Wind and Pressure

Introduction

Although the wind is, in itself, a very obvious constituent of the weather, it is also an important determinant of other elements of the weather at a location; such as, temperature and precipitation. From the general flow of air at a location, one can determine, to some extent, the previous history of the air. If this air had a long journey over lands to the north and arrived at some locality as a north wind, it would usually be cold (at least in the Northern Hemisphere). If the air came from the south, arriving as a south wind, it would usually be warm (again, in the Northern Hemisphere). Terrain effects, such as the location of mountainous regions in the vicinity of the locality may alter this general pattern. The water vapor in the air, which is the source of any clouds and precipitation, seldom is obtained locally, but is usually transported from distant regions by the wind. Therefore, it is important to know where the air has been; i.e., where it is coming from, to be better able to forecast the type of weather it will produce in your locality.

Air moves because of an imbalance in the forces acting on the air molecules. Newton's second law of motion states that the rate of change of momentum of a body is proportional to the force acting upon the body and is in the direction of the applied force.

There are many forces interacting which cause the air to move in the manner it does. Wind is the atmosphere's way of trying to bring the interaction of these forces into a balance; an equilibrium. However, the factors that cause the imbalance are constantly changing so the balance is never achieved and the air molecules move, which is wind. The forces acting on a molecule of air may be considered at real forces and apparent forces as listed in the following table.

Table 1. Forces acting on an air parcel in a
rotating coordinate system

Real Forces
Horizontal Pressure gradient force
Vertical Pressure gradient force
Gravity
Centripital force
Friction

Apparent Force
Coriolis force

Since we are on the Earth's surface and the Earth is rotating, our frame of reference (our coordinate system) is moving, changing direction. The proper coordinate system is one with the origin at the Earth's center but which does not rotate with the Earth. However, as observers on the moving Earth surface, our reference (the Earth's surface) is moving, so, it is convenient to introduce apparent forces which account for the acceleration (the change in direction) of our frame of reference and which accounts for the observed motions of air parcels. We can thus call the forces acting on air parcels as real forces - those which exist regardless of our frame of reference, - and apparent forces. - those which we use to account for observed motions of air parcels due only to our moving frame of reference.

Vertical Pressure Gradient Force and Gravity

We mentioned in the exercise on pressure that air is a fluid and that the atmospheric pressure measured at any height above sea level may be considered as an expression of the effects of the air molecules above that level. The molecules of air are trying to move toward the earth because of gravity, just as you would fall toward the earth if you jumped off a chair. Then, why don't the molecules high in the atmosphere move toward the earth and cause a very dense atmosphere? It is because the molecules below the level at which we are measuring pressure are also pushing upward, besides pushing downward and sideways.

Imagine a parcel of air, like a balloon. The molecules of air above this parcel/balloon are pushing downward on the parcel. Also acting on the parcel and trying to move it downward is gravity. The molecules of air below the parcel/balloon are pushing upward. When the forces are in balance, the parcel neither moves up or down.
If the sum of the downward directed pressure gradient force plus gravity is greater than the upward directed pressure gradient force, the balloon/parcel will move downward.

Conversely, if the sum of the downward directed pressure gradient force plus gravity is less than the upward directed pressure gradient force, the balloon/ parcel will move upward.

Horizontal Pressure Gradient Force

To understand the wind systems which are so important in meteorology, one must first understand the pressure systems which result from the imbalances mentioned earlier and which determine the direction and speed of the wind.
In the exercise on pressure, we went through a discussion concerning warming a column of air and cooling a column of air.
In the warm column, the pressure at the level of 5,500 meters was greater than originally (600 hPa rather than 500 hPa).

In the cold column, the pressure at the level of 5,500 meters was less than originally (400 hPa rather than 500 hPa). The difference in pressure between the two columns initiated air molecules to begin flowing from the regions of higher pressure in the warm column to the lower pressure in the cold column.

This image below shows the resultant air circulation between the two columns.

Air is moving (wind) from the region of high pressure (for example: 600 hPa) at upper levels in the warmer column of air (such as exists near the equator) toward the lower pressure (for example: 400 hPa) at upper levels in the cooler columns of air (such as exists near the polar regions).

