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S'
RR
W Entropy anomaly estimated from radar reflectivity,
(18.43)
S'
DR
W Entropy anomaly estimated from differential reflectivity.
(18.44)
In this experiment, for simplicity, we assume that
S'
RR
' L
=
T DZ
(18.45)
and
S'
DR
' L
=
TDZ
DR
:
(18.46)
where L is the latent heat of phase transition of microphysical process, excluding
non-phase transition processes such as advection. It will be discussed in Chap.
11
for a selected process. Note that the instantaneous cloud physical phase change
(Fig.
18.15
) should be captured better by a small temporal interval dt in ((
18.40
),
(
18.41
), (
18.42
), (
18.43
), and (
18.44
)) because the time scales of the environmental
atmospheric flow system, supercell, mesocyclone, and tornado are much larger.
However, as we discussed in Sect.
18.7
(D), the advection term of the wrap-around
mechanism is the needed important nonlinear process to include for tornadogenesis.
However, for simplicity, we focus our initial testing of the entropic balance theory
on the diabatic heating and cooling d'Q estimates on a moving coordinates with
tornado from radar observations.
18.11
Estimating Entropy from Polarimetric Radar Data
As discussed in previous chapters, the entropic sources and sinks can be created by
evaporative cooling or condensational heating:
d'Q D TdS
;
same as
.18:26
b
/
and
.18:39/
(18.47)
where d'Q is the heating or cooling. To estimate what changes in entropy dS could
look like in radar data, we make use of the evaporation model of
Kumjian and
Ryzhkov
(
2010
). In this simplified one-dimensional model, raindrops in the 3 km
column evaporate as they descend to the surface. Evaporation leads to a decrease in
radar reflectivity Z and an increase in the differential reflectivity Z
DR
(e.g.,
Li and
Srivastava 2001
;
Kumjian and Ryzhkov 2010
). The magnitude of these changes in
the radar variables depends on the initial drop size distribution (DSD) aloft as well
as the environmental conditions in the model domain. The cooling rate owing to
evaporation of liquid water can be expressed as (e.g.,
Pruppacher and Klett 1997
;
Bohren and Albrecht 1998
):
d'Q
=
dt D L
v
dm
=
dt
;
(18.48)
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