Hypsometric Relation

Heating the atmosphere causes it to expand (special application of the gas law, explained below) obtained by substitution of the hydrostatic equation (4) into the equation of state.(1).  This relation provides the basis of explaining many, many things that synoptic meteorologists see on weather maps and charts.

Thickness of layer between two pressure surfaces is directly related to the mean temperature of the layer.

Also, if we consider the thickness of a layer that is often of importance to synoptic meteorologists, the layer approximately between the ground (1000 mb) and about 6 km (500 mb), the Hypsometric Relation is

where k = R/g ln 2 and ∆Z is the thickness of the layer between 1000 mb and 500 mb and Tv is the Virtual Temperature, which we will assume here is very close to the actual temperature.