Near sea level air is moving from the high pressure (for example: 1004 hPa) in the cooler column toward the lower pressure (for example: 996 hPa) in the warmer column. Notice the pressure at the bottom of the column change as molecules leave the warm column at upper levels and are added to the cold column. Again, the top of the columns are representing the level of the troposphere.
This difference in temperature results in a difference in pressure which initiates the movement of air from one location to another.

If we consider this process on a hemispheric scale, on an ideal planet (only the pressure gradient forces and gravity acting, no Coriolis force, Centrifugal Force or friction) and the surface is the same substance with no mountains, we should see a similar pattern to the air flow as we did for the above considerations; such as this one to the right.

From our example, the difference in pressure near sea level between the two columns is 8 hpa, (1004 hPa - 996 hPa). We'll call this , the change in pressure. Let's say that the warm column of air is at the equator and the cold column of air is at the north pole. Then, the distance between the center of these two columns would be approximately 10000 kilometers, roughly one-fourth of the circumference of the Earth. This is the distance between the two pressure values along the surface of the earth. We'll call this distance . The horizontal pressure gradient is then defined as:

Horizontal Pressure Gradient =

or,

Horizontal Pressure Gradient = 8 hPa/10000 km = 0.0008 hPa/km.

This is of small magnitude because the distance we are considering (equator to the poles) is so large, however, this effect exists throughout the atmosphere, wherever there is a difference in temperature which produces a pressure difference.

At those locations where the temperature difference is large, (producing a large pressure difference) and the distance is small, the horizontal pressure gradient will be large.

Remember, that pressure is force/area. The horizontal pressure gradient then gives us an expression for the magnitude of the force causing the molecules of air to move horizontally from the region of high pressure toward the region of lower pressure.

If we were to graph the pressure values between stations along a straight line from the first station to the last, we might have a graph similar to this one. As can be seen from the graph, the horizontal pressure gradient is then just the slope of the line connecting the plotted values. Where the slope is steep, there is a large change in pressure in a short distance.

If we analyzed a surface map for sea level pressure and kept the interval between the isobars constant (at 4 hPa), then 4 hPa could be used as our value. Then, the greater the distance between the isobars on our analyzed surface map, the , the smaller will be the horizontal pressure gradient force and the weaker will be the wind.

Problem 1.

Open this sea-level pressure analysis map.
Considering only the analysis of sea level pressure in Texas, Arkansas, Florida, and Pennsylvania, rank the states according to which state should have the fastest surface winds as number 1, to the state which should have the slowest surface winds as number 4.
Record your answers on the answer sheet.

At upper levels, we can use the difference in height of a particular pressure value and obtain a similar expression which relates to the magnitude of the force causing the molecules to move. This is called a height gradient.

Consider this figure. Let's assume that 500 hPa (at the yellow line) was measured at a height of 5880 meters in the warm column of air and 500 hPa was measured at a height of 4800 meters in the cool column of air. Then the height difference for the pressure of 500 hPa between the two column would be 1080 meters. Let's call this . The distance between the columns, , is still approximately 10000 kilometers. Then the Height Gradient would be:

Height Gradient =

= 1080 m/10000 km, or 0.108 m/km.

Problem 2.

Open this figure.
Consider the isoheights (the black lines) on this image. Compare the analysis along the west coast of the United States to the analysis along the east coast of the United States. Which coast should have greater wind speeds at the 500 hPa level, the east coast or the west coast?
Record your answer on your answer sheet.

If we were to look down at a small volume of air under the infuence of a horizontal pressure gradient force, (the pressure gradient force is directed horizontal to the Earth's surface, not vertically upward) it might look something like the figure to the right below.

The straight lines are either isobars or isoheights and the LOW represents a region of either low pressure or low heights and the HIGH represents either a region of high pressure or high heights.

Under no other forces, the volume of air would move in the same direction as the pressure gradient force (the black arrow), directly from the high (pressure or height) region to the low (pressure or height) region.

Coriolis Force

You have seen, again by the figure at the right, that with an ideal earth, air should rise near the equator, move toward the poles in each hemisphere at upper levels, descend near the poles and move equatorward near the earth's surface. This is the type of air movement that would occur if the earth were not rotating. The earth, however, is rotating and for an observer standing on the earth's surface, the coordinate system (by which they are evaluating the wind direction and wind speed), is also moving.

