The property responsible for the distinctly different character of the troposphere and stratosphere is vertical stability. Because it applies even under motionless conditions and because displacements of air remain in hydrostatic balance, vertical stability is also referred to as static stability. Although forces are never far from hydrostatic equilibrium, vertical motions are introduced by forced lifting over elevated terrain and through buoyancy. Buoyantly driven motion is related closely to the stability of the atmospheric mass distribution. The latter, in turn, is shaped by transfers of energy between the Earth's surface, the atmosphere, and deep space. By promoting convection in some regions and suppressing it in others, vertical stability controls a wide range of properties.
REACTION TO VERTICAL DISPLACEMENT
Because of hydrostatic equilibrium, together with the compressibility of air, density decreases upward regardless of temperature structure (Fig. 6.5b). Thus, mean stratification invariably has lighter air configured over heavier air. This suggests stability with respect to vertical displacements. Were air incompressible, this would indeed be the case.
Consider an arbitrary air parcel, inside the layer pictured in Fig. 7.1. In a linear stability analysis, this parcel will be used to establish how the layer reacts to infinitesimal disturbances from equilibrium. Although the analysis focuses on an individual parcel, stability actually refers to the layer as a whole.
Suppose the parcel is disturbed by a virtual displacement δz′ = z′, where primes distinguish properties of the parcel from those of its environment.