Entropic Balance Theory and Radar Observation for Prospective Tornado Data Assimilation - Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications - page 420

Chapter 18
Entropic Balance Theory and Radar
Observation for Prospective Tornado
Data Assimilation
Yoshi K. Sasaki, Matthew R. Kumjian, and Bradley M. Isom
Abstract This article reports further theoretical development on the entropic bal-
ance theory applied to tornadogenesis ( Sasaki 2009 , 2010 ), and the first preliminary
application of the theory to radar observations. The entropic balance is a newly
found balance, different from the other balance conditions, such as hydrostatic,
(quasi-)geostrophic, cyclostrophic, Boussinesq, and anelastic. The entropic balance
condition is described as the sole diagnostic Euler-Lagrange equation derived from
the Lagrangian of the variational formalism. The entropic balance is most general
and involves no additional assumptions other than for the flow with high Reynolds
and Rossby numbers estimated as appropriate for supercell storms and tornadoes.
The entropic balance theory and the deduced wrap-around mechanism explain well
the observations and simulations of tornado, RFD, hook-echo, upward tilting of
horizontal vorticity, the vertical in-phase superimposition between upper and lower
mesocyclones, and sudden transition from supercell, mesocyclones totornado. In
the application, new variables DZ (temporal difference of radar reflectivity) and
DZ DR (temporal difference of differential reflectivity) are introduced to compute the
entropy anomaly based on the entropic balance theory. The conditions necessary for
the transition from supercell to tornado are clarified from the theory and verified
from the DZ and DZ DR analyses for a non-tornadic supercell case compared with
VORTEX2 tornadic case.