Consider the figure to the right. The plane begins flying from the north pole straight towards the bottom of the image; i.e., toward the south along the 0^o longitude line. Let's say it is headed for London, England. However, as the plane moves, the earth's surface is moving toward the east beneath the plane. If at every hour, you were to mark the position on the earth's surface directly below the location of the plane, (yellow and black dots), you would find that the plane's path, on the earth's surface, would seem to curve (to the right of the direction the plane is moving). But from the perspective of a person looking down on the earth and not moving with the earth, you can see that the plane is traveling in a straight line, toward the bottom of the image. Because we are observers on a moving earth surface, we must use the Coriolis force to account for this apparent movement of the plane to the right of its path. After the earth has turned 1/4 turn on its axis,our plane would be flying towards the United States somewhere west of the Great Lakes, not England.

The moving wind on the earth can be considered similar to our plane. It begins moving toward one direction, but the earth's surface moves eastward beneath it. The rotation of the earth requires this apparent force, the Coriolis Force, to account for the average wind direction we obtain when we (weather observers on a rotating earth) measure wind direction. It is considered apparent because from the perspective of an observer located on the earth's surface, the air appears to change direction whereas the change actually results from the observer's movement, the moving coordinate system of the observer.

Now consider what an observer would see. The image to the right shows some arrows pointing from London, England, towards the plane. We have an observer in London telling us where the plane is going. The arrows point from London toward the plane represent the line along which the observer is looking. They appear curved on this flat image but on a curved globe, they would be straight lines pointing toward the plane.
Notice what happens to the observer's line of sight. It begins by pointing north, but as the plane and earth move, the line of site moves toward the northwest and finally toward the west, making it appear to the observer that the plane is curving toward the west.

Simarly, when an air mass (in the northern hemisphere) moves directly south, to an observer located on the moving earth's surface, it will seem as if the airmass is curving toward the right of its initial direction of motion. If we put the plane at the south pole and it flew directly north, to an observer in the southern hemisphere the plane would appear to turn toward the left of its original direction.

Now, consider a parcel of air located at the equator which will begin moving toward the north. (Note: This simplified explanation considers only the linear motion of an air parcel moving from near the equator toward the poles rather than the angular motion of the parcel which should be taken into consideration. However, for our purposes, the following is sufficient.)

This parcel of air located at the equator is calm (not moving) with respect to an observer located on the Earth's surface, we know this parcel is actually moving at the same velocity as the Earth's surface at the equator. We can determine how fast the Earth's surface is moving and thus, how fast the parcel of air at the equator is also moving by the following procedure.

At latitudes away from the equator, the rate of motion of the Earth's surface is less since the distance traveled in 24 hours is less. For example, at 30^oN, using the figure below, the radius of motion can be determined as shown.

Problem 3.

Using the same procedure, determine the rate of motion of the earth at 60^oN. The dashed lines are given in the above figure to aid you.
Record your calculations and answer on your answer sheet.

Problem 4.

What is the rate of motion of the earth's surface at the North Pole and the South Pole?
Record your answer on your answer sheet.

Now, consider a parcel of air near the equator, initially moving toward the east at the same velocity as the earth underneath it, (1668 km/hr). To an observer on the earth's surface at the equator, however, the air would seem to be not moving. They would record a calm wind.
Due to a horizontal pressure gradient force acting on the parcel of air, the air begins moving northward while retaining the same motion toward the east.

However, as the air parcel moves towards the poles, the Earth's surface underneath the parcel is not moving eastward as rapidly. When the air arrives at 30^oN latitude, the Earth's surface is moving eastward at 1444.5 km/hr but the air parcel is still moving eastward at 1668 km/hr.

Thus, to observers on the Earth's surface at 30^oN, it appears that as this parcel has been moving toward north latitudes it has been given an eastward component which seems to make it move faster toward the east at 223.5 km/hr. Thus, in the northern hemisphere its path appears to curve right as shown in the above image.

