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where L
v
is the latent enthalpy of vaporization, and dm/dt is the rate of change of
mass owing to evaporation (which is negative, implying a cooling rate). The change
in mass of water in the one-dimensional model is calculated based on the change in
liquid water content (mass of water per unit volume),
M D
.=6/
w
Z
N
D
3
dD
.
D
/
:
(18.49)
Here, N(D) is the number concentration (per unit volume) of drops of diameter D,
and
w
is the density of liquid water. Thus, we can obtain an estimate of the change
in entropy per unit volume based on model output:
L
v
T
/
dS
.
dM
;
(18.50)
where T
is the average temperature of the model domain. Using a number of
different environmental profiles and DSDs, we can estimate the entropy anomalies
S
0
RR
and S
0
DR
as a function of the evaporative changes DZ and DZ
DR
. In general,
larger changes in Z and Z
DR
correspond to larger changes in entropy for a given
DSD (not shown).
18.11.1
1 June 2008 case
The temporal difference method is applied to the rapid-scan radar data from the
1 June 2008 case of a cyclic nontornadic supercell in Oklahoma (see
Kumjian
et al. 2010
). Figure
18.17
shows the temporal difference fields of Z and Z
DR
over
the period 0341:36 UTC to 0346:26. At this time, the storm is undergoing cyclic
mesocyclogenesis, and the new mesocyclone is developing along the RFD gust
front. This time is marked by an increase in the strength of the updraft. Note that
the signal of storm advection is evident in each panel (the C/ difference “dipole”
is clearly seen in the hook echo at each time). However, meaningful patterns of
differences exist. For example, in panels (d), a relatively large region of positive
DZ (indicating an increase in Z from one scan to the next) is located across much
of the RFD north of the hook echo. At the same time, a large positive DZ
DR
is
located farther downstream along the forward-flank downdraft echo, after several
consistently negative differences in the preceding scans. Such changes in behavior
of the storm microphysics may be related to changes in entropy (e.g., increased
Z could mean more precipitation produced by condensation and accretion aloft,
indicating a positive entropy anomaly). A positive DZ
DR
along the forward flank
indicates suddenly larger drops are falling there, as a result of enhanced size sorting
or some other process.
It is interesting to note that this case is an excellent example of baroclinicity
development at the front edge of RFD, (see Fig.
18.5
for schematic illustration,
applying the righthand rule of Fig.
18.1
), which is known as favorable for tornado-
genesis (
Lemon and Doswell 1979
). However, a tornado did not develop from this
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