A reference atmospheric model describes how the ideal gas properties (namely: pressure, temperature, density, and molecular weight) of an atmosphere change, primarily as a function of altitude, and sometimes also as a function of latitude, day of year, etc.
"[1] For example, the U.S. Standard Atmosphere derives the values for air temperature, pressure, and mass density, as a function of altitude above sea level.
Assuming density is constant, then a graph of pressure vs altitude will have a retained slope, since the weight of the ocean over head is directly proportional to its depth.
This atmospheric model assumes both molecular weight and temperature are constant over a wide range of altitude.
The increase in altitude necessary for P or ρ to drop to 1/e of its initial value is called the scale height: where R is the ideal gas constant, T is temperature, M is average molecular weight, and g0 is the gravitational acceleration at the planet's surface.
Using the values T=273 K and M=29 g/mol as characteristic of the Earth's atmosphere, H = RT/Mg = (8.315*273)/(29*9.8) = 7.99, or about 8 km, which coincidentally is approximate height of Mt.
The U.S. Standard Atmosphere model starts with many of the same assumptions as the isothermal-barotropic model, including ideal gas behavior, and constant molecular weight, but it differs by defining a more realistic temperature function, consisting of eight data points connected by straight lines; i.e. regions of constant temperature gradient.
[3] The GRAM series also includes atmospheric models for the planets Venus, Mars and Neptune and the Saturnian moon, Titan.
This problem of decreasing g can be dealt with by defining a transformation from real geometric altitude z to an abstraction called "geopotential altitude" h, defined: h has the property Which basically says the amount of work done lifting a test mass m to height z through an atmosphere where gravity decreases with altitude, is the same as the amount of work done lifting that same mass to a height h through an atmosphere where g magically remains equal to g0, its value at sea level.