart Publications, P.O.
Box 6124, Fargo, North Dakota, 58206-6124, USA (email: radarwx@aol.com)

Doviak, Richard J., and Dusan S. Zrnic, 1993: Doppler Radar and Weather
Observations, 2nd Edition. Academic Press, Inc., Orlando, FL
(www.academicpress.com)

Skolnik, Merrill, 1990: Radar Handbook 2nd Edition, Chapter 23- Meteorological Radar,
McGraw-Hill, New York, NY. (www.mcgrawhill.com)