Entropic Balance Theory and Radar Observation for Prospective Tornado Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 442

Fig. 18.14 Change of entropy. Note that dS is totally differentiable while 'Q is not, and dS D

.@ t C v r / S

18.10 Temporal Discretization of Radar Data

for Entropy anomaly

The hypotheses 1 and 2 used for the Lagrangian in Sect. 18.2 are restated here.
Hypothesis 1 states that microphysical phase changes of a small ensemble of
hydrometeor molecules is instantaneous, creating a new entropy level with adiabatic
conditions before and after the phase change, and having a much shorter time-scale
than the time-scales of convective storms and tornadoes,

t phase change << t supercell, tornado : same as ( 18.2 ) (18.38)

Hypothesis 2 states that variations of the initial entropy levels are small enough to
allow us to approximate them by their ensemble means. These hypotheses are shown
schematically in Fig. 18.15 .
The entropic source and sink are created by diabatic heating and cooling
(Fig. 18.4 ), and (18.26b) is rewritten as

.@ t S C v r S / D d'Q = T : same as .18:26 b / (18.39)