Conceptually,
the pressure gradient is the rate at which pressure decreases over
distance. On a level surface
(e.g., sealevel, 10000 feet, etc.) mathematically, this is estimated by the
terms

in
the Cartesian or rectangular coordinate system, and

in
the natural coodinate sytem

In
the example used in class, if the air parcel has dimensions of 100 km along the
x-axis, the pressure gradient would be evaluated

There
is no pressure gradient along the y-axis for this case.

As
we will see in future lectures, instead of looking at level surfaces,
meteorologists and oceanographers often look at constant pressure
surfaces. For example, we often
refer to the Ò500 mb height mapÓ that is rounded off to be about at around
18000 feet elevation.

On
a level surface, isobars can be used to express the pressure gradient. As we will see, on a constant pressure
surface, ÒheightÓ contours can be used to express the same mathematical
concept. ÒHeightÓ refers to the
elevation (usually in meters or decameters) above sealevel at which the given
pressure is found.

On
height maps, the expressions analogous
to those above are:

where
z is the height of the given pressure surface above sealevel (meteorology) and
above mean ocean surface levels (oceanography). Oceanographers commonly use these latter expressions to
develop their ideas about motion in the ocean.