Thus, we have the horizontal Pressure Gradient Force acting on air parcels trying to make them move directly from regions of high pressure to regions of low pressure and also acting on the same air parcel is the Coriolis Force trying to make it move to the right of the direction the horizontal Pressure Gradient Force starts it moving. The actual direction the parcel moves depends on the magnitude of these forces and the direction the forces are acting.

In the southern hemisphere, the path would appear to curve toward the left. For the whole earth, the general wind pattern would appear as shown below. This wind pattern is called the general circulation, global circulation, or primary circulation. Know this image

Notice that because of the rotation of the earth, the one cell of circulation in each hemisphere has become three cells with air rising at the equator and at 60^oN and 60^oS. These are regions of generally LOW sea level pressure. Air now sinks at about 30^oN and 30^oS and also at each pole. These are regions of generally HIGH sea level pressure. The region of the jet streams are generally regions where there are significantly different average temperatures of the columns of air to the north and south of the jet location, producing a horizontal pressure gradient of high magnitude and thus strong winds.

Near the equator, air near sea levels is converging along the Intertropical Convergence Zone (ITCZ). Winds in this region are generally light and the region is often called the Doldrums.

Because the air is generally rising, the region is characterized by much cloud cover and precipitation. The ITCZ can be seen as a band of clouds along the center of this image near the equator. North and south of this ITCZ are bands showing very little cloudiness and then poleward of these relatively cloud-free bands are regions showing the whirls characteristic of cloud cover about the extratropical low pressure centers which are moving near the polar front zones.

The cumulonimbus clouds associated with the ITCZ just north of Australia, can be seen on this image as bright spots with thin anvil clouds extending outward.

The result for our little volume of air which is under the influence of both a horizontal pressure gradient force (black arrow) and a Coriolis force (red arrow - always acting to the right, in northern hemisphere to the direction of movement of the

air) will eventually look like the image above after the parcels path goes through a few oscillations.

The parcel will eventually settle on a path which is in a direction parallel to the contours (for air parcels above the near ground friction layer, so the force of friction, discussed later, is negligible), as shown by the last position of the air parcel in the above figure.

The magnitude of the Coriolis force is, in part, dependent on the latitude of the volume of air that is moving, and also on the velocity of movement of the volume of air.

The faster the air moves, the greater is the magnitude of the Coriolis Force. As our parcel of air (under the influence of only the horizontal pressure gradient force and the Coriolis Force) moves from the region of high pressure/height toward the region of low pressure/height, it curves to the right (in the northern hemisphere) until eventually it is moving parallel to the isobars/isoheights. Movement parallel to the isobars/isoheights occurs when the wind speed increases sufficiently such that the pressure gradient force and the Coriolis force are of the same magnitude and directed in the opposite direction to each other; they are in balance.

Problem 5.

On your answer sheet is an image similar to the one above, but without the forces shown or the arrow showing the movement of the air parcel. Assume that this air parcel is located in the Southern Hemisphere. Assume that the parcel has "settled on a path", (i.e., no change of direction is occurring). Draw an arrow showing the direction of the horizontal pressure gradient force acting on the parcel, another arrow showing the direction of the Coriolis force acting on the parcel, and a double arrow showing the direction of the movement of the parcel. Note: We are assuming that forces acting vertically (gravity and vertical pressure gradient forces) balance to zero.

Centripetal Force

As you can see on the image of the general circulation pattern, the Polar Front Zone lies near 60^oN and 60^oS. The image shows a series of wave patterns along this zone. As warm air from the high pressure region near 30^oN and 30^oS moves toward the poles and as cold air from the polar regions moves toward the equator, it does so in a series of wave-like motions. Associated with these wave motions are systems called extratropical lows or wave cyclones and high pressure/isoheight centers. These waves and associated wave cyclones are produced, in part, by the difference in heating between land and ocean areas. Poleward of this frontal boundary lies generally cooler air and towards the Equator lies generally warmer air. The boundary separates air of sufficiently different temperature that strong winds are associated with the Polar Front boundary and the associated wave cyclones along the boundary. The general region of the movement of the wave cyclones tends to move poleward during the summer months of each hemisphere and equatorward during the winter months of each hemisphere. Air flows about these centers low centers in counterclockwise (cyclonic) manner and about the highs in a clockwise (anticyclonic) manner. In order for an air parcel to continue changing direction to move about these centers rather than to move in a straight line, a force must be acting to change the direction of the air parcel. This force is called the centripetal force, an inward acting force. It always acts toward the central location about which the air parcel is turning. On upper-air maps, a centripetal force must be acting to cause the air to curve about the troughs and ridges. The magnitude of the centripetal force is given by:

