Prioritize...
At the end of this section you should be able to describe how the pressure gradient force, the Coriolis force, and friction act to determine the wind direction and speed. More importantly, you should know how to determine the geostrophic wind and surface wind direction given a map of sea-level pressures.
Read...
Now that we've learned about all of the forces that play a role in determining the speed and direction of the wind, let's consider a sample air parcel released in a uniform pressure field. To examine the contribution of each force, we'll look at this interactive force diagram (keep the window open for the duration of our discussion). This tool will help you see the effects of adding various forces to a parcel of air. We'll look at the magnitudes and directions of the forces acting on the air parcel as well as its velocity (the "wind" also has magnitude and direction). By convention, I'll use arrows to keep track of the pressure-gradient force, friction, the Coriolis force and the parcel's velocity.
To get your bearings on the interactive force diagram, first turn on the pressure-gradient-force (PGF) only. Make sure that the Coriolis force and friction are turned off for now. Change the magnitude of the PGF and watch how the spacing of the isobars changes. Also notice that the parcel's velocity increases as the PGF increases. Conversely, the velocity decreases as the PGF decreases. At this point, the velocity vector points northward, indicating an unrealistic wind direction on some fairy-tale planet that lacks both friction and rotation about its axis (no Coriolis force).
By the way, the parcel would continue to accelerate because there aren't any other forces to offset it. That's also unrealistic. Generally speaking, the atmosphere always works toward achieving a balance. Of course, when all the forces acting on a parcel are in balance, an object at rest will stay at rest and a moving object will move at a constant velocity (zero acceleration). Okay, how does the atmosphere achieve some semblance of balance? To answer this question, let's add the contribution of the Coriolis force (make sure the pressure-gradient force is "on" and friction is "off"). Remember that the Coriolis force is, in part, a function of latitude -- its magnitude is relatively small at low latitudes and relatively large at high latitudes. Select the latitude where you want the action to take place by moving the marker up (higher latitude and larger Coriolis force) or down (lower latitude and smaller Coriolis force).
Note that the Coriolis force exactly offsets the pressure gradient force in order for balance to occur. Of course, visually displaying how balance occurs is beyond our technical means, mainly because some of the subtle adjustments that the atmosphere makes are difficult to graphically model. Nonetheless, I can give you a general idea of what happens when an air parcel is artificially released in a uniform pressure field like the one shown on your interactive force diagram.
As the air parcel accelerates northward in response to the pressure-gradient force, the magnitude of the Coriolis force also steadily increases (please remember that the magnitude of the Coriolis force is also a function of wind speed). As a result, deflections to the right become greater with time. The greater deflection always means a new course adjustment for the air parcel. No matter how much the parcel deflects to the right, the Coriolis force always shifts its direction accordingly, making necessary adjustments so that it can continue to act 90 degrees to the right of the new path of the air parcel. In a nutshell, as the parcel accelerates, the direction in which the Coriolis force acts steadily shifts like an hour hand on a clock while the magnitude of the Coriolis force increases.
With the atmosphere's preoccupation with tidiness in mind, it should come as no surprise that the pressure-gradient and Coriolis forces eventually reach the balance you just observed on the interactive force diagram. Indeed, the hour-hand vector that represents the Coriolis force will eventually balance the vector representing the pressure-gradient force (in the case shown here, the vector clock reads 6 o'clock). At this point, there is no net force acting on the air parcel and, according to Isaac Newton, the parcel will cease its acceleration and continue to move in a fixed direction at a constant speed. In this case, the final direction of the air parcel is directly eastward (in other words, the wind blows from the west). Indeed, note that the velocity vector parallels the isobars on your interactive force diagram. I suggest that you experiment by changing the magnitude of the pressure-gradient force and observe what happens to the magnitude of the Coriolis force and the wind speed when the two forces are in balance. Is it clear to you that, no matter how large the pressure gradient becomes, the wind always will blow parallel to the isobars when only the PGF and the Coriolis force "duke it out?" Do you see the direct connection between the magnitude of the pressure gradient and the wind speed?
Don't let the idea that a parcel released in a uniform pressure field will end up moving parallel to the isobars rather than making a beeline directly toward the area of lowest pressure "blow you away." Such a result shows the huge impact of the Coriolis force. The name given to the wind that results when the pressure gradient force and the Coriolis force come into balance is geostrophic. If you're into the topic of word origin, "geo" means "earth" and "strophic" means "turning," a clear reference to the importance of the role of the Coriolis force in creating the geostrophic wind. Formally, the idealized state at which the pressure-gradient force and the Coriolis force are in perfect balance is called geostrophy.
The geostrophic wind is an idealized wind (it never really occurs in nature) Indeed, the real world is subject to friction, for example. So the geostrophic wind, which results from the picture-perfect balance of the pressure-gradient force and the Coriolis force, is unrealistic. True, the real atmosphere can, at times, get very close to geostrophic balance, particularly at high altitudes, where friction becomes negligible. So we can look at isobars on an upper-air weather map and immediately get an idea of the wind direction. How do we do this? First, always remember that the geostrophic wind blows parallel to the isobars, so that narrows down the possibilities for wind direction to essentially two choices. Now imagine standing on the map with the geostrophic wind at your back. Low pressure should be on your left in the northern hemisphere. This observation should allow you to make the right choice. This rule is an idealized form of Buys Ballot Law.
