 Let's look at four force balances. We'll start with diastrophic balance, which occurs in straight line flow in the free troposphere. In diastrophic flow, only the pressure gradient force and the Coriolis force are important. The pressure gradient points to low pressure on the high surface, or low height, and thus low geopotential, on a constant pressure surface. It is opposed by the Coriolis force, which is to the right of the velocity vector in the northern hemisphere, and to the left of the velocity vector in the southern hemisphere. Note that we can find the geostrophic velocity if we know the pressure gradient on a constant height surface or the geopotential or height gradient on a constant pressure surface. For inertial balance, the Coriolis force is balanced by the horizontal centrifugal force, with the Coriolis force to the right of the velocity vector in the northern hemisphere and to the left in the southern hemisphere. This balance is rarely seen in the atmosphere because there is almost always a pressure gradient force of the same magnitude as the centrifugal force and the Coriolis force. In cyclostrophic balance, the pressure gradient force is balanced by the centrifugal force. In this case, the velocity vector can be either to the right or to the left of the centrifugal force in both hemispheres, and the Coriolis force is much smaller. This balance is seen in tornadoes and other small vortices. In the northern hemisphere, tornadoes are mostly cyclonic, with only a few percent anti-cyclonic. While smaller vortices are about as often anti-cyclonic as they are cyclonic. For gradient wind bales, the pressure gradient force, Coriolis force, and horizontal centrifugal force are all about equal. The two physical cases are shown for the northern hemisphere in the figure, along with the geostrophic balance. For the cyclonic gradient, that is, curvature around the low pressure center, the PGF points to the low in its constant as long as the pressure gradient is constant. In this case, the PGF is opposed by both the Coriolis force, which depends on the velocity, and the centrifugal force, which depends on the velocity squared. Since the PGF is constant, then the sum of the centrifugal and Coriolis force must be equal to it. And since they both depend on velocity, the velocity must be less than in the geostrophic case in order for it to be a forced balance. This velocity is called sub-geostrophic because it is less than the geostrophic velocity. For the anti-cyclonic gradient, which is flow around the high, the PGF points away from the high. It is joined by the centrifugal force, which means that the Coriolis force must be stronger in the geostrophic case than in the geostrophic case because it must balance both the PGF, which is the same in the geostrophic case, and the centrifugal force. The Coriolis force can only be greater if the velocity is greater. Thus, this velocity is called super-geostrophic because it is greater than the geostrophic velocity.