Entropic balance theory and radar observation for prospective tornado data assimilation

This article reports further theoretical development on the entropic balance 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 DZDR (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 DZDR analyses for a non-tornadic supercell case compared with VORTEX2 tornadic case.Since the entropic balance theory is found to fit well with all analyzed results of tornado and visual observations, it is suggested to use the entropic balance equation as a constraint for variational data assimilation in future development as a challenge.