Dry Adiabatic Lapse Rate (DALR)
The dry adiabatic lapse rate is the rate of change of temperature with height of a parcel of dry air that moves about the earths atmosphere, whist satisfying the conditions below:
The air parcel is assumed to be:
1) Thermally insulated from its environment so that its temperature changes adiabatically as it rises or sinks, always remaining at exactly the same pressure as the environmental air at the same level, which is assumed to be in hydrostatic equilibrium...and
2) Moving slowly enough that the macroscopic kinetic energy of the air parcel is a negligible fraction of its total energy.
The actual lapse rate of temperature in a column of air is as follows:
Differentiating this expression for potential temperature and using hydrostatic balance and the ideal gas law, the lapse rate can be written as:
In a well mixed atmosphere the change in potential temperature Ø with height = 0. There the above equation is simplied and becomes the dry adiabatic lapse rate (DALR):
The DALR is ~9.8 K km^-1