Aerospace and Electronic Systems Magazine July 2017 Tutorial XI - 56
Weather Radar: Operation and Phenomenology
Figure 5.
A radar radial velocity image containing a tornadic vortex signature (TVS). The TVS is marked by a significant gradient in the velocity field.
where ˆ· denotes an estimate, yi is the measurement of a single pulse
for a single-resolution cell and σˆ n2 is the estimated noise power of
the radar. The exact number of averaged samples depends on the
VCP of the radar, which dictates spatial and temporal resolution
ˆ
requirements. Replacing Pr with Pr in (31) yields the estimate for
reflectivity:
Zˆ = 10log10 ζˆ
ˆ
512 Pr λ 2 R 2 L2 ( R ) Ls
,
= 10log10 2ln(2)
2 2
PG
θ3 cτπ 3 | K |2
t
(35)
ˆ
where ζ is the estimated linear scale reflectivity.
B. RADIAL VELOCITY
The radial velocity product is an estimate of the reflectivityweighted average motion of targets toward or away from the radar
within a given sample volume. The radial velocities detected during the May 20, 2013, tornadic supercell discussed in Section V.A
are shown in Fig. 5. The radial velocities of the supercell show a
large-scale circulation both toward the radar (depicted in green)
and away from the radar (depicted in red). Within the area circled
56
in white, a tight couplet of red and green indicates the area of increased circulation near the tornado core. This couplet is co-located with the area of increased reflectivity ascribed to the debris ball
in Section V.A.
Several independent mechanisms contribute to the apparent
motion of the numerous hydrometeors in a resolution cell. By the
Central Limit Theorem, it is common to model the power spectrum
of the coherent pulse sequence as Gaussian. Furthermore, it is estimated that more than 75% of all observed spectra are Gaussian
shaped [31].
1. Phenomenology
Measurement of the Doppler frequency, described in Section II.F,
is the method by which scatterer velocity is determined. As mentioned previously, the radar is only capable of measuring the radial
velocity component of a target. The measured radial velocity is
a linear combination of the line-of-sight components of the horizontal and terminal-fall velocities of hydrometeors in the antenna
beamwidth:
Vr = −Vx cos (θ ) cos (φ ) − Vy sin (θ ) cos (φ ) + V f sin (φ ) ,
(36)
where Vx and Vy are the horizontal hydrometeor velocities in the x
and y directions, respectively, and Vf is the fall speed of the hydrometeor [32].
IEEE A&E SYSTEMS MAGAZINE
JULY 2017, Part II of II
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