Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 52

Weather Radar: Operation and Phenomenology
than just applying a textbook spherical-to-Cartesian conversion,
because the gradient of the refractive index of the atmosphere has a
nonnegligible impact on EM wave propagation. The wave follows
a curved path, with curvature proportional to the derivative of the
refractive index. In general, the refractive index is assumed to be
horizontally homogeneous and change only as a function of height
[11]. The curvature of the path of propagation is expressed as
Cp = −

dn
,
dh

(22)

where n is the refractive index and h is the height above sea level.
As a result of this phenomenon, it is common to use an equivalent
Earth model [11] in which the radius of Earth is assumed to be
R = ke Re ,
E
e

(23)

where Re is the true radius of Earth and ke = 4/3. With this model,
the ground range is well approximated by
 R cosθ 
Rg = ReE sin −1  E
 ,
 Re + h 

(25)

C. RADAR PARAMETERS
The quality, resolution, and volume coverage of level II data depend on the operational parameters of the radar. Many of these
parameters are adjustable and chosen based on current weather
conditions. Most adjustable parameters are set by selecting a volume coverage pattern (VCP), described in detail in Section IV.D.
There are a variety of VCPs, each defined for specific meteorological conditions. The most notable parameters varied in VCPs are
PRF, pulse width, cut elevation angles, and antenna rotation rate.
Parameters specified by the adjustable VCPs are described later.

1. PRF

(27)

where Rt is the true target range. Target ranges can be disambiguated by using two or more PRFs. By applying algorithms based on
the Chinese remainder theorem, range measurements across different PRFs are aligned [23]. Power and velocity measurements are
then compared to determine the range of the dominant return [24].

2. Pulse Width
The WSR-88D has two pulse width options, a short pulse and a
long pulse [10]. The short pulse provides higher range resolution
and is used in a high PRF mode for a greater span of unambiguous velocity measurements. However, the long pulse yields higher
average signal power.8

Cut elevation angles are selected based on a number of factors,
including the type, rate of change, range, and extent of the weather
observed. For example, if significant weather is observed at far
ranges, a VCP with more low elevation cuts may be selected to
obtain a sufficient vertical sampling at those ranges. If meteorological conditions are changing rapidly, a VCP with fewer elevation cuts may be selected such that an overall volume scan rate
may be maintained. In clear weather, a VCP with fewer elevation
cuts scanning at a slower rate may be selected to maintain a certain
volume coverage rate while obtaining increased sensitivity by increasing the duration of a CPI.

4. Antenna Rotation Rate
A mechanically steering radar such as the WSR-88D scans a single
elevation cut at a time, scanning in azimuth. The antenna rotation
rate and the PRF determine the maximum number of pulses in a
CPI:
Np ≤

θ 3 PRF
,
dθ

(28)

The PRF is the frequency at which the radar transmits pulses, as
reviewed in Section II.F. In addition to determining the unambiguous velocity interval, the PRF determines the maximum range
at which objects are detected unambiguously. If an object is far
enough in range, then it is possible that the reflected pulse will not
be received until after a second pulse has been transmitted. The
reflection of the first pulse from a far-range object is indistinguishable from a reflection of the second pulse from a near-range object,
resulting in range ambiguity. Choosing the PRF involves trading
off unambiguous velocity against unambiguous range. Recall from
(15) that the maximum unambiguous target velocity is directly proportional to the PRF, whereas the maximum unambiguous range is
inversely proportional to PRF:
Rua =

Ra = Rt modRua ,

3. Cut Elevation Angles
(24)

where R is the slant range (or simply range) to a scatterer. Similarly, the height above sea level is well approximated by
h = R 2 + ReE + 2 RReE sin θ − ReE .

The apparent range of any target beyond the maximum unambiguous range is

cPRI
c
=
.
2
2 PRF

(26)

dθ
is the rotation
dt
rate of the antenna in radians per second. This criterion ensures that
the antenna beam overlaps for all pulses in the CPI. Hence, lower
rotation rates provide higher SNR and improved velocity resolution at the expense of slower volume coverage.
In traditional radar applications, in which the target is a point
target, scanning the antenna over the course of a CPI results in a
signal processing loss from the amplitude modulation of the beam

where Np is the number of pulses in a CPI and

Although weather radars could simultaneously achieve high resolution and high SNR by exploiting more sophisticated waveforms than simple rectangular pulses [25], the current waveform
set of the WSR-88D is likely to remain standard for the foreseeable future.

IEEE A&E SYSTEMS MAGAZINE

JULY 2017, Part II of II

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine July 2017 Tutorial XI