Vertical Gradients in the Atmosphere - Terrestrial Hydrometeorology - page 33

δ z , along the vertical gradients of virtual temperature, T v , or virtual potential

temperature, q v , buoyant acceleration can be written as:

⎛⎞∂ T

g ⎛ ⎞

a =−

v

+Γ δ z

(3.22)

⎜ ⎟

⎜⎟ ⎝

p d

T ∂ z ⎠

⎝⎠

v

or:

⎛⎞∂
=− ⎜⎟ ∂

θ

g

a

v

δ z

(3.23)

p

θ z

⎝⎠

v

The static stability parameter, s , is defined from buoyant acceleration using this last
equation and has the form:

⎛⎞∂
=− ⎜⎟ ∂

θ

g

s

v

(3.24)

θ z

⎝⎠

v

The parameter s provides a quantitative measure of the static stability of atmos-
phere at any level in terms of the potential temperature gradient at that level. Thus,
the atmosphere is said to be:

(a) Unstable : when s Γ d

That is, when virtual temperature falls more quickly than the dry
adiabatic lapse rate - in which condition the atmosphere is said to be
superadiabatic .
(b) Neutral : when s

< 0, i.e., when (∂ q v ∂z) < 0 or (∂ T v ∂z) < −

Γ d
That is, when virtual temperature falls at the dry adiabatic lapse - in which
condition the atmosphere is said to be adiabatic .
(c) Stable : when s

= 0, i.e., when (∂ q v ∂z) = 0 or (∂ T v ∂z) = −

> 0, i.e., when (∂ q v ∂z) > 0 or (∂ T v ∂z) > − Γ d

That is, when virtual temperature falls less quickly than the dry
adiabatic lapse rate - in which condition the atmosphere is said to be
subadiabatic .

In addition, certain subadiabatic (stable) atmospheric conditions are further
distinguished by their gradients of virtual temperature, as follows:

(1) if T v is constant with height, the atmosphere is said to be isothermal;

(2) if T v increases with height, there is said to be an inversion,

Figure 3.4 illustrates how the vertical gradient of virtual temperature is used
to characterize atmospheric conditions. In Chapter 20 an alternative measure
of atmospheric stability is defined based on the turbulent fluxes through
the atmosphere.