A Weather Moment

• ∂p/∂(x/y) refers simply to how quickly the pressure changes from West to East or North to South. This is known as the pressure gradient.
• ρ is the density of the air
• f is the Coriolis parameter
• v is the speed of movement

I’ll quickly go over what each of these are.

The Pressure

The pressure is simply a measure of the force the atmosphere exerts at a specific point. The most common pressure is MSLP, or mean sea-level pressure (which is always the “ground-level” pressure). It is what most of us see when we see the evening weather report on the news. This value is in reality a measure of the mass of the atmosphere. A higher pressure means you physically have more mass pressing down on a particular location. We can get a pressure from anywhere in the atmosphere. If we take it from some height above the ground, it is lower than what the MSLP is beneath it, since there is less air above that point than beneath it.

The Density

The density of air is the amount of mass in a cubic meter of it. This value pretty much never changes, except when moving up and down through the atmosphere.

The Coriolis Parameter

The Coriolis Parameter is a measure of the Coriolis Force, or the apparent curvature that shows up in atmospheric motions due to the earth spinning beneath it. The key thing to take away here is that it is only dependent on how far away from the equator the moving air is. The further towards the poles, the bigger the Coriolis Parameter

The Velocity

This is very simple, it is a measure of how fast the air is moving. This is essentially how fast the wind is.

What It All Means

The geostrophic approximation is based on a few basic assumptions:

• The Coriolis Force balances the horizontal pressure gradients
• The flow has no acceleration (the wind speed does not change)
• Horizontal velocites are much larger than vertical velocities
• The only external force is gravity
• The effects of friction are negligible

So what does this tell us? If we look at the first two equations for movements North/South or West/East, we can simplify them with everything we now know. We’ve said that density doesn’t change, and that the Coriolis force only depends on how close to the poles you are.

So, for any given point at any given time, we can simplify all this down to saying that the wind speed, v, is equal to the pressure gradient. Very simple, and very easy to understand. It is this basic principle that lets the weatherman on T.V. explain to you that as the back lines (of constant pressure, or isobars) become squished together, the winds will be faster. And as they become wider spaced, the wind speeds will die down.

If these black lines were isobars, we would see fast winds on the left-hand side, where they are bunched together, and slower winds where they are spaced further apart.

While what happens in the areas where we live (namely, the ground), are influenced by the fact that friction plays an important role, the general idea of the geostrophic approximation still holds. With this knowledge, you should be able to look at a surface map of Canada and the Northern US and very quickly determine if it will be windy wherever you’re interested. I’ll attach a surface map pointing out where, by using this simple theory, we can tell where winds may be a concern.

From this, we can see that it is going to be windy off the coast of British Columbia, through North and South Dakota, and into southern Manitoba. Ships in the eastern basin of Hudson Bay may experience some strong winds, and even some places in Western Greenland and extreme Northern Canada may be seeing some very strong winds!

Next week, separating the upper atmosphere from the boundary layer.