438 DANIELSEN NORTH SOUTH NORTH SOUTH FRo Nigc} On,& NORTH SOUTH NORTH SOUTH Fig. 1—Schematic illustrations of tropopause folding and tropospheric frontogenesis. Lower right diagram is erroneous conventional analysis of lower left diagram. Thin lines represent potential temperature. energy, the potential vorticity can be derived, Its exact and approximate mathematical forms are, respectively, P=aVe- (Vx V + 2) and 00 Py “~8 op (fq + f) where P = potential vorticity a@ = specific volume V = wind velocity Q = angular velocity of earth © = potential temperature p = pressure g = acceleration of gravity Eg =K-VxXV, f=K- 22 K = unit vector in vertical Excluding vertically oriented © surfaces, the approximate form is sufficiently accurate for our purposes and more readily evaluated. In