Both CLAMPS and SPARC capture the expected semipermanent lifting of the stable surface layer that accompanies the initial wave (most easily seen as the 304-K isentrope
As depicted, the upper-tropospheric "frontal" boundary separating relatively warm and cold air masses reached as low as 9.5 km on 31 December along the 330-K isentrope
, eventually capping out at 13.0 km near 0000 UTC 2 January.
Is it a tilted isentrope
, a horizontal density gradient, or a combination of different variables?
If the wind field used in the total derivative is the geostrophic wind, then Petterssen frontogenesis is also related to the forcing for quasigeostrophic vertical velocity associated with the divergence of the component of the Q-vector normal to the isentropes
(e.g., Keyser et al.
During the genesis of extreme moist convection over west Texas ~0600 UTC 11 February (see Figure 15(a), where vertically erect isentropes
can be seen near 28.5[degrees]N, 29.5[degrees]N, and 31[degrees]N), the aforementioned precipitation bands formed close to the adjustments leading to the dual LLJ convergence zone.
Haynes and McIntrye  showed that potential vorticity can be diluted or concentrated only by flow across isentropes
and it cannot be created or destroyed within a layer bounded by isentropic surfaces.
Flow is approximately along isentropes
(thin lines); straight arrows indicate wind speed, curved ones turbulence.
The downward motion over the stratospheric fountain merely means that the isentropes
on which the air is constrained descend toward the wind direction.
The gray dashed lines are manually analyzed isentropes
at an altitude of I km AGL, which depict the horizontal gradient at that level.