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In the atmosphere, (see figure 1.15), we interpret:
is the pressure 
(1.10) 
is the vertical velocity in coordinates 
(1.11) 
is the geopotential height 
(1.12) 
is the buoyancy 
(1.13) 
is potential temperature 
(1.14) 
is the specific humidity 
(1.15) 
where
is absolute temperature 

is the pressure 



is the height of the pressure surface 



is the acceleration due to gravity 

In the above the ideal gas law, , has been expressed in terms of
the Exner function given by (see Appendix Atmosphere)

(1.16) 
where is a reference pressure and
with the gas
constant and the specific heat of air at constant pressure.
At the top of the atmosphere (which is `fixed' in our coordinate):
In a resting atmosphere the elevation of the mountains at the bottom is
given by
i.e. the (hydrostatic) pressure at the top of the mountains in a resting
atmosphere.
The boundary conditions at top and bottom are given by:


at (top of the atmosphere) 
(1.17) 


; at (bottom of the
atmosphere) 
(1.18) 
Then the (hydrostatic form of) equations
(1.11.6) yields a consistent
set of atmospheric equations which, for convenience, are written out
in coordinates in Appendix Atmosphere  see
eqs(1.59).
Next: 1.3.3 Ocean
Up: 1.3 Continuous equations in
Previous: 1.3.1 Kinematic Boundary conditions
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