Meteo 300  -- Introduction to the Atmospheric Sciences
Chapter 2 -- Thermodynamics  -- hydrostatic equation
 

A.  Hydrostatic equilibrium.

The atmosphere is in constant motion.  Yet despite this motion, the vertical motion is on average quite small.  To first order, we can assume that the vertical forces are in balance.  We will derive the Hydrostatic Equation based on the assumption that these forces are in balance.

Consider a slab of air with a thickness dz at altitude z.  If the air has density r, then the downward force on the slab due to gravity is g  r dz.  Now consider the force due to the pressure difference at the top and bottom of the slab.

-dp = g  r dz   or  dp/dz = - g  r

We can do the integration to get the pressure change with height, as I showed you a week ago.
 
 

B.  Geopotential.

The geopotential is the work that must be done against Earth's gravity in order to raise a 1 kg mass from sea level to altitude z.  The units are J kg-1, or m2s-1.  We can define the geopotential height as the geopotential divided by the acceleration due to gravity at the surface.
 
 
 

C. Scale height.

Usually we consider the scale height, H, to be equal to 7 km.  However, the actual scale height depends on the temperature structure of the atmosphere.  We can derive the equation for the scale height using the hydrostatic equation.
 
 
 

D.  Reduction of pressure to sea level.

The other day, I said that the ASOS pressure was listed as 1013 mb (hPa), when in reality, the pressure was closer to 950 hPa.  The ASOS system was reducing the pressure to sea level values.  Why do we need to reduce pressures to sea level values?