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 “500 mb height map” 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, “height” contours can be used to express the same mathematical concept. “Height” 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.