Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 54

Weather Radar: Operation and Phenomenology
CPI that satisfies (28). By choosing a maximum length CPI, the
maximum possible velocity resolution is attained and the statistical
variations of the spectral moment estimations are minimized. This
is called legacy resolution. However, the motivation for a superresolution mode is described in detail in [27] and [28], which show
that certain severe storm reflectivity and Doppler signatures are
better and more frequently identified by generating a grid with
a finer azimuthal resolution of 0.5° (i.e., super-resolution mode)
rather than 1° (i.e., legacy resolution).
The term "super resolution," in the context of weather radar,
simply refers to the ability to collect more CPIs at an increased azimuthal resolution.9 This increased azimuthal resolution is achieved
by decreasing the duration of a CPI by half; however, the negative
consequence of a shorter CPI is an increase in the standard deviation of the reflectivity and Doppler estimates. In addition, because
the purpose of super-resolution mode is increased spatial resolution, this mode always uses the short-pulse waveform for increased
range resolution.

F. DUAL POLARIZATION
Originally, the WSR-88D operated using only horizontally polarized waves. However, all WSR-88Ds now possess a dual-pol
capability, i.e., the ability to simultaneously transmit and receive
both horizontally and vertically polarized waves [2]. The initial
performance analysis and calibration process is detailed in [29]. A
dual-pol weather radar is not capable of switching polarizations (as
in a polarization diversity radar) or waveform diversity (as in a polarization agile radar) [30] and thus is not capable of measuring all
four scattering coefficients of a target; instead, it measures the sum
of the co-polar (co-pol) and cross-polarization (cross-pol) powers
received in each channel, i.e., S hh2 + Shv2 and Svv2 + Svh2 . For applications involving raindrops, the cross-pol terms are often considered
negligible, because most raindrops fall with a nearly vertical axis
of symmetry. For applications involving more complex scatterers
(e.g., snowflakes, birds, and tornadic debris), it is common to resort to data mining algorithms to predict the dual-polarized returns.
With the capability of the dual-pol operation, three additional
data products, over single polarization (single-pol), are available:
differential reflectivity, the co-pol correlation coefficient, and the
(specific) differential phase. The primary motivation for these
supplementary data products is the added ability to discriminate
various hydrometeors and improve quantitative forecasts by inferring the size, shape, distribution, and concentration of scatters.
Spherical hydrometeors have a similar RCS for both horizontal
and vertical polarizations; however, raindrops become more oblate
as they grow in size and hence yield greater differences between
the scattered waves of the two polarizations. The three dual-pol
products measure these differences in various ways and are explored in more detail in Section V.
9

The application of the term "super resolution" is contrary to its
traditional usage in signal processing applications in which it
refers to autoregressive processing techniques that achieve super-resolution by assuming a specific form for a signal to be
estimated.

Despite the addition of the vertically polarized channel, all
three of the original base products (i.e., reflectivity, radial velocity,
and spectral width) are still measured from the horizontally polarized channel. The vertical channel is simply employed to generate
the required measurements for the three dual-pol products.

V. WEATHER RADAR DATA PRODUCTS
A coherent dual-pol weather radar (e.g., the WSR-88D) yields six
level II data products for each resolution volume. Level II data include any quantity derived directly from the I-Q data of the radar.
The six level II data products are reflectivity, mean radial velocity,
spectral width, differential reflectivity, co-pol correlation coefficient, and differential phase. The first three data products are the
classic single-pol data products, whereas the last three are the more
recently added dual-pol data products. Each of these data products
is described in detail here. Throughout, an effort is made to distinguish between underlying theoretical quantities, such as a "perfect" reflectivity measurement, and the estimates of such quantities
derived from raw radar measurements.

A. REFLECTIVITY
Reflectivity is the measure of the efficiency of a target in intercepting and reflecting radio energy back toward the radar [22]. More
specifically, it is a measure of the unit area or unit volume (in the
case of meteorological scatterers) RCS of objects observed by a
radar [7]. An example image of radar reflectivity for a tornadic
classic supercell, which affected Oklahoma City, OK, during the
afternoon of May 20, 2013, is shown in Fig. 4. The main body
of the supercell is the large body of high reflectivity depicted as
yellows and reds in the center of the figure. At the bottom left of
the main supercell, a hook and possible debris ball can be seen.
An area of lower reflectivity, indicating inflow into the tornado, is
positioned to the right and above the hook and debris ball.
For a single hydrometeor, reflectivity is a function of size,
shape, physical state (e.g., water or ice), and aspect angle. However, some simplified models are often used to model the RCS of
certain hydrometeor types. We focus specifically on rain.

1. Phenomenology
In the most simplistic case, raindrops are modeled as perfect
spheres. Furthermore, because the circumference of raindrops is
significantly smaller than the wavelength at S band, it is valid to
assume that the raindrops act as Rayleigh scatterers. With these assumptions, the RCS of an individual raindrop is [15], [16]

σ=

π 5 | K |2 D 6
.
λ4

(29)

This model gives rise to the term reflectivity factor, which is defined as

ζ =

1
ΔV

IEEE A&E SYSTEMS MAGAZINE

D
i

6
i

λ 4η
π5 K

(30)

JULY 2017, Part II of II

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