where v is the wind speed and r is the radius of the winds movement along a curved path; either about a cyclone, an anticyclone, a trough, or a ridge. From the equation for centripetal force, you can see that the greater the magnitude of the wind speed, v, the greater in magnitude will be the centripetal force. Also, the smaller the magnitude of the radius of curvature, r, the greater in magnitude will be the centripetal force.

With the horizontal pressure gradient force (PGF), the Coriolis force (C.F.), and the centripetal force (Cent. F) acting on a parcel of air, the result will be as shown below, with the air parcel finally settling on movment parallel to the isobars/isoheights.

Although the above figure shows the forces about a low center and a high center, the same forces occur any time the parcel moves on a curved path. The curving, wave pattern can easily be seen on upper air maps. The air is moving parallel to these isoheights. This figure shows a series of wave patterns with troughs and ridges.

Problem 6.

On your answer sheet is a section of this figure taken from near the Great Lakes. Imagine that the dot on the figure on the answer sheet is an air parcel subject to a horizontal pressure gradient force, a Coriolis Force and a centripital force. Use short arrows to draw the forces acting on the air parcel in the same manner arrows were used in the above figure. Use a double arrow to show the direction the air parcel is moving.

Friction

Friction always acts opposite to the direction of movement of the air. Near ground level, the magnitude of the frictional force is large and friction plays a significant role in trying to slow the air's rate of movement. Over rough terrain, such as mountainous regions, friction is quite significant. Above about 1000 meters (about 3,300 feet above ground level), the magnitude of the frictional force becomes negligable. Thus, on upper-level maps, the main forces acting on the air molecules to make them move horizontally are only the horizontal pressure gradient force, the Coriolis force, and - where the air parcel is moving in a curved path - the centripetal force. Again, we are assuming here that vertical forces balance to zero. Near ground/sea level, the horizontal pressure gradient force, Coriolis Force, centripital force and the frictional force are all important forces when considering the horizontal direction and rate of movement of air. The figure below shows the effects of friction when included with the horizontal pressure gradient force and the Coriolis force for non-curved flow.

Since friction reduces v, the speed of the wind, then the Coriolis force and the centripetal force are also reduced in magnitude since they are a function of wind speed. Now, as can be seen by the image above, the horizontal pressure gradient force is balanced by the resultant of the friction force and the Coriolis force. The resultant of these two forces is labeled the resultant force in the image above. It is not a new force, rather it is simply showing the effect that the Coriolis force and the friction force have in a direction opposite to the horizontal pressure gradient force.

Tertiary Circulation

The forces we have been considering operate in the global scale of circulation as well as very small scales of circulation. We have discussed the global or hemispheric scale of motion when considering large columns of air near the poles. Also, we have looked at the secondary circulaiton, sometimes called synoptic circulation, in which we saw troughs, ridges, low pressure/height centers and high pressure/height centers which are produced by differences in heating between oceanic and continental land areas. Lastly, we will consider tertiary circulation, which deals with circulations from about 100 square kilometers down to the smallest size. Consider the image below.

Because this is a water surface and a land surface, we know that there will be a difference in the maximum temperature to which each surface will warm during the day and the minimum temperature to which each surface will cool during the night, even though each surface may receive equal amounts of solar radiation. The temperature of each surface will cause either warming or cooling of the air above the surface, depending on whether the land or water surface temperature is warmer or cooler than the air above it. Remember that in summer, land will warm to a higher temperature (than water does) during the day and cool to a lower temperature (than water does) during the night. Also, you know that as air warms, it becomes less dense and rises; and that if it rises sufficiently, it will cool by adiabatic cooling to the dew point and clouds will begin to form. Similarly, descending air will warm.

Problem 7.

Consider the image above and on your answer sheet, draw arrows to show the vertical and horizontal motion of the air in each situation. One is for a daytime situation and one is for a nighttime situation. Also draw a cumulus type cloud to indicate where clouds