Definition of the pressure gradient

The pressure gradient is the change of pressure over a unit distance in a specified direction. The pressure gradient in the x direction is the change of pressure over a unit distance in the x direction. It is represented by

It is positive if the pressure increases with increasing value of x and negative if the pressure decreases with increasing value of x.

The pressure gradient in the y direction is represented by

Similarly, it is positive if the pressure increases with increasing value of y and negative if the pressure decreases with increasing value of y.

If no direction is specified, the pressure gradient is the resultant pressure gradient in the x and the y directions. Its magnitude is represented by

It is positive and its direction is perpendicular to the isobars and pointing to the high pressure, as shown in the arrows in the following figure.

In vector form, the pressure gradient is defined as

Computation of the pressure gradient

Suppose we have the following isobars.

There is no pressure change in the x direction, and therefore, the pressure gradient in the x direction () is zero. The pressure decreases in the y direction, and the pressure gradient in the y direction () is negative. There are several ways to compute the pressure gradient. The most commonly used method is to measure the distance between two isobars and divide the difference of the isobars by this distance. Suppose the distance between the isobars is 200 km. Than, = -4 mb = -400 Pa. = 200 km = 200000 m. and

The resultant pressure gradient is pointing toward south (negative y direction), as show in the above figure. In vector form

The direction of is pointing toward south and the magnitude of is

Now let us look at the following isobars.

Using the scale at the upper right corner of the figure, we find the distance between the 1000 mb and 960 mb lines across point A in both the x and the y directions is 300 km. The distance between these two isobars across point B in the x and the y directions is also 300 mb.

At point A,

At point B,

The resultant pressure gradient at both points are

and the direction of the pressure gradient is perpendicular to the isobars and pointing outward from the center of the low.

If we measure the distance on a line perpendicular to the isobars across A, we will find that this distance is about 213 km. The pressure gradient in this direction is therefore

This is the same as if we compute the pressure gradient using the vector notation, which gives