Vertical integration of the hydrostatic equation
The hydrostatic pressures correspond to the coordinate surfaces, and
are used to interpolate the non-hydrostatic pressure and Exner
functions, and the geopotential in a consistent manner.
The non-hydrostatic Exner function
at layer centers is computed as
 |
(195) |
The hypsometric equation
(the form defined by Eq. 20)
is used to obtain
the geopotentials on levels from
where
at the lower boundary.
Note that one can define the following consistent relationship
for the layer center geopotential as
where
can be equal to either
or
.
Subtracting Eq. 199
from Eq. 200
and solving for
yields Eq. 197.
Finally, by eliminating
between
Eq.s 199-200,
an equation which depends only on
and
can be defined as
 |
(200) |
This equation can be useful in particular during pre or post processing steps
when, for example, only
and
are known.
In the model, Eq. 199 is used to diagnose the geopotential at the
layer centers after
has been determined.