Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 59

Reed, Lanterman, and Trostel

1. Phenomenology
When an EM wave is scattered forward by raindrops, a polarization-dependent phase shift occurs over the path of propagation.12
The difference between the phase shifts of the forward scattered
wave in the horizontal and vertical channels is the specific differential phase. Assuming the backscatter phase shift is negligible, the
one-way specific differential phase shift in radians per kilometer is
2π
kw

Φ HV =



∞

{ℜ  S

( D ) − ℜ  Svv ( D )}N ( D ) dD,

(57)

where Shh and Svv are the forward scatter coefficients and ℜ denotes
the real part of a complex number. In the case of an oblate spheroid, the horizontal wave will have a higher RCS, be attenuated
more, and have a greater phase shift than the vertical wave. A good
approximation relating the specific differential phase, in degrees
per kilometer, to underlying meteorological parameters is [40]
2π
kw



108


W λC 1 − r ,

Φ HV =
=

∞

D 3C (1 − r ) N ( D )dD

(58)

where W is the liquid water content in units of grams per cubic
meter and C depends on the operational frequency of the radar.

2. Calculation
The differential phase is estimated from the angle of the zero-lag
co-pol correlation term, i.e.,

1
2

 1
 N p

φˆhv = arg 



 y ( y ) .
i =1

h
i

v
i



(59)

The specific differential phase is estimated as the range derivative of the estimated differential phase, sometimes averaged over
several range resolution cells to reduce statistical variations, i.e.,

ˆ =
Φ
hv

φˆhv ( R2 ) − φˆhv ( R1 )
R2 − R1

(60)

A similar polarization-dependent phase shift occurs upon backscatter, but this phase shift is considered negligible [41].

JULY 2017, Part II of II

The newly available dual-pol data products are being increasingly
exploited by the NWS. This section illustrates the utility of some of
these new data products by discussing the application of differential reflectivity and the correlation coefficient in detecting tornadic
storms.
Dual-pol parameters, such as correlation coefficient ρ and differential reflectivity ZDR, are being combined, operationally, with
more traditional single-pol measurements, such as standard reflectivity Z and radial velocity Vr, to detect low-end tornadic storms.
These types of storms are fairly common in the winter and early
spring in the southeastern United States. The storms often occur
late at night, are wrapped in rain, and exhibit less vertical development than storms seen later in the severe weather seasons of the
spring and summer. Therefore, these early storms are often difficult to detect by direct observation or by using single-pol measurements.
A promising method of detecting these storms is to examine
the dual-pol data products for a dual-pol tornado debris signature
(DPTDS). These signatures are produced by the debris lofted when
a tornadic storm touches the ground. In addition to having a high
reflectivity value Z and radial velocity Vr couplet, as described in
Sections V.A and V.B, respectively, the data can be examined to
search for relevant values of ρ and ZDR. Areas containing lofted tornadic debris should tend to have very low values of ρ, because the
debris consists of a variety of sizes and shapes of materials affected
by the tornado. In addition, ZDR is usually near zero, indicating no
specific preferred orientation of the debris.
Fig. 6 shows reflectivity Z, radial velocity Vr, differential reflectivity ZDR, and the correlation coefficient ρ for an operational
case of an EF3 tornadic storm that occurred near Adairsville, GA,
on January 30, 2013. (The area affected by the tornadic storm is
enclosed in the white circle in all four plots.) The reflectivity Z plot
shows a long line of storms along a squall line but no distinctive
supercell thunderstorm. Radial velocity Vr shows a large area of
circulation, but a tight couplet is not seen. There is, however, a distinct area of near-zero ZDR and low values of ρ within the area of interest. These strong signals, associated with high Z and indications
of rotation in Vr, allow the detection of a tornado on the ground.

VII. CONCLUSION

where R1 and R2 are the first and last ranges over which the average specific differential phase is computed. In some cases, a least
squares fit may also be used to estimate the specific differential
phase.

VI. USE OF DUAL-POL RADAR PARAMETERS IN TORNADO
DETECTION

This article reviews the basic phenomenology of radar meteorology. The concepts described herein provide guidance on the
physical significance of the level II data products provided for
meteorological applications. These physical concepts provide intuition on how these data products may be applied to problems
such as hydrometeor classification and characterization, clutter identification, rain rate estimation, and detection of tornadic
vortex signatures. Perhaps similar concepts may be exploited in
other areas of radar application, such as target identification and
characterization. Furthermore, with input from other radar communities, perhaps the utility of the data provided by the WSR88D and other weather radar systems may be exploited in new

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