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from the baroclinic stageto the barotropic stage (Fig.
18.3
). The wrap-around
mechanism was apparently missing in this case. It could be because the low-level
mesocyclone was incapable of producing the wrap-around process and cyclic sym-
metry necessary for tornado development. This could be due to the large distance
between the major entropic source and sink regions outside of the hook echo (RFD)
area, which cause too small of an entropic gradient and thus too weak vorticity.
18.12
Temporal Discretization Necessary for Phase
Change Ensemble
The previous case illustrates the potential for the use of entropic balance theory
with standard weather radar outputs, Z and Z
DR
. However, data from this case
were collected at approximately 70-s intervals, a rate much higher than is used
operationally for the NEXRAD network, which usually receives updates for a
particular elevation every 5 min. It is clear from the rapidly evolving scenario
presented that, even at this high temporal sampling rate (70 s), storm advection
produces a bias in the calculation of DZ and DZ
DR
. Since the parameters used to
calculate the system entropy depend on the microphysical changes within a radar
resolution volume, it can be assumed that over a necessarily short period of time,
the molecular phase state fluctuations will dominate (see Fig.
18.13
). The question
of how short a time interval is appropriate will be addressed in this section.
The temporal difference method was applied to data collected from the Atmo-
spheric Imaging Radar (AIR), a multi-channel, X-band, mobile imaging weather
radar capable of gathering
20
ı
range-height indicator (RHI) scans at approximately
1 s time intervals. A detailed description of the radar and its capabilities can be
found in
Isom et al.
(
2011
). It should be noted here that this radar is horizontally
polarized and thus we cannot calculate the DZ
DR
parameter. This extremely high
temporal resolution made it possible to examine the calculated values of DZ at
various intervals and determine an appropriate dt in which the changes in reflectivity
are dominated by microphysical processes and not advection.
Three examples of varying interval lengths are given in Fig.
18.18
. Data were
collected during a squall line that moved through the Norman, OK area on August
9, 2011 at approximately 0200 UTC. RHI scans at a single azimuth angle (no
azimuthal scanning) and
1
ı
1
ı
angular resolution were used to achieve the high
temporal sampling. Range corrected power for 0228:15, 0229:00 and 0231:36 UTC
are given in the left column of Fig.
18.18
and DZ/dt for time intervals of 1, 45 and
154 s are given in the right column. Again, several entropic dipoles can be seen
throughout the storm cross-sections, especially at the shorter two time intervals.
Qualitatively, there is good agreement between the 1 and 45-s DZ calculations,
particularly in the convective portions of the storm (4-5 km range) and along
the gust front (8-9 km range). The dipole structure has significantly degraded by
the 154-s interval, thus indicating that the time-span is dominated by advection.
While advection plays a role in the 45-s interval as well, it can be argued that,
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