I will discuss upper-level winds in later lessons. For now, it's time to "ground" ourselves with a dose of reality, so let's add friction. Time to return to the interactive force diagram, but this time we will allow friction to act. Make sure that the PGF, Coriolis and frictional forces are all turned on so that we can simulate real game conditions on a surface weather map. Experiment with the magnitude of the pressure-gradient force and observe the resulting magnitudes of the Coriolis force and friction (and the directions they act) when the three forces are in balance. Also observe the magnitude and the direction of the surface wind. With regard to direction, imagine standing on the map with the surface wind at your back in the northern hemisphere. Low pressure should be on your left, but on average, it will lie about 30 degrees clockwise from your left arm. (the other form of Buys Ballot Law). More succinctly, the surface wind blows across the isobars inward toward lower pressure, crossing the isobars at an acute angle.
How was such a balance achieved? Once a parcel of air, which I'll again assume was initially at rest, starts to accelerate in response to the pressure-gradient force, friction instantly acts in the opposite direction. In relatively short time, the Coriolis force deflects the parcel ever so slightly to the right (remember, because friction acts to slow down the parcel a bit, the Coriolis force is initially a tad weaker than it was in the no-friction case). With the parcel's path no longer making a beeline directly toward lower pressure, the friction vector now points in a new direction because it always acts in the direction opposite forward motion.
As the speed of the parcel increases, the magnitude of friction also increases. Meanwhile, the Coriolis force gains strength as the parcel continues to accelerate, acting to deflect the parcel more and more to the right. Notice that both friction and the Coriolis force work to oppose the effects of the pressure gradient force. Again, it should come as no surprise that the atmosphere moves toward achieving a balanced state. Indeed, the Coriolis force and friction, both strengthening individually and as a team, eventually offset the pressure-gradient force, causing the parcel's acceleration to cease. From this point on, the parcel will move in a constant direction at constant speed.
Again, note that the final heading of the parcel takes it across the isobars inward toward lower pressure and away from higher pressure.
Over land, the wind crosses the isobars at approximately 30 degrees or so, on average. Over the ocean and Great Lakes, the crossing angle is generally less than 30 degrees, owing to less friction over usually smoother water (compared to rough land). In mountainous areas, where the effects of friction are greater, the crossing angle can be 45 degrees or even more. This difference can frequently be seen on weather maps (like the idealized map above).
Explore Further...
I should add a few comments about our treatment of how an air parcel comes into geostrophic balance. First, you should know that force balance described in this section is achieved almost instantaneously. In the explanation above, we slow things way down so that you might envision the process in a more linear fashion. Secondly, we assume a constant pressure gradient throughout the process of achieving geostrophic balance. This assumption allows us to focus solely on what is happening to the parcel without the complication of the background environment changing as well.
In the real world, this is not the case. As parcels move, they carry their mass with them. This movement of mass affects the surrounding pressure gradient in the same way that the movement of water in the two-compartment water box eventually equals out the pressure gradient between the two compartments. The change in the surrounding pressure gradient in turn causes the force-balancing process to alter (which causes more change in the pressure gradient, etc.). Eventually, through this process of geostrophic adjustment, the parcel ultimately achieves the force balance that we refer to as geostrophic balance. You might also suspect that the same logic holds true for the case of frictional wind... and in fact it does.
Key Skill...
Being able to determine wind direction from a map of isobars is a key skill from this lesson. Make sure that you do not move on from this page without this skill. You can use the interactive tool below to practice what you have learned. If you want to work from a paper copy, click for a printable map (once the window opens, right-click on it and select "Print Picture").
Recipe
When learning a new skill it often helps to have a recipe to follow. Here is a recipe to help you determine the geostrophic and surface wind directions:- The first thing that you should focus on is the geostrophic wind direction. Remember that the geostrophic wind always follows the isobars, with lower pressure on the left. If you're finding the wind direction for an upper-level wind (not at the surface), this is all you need to do. Remember that wind direction is always given as the direction that it is blowing from.
- Next, if you are finding a surface wind direction, you need to take the geostrophic wind (which you just determined) and turn it inward towards lower pressure. This is called the crossing angle -- it's the angle that the wind crosses the isobars. Remember that the crossing angle is typically around 30 degrees, but can range from as little as 10 degrees (over water) to more than 45 degrees (over mountainous terrain). Finally, don't forget to express the wind direction as the direction that it is blowing from.
So, are you ready to practice? Using the map below (or your paper copy) pick a point on the map and figure out the wind direction. To check your answer, hold down the left-mouse button over the location that you chose and the local wind vector will appear along with the wind direction expressed in degrees. The orientation of the arrow represents the local wind direction and the length of the arrow serves as a qualitative measure of wind speed. If the wind vector seems less intuitive than station-model winds, simply click on the Simulated Station Model in the menu below the surface analysis. This option will give you a quantitative sense of wind speeds. Keep in mind, however, that these wind speeds are simply a reference. This tool does not actually calculate the real wind speed (which can be a very involved calculation, especially for surface winds).
No matter what your preference is, you'll receive immediate feedback on how the pressure-gradient force and the proximity of closed centers of high- and low-pressure systems impact surface wind direction and wind speed. If, at any point, you're perplexed about the wind direction, simply select the Surface Wind Force Diagram to observe the balanced state between the PGF, the Coriolis force and the force of friction.
For the idealists, you might want to explore this interactive exercise by selecting the Geostrophic Wind Vector. In this way, you can observe the idealized wind (the geostrophic wind) that results from the balance between the pressure-gradient force and the Coriolis force (select the Geostrophic Wind Force Diagram to see the interplay between these two forces).
Watch...
Need a bit more help in determining wind direction? Check out this short video lecture that explains how to find the wind direction on a map of isobars.
Video Transcript: Determining Surface Wind Direction (under construction)