Vertical instability

The vertical movement of an air parcel is governed by the vertical equation of motion

For a very small parcel that will not disturb the atmosphere when it moves vertically, we can assume

and

Let us move an air parcel from a reference level where the height is zero and the temperature is . At height z from the reference level, the parcel temperature and the environmental temperature can be expressed as

Substitute these equations into the vertical equation of motion

we get

Stability criteria

unstable

neutral

stable

Using similar argument, we can get

unstable

neutral

stable

For saturated atmosphere

or unstable

or neutral

or stable

Richardson Number and stability

For vertical stability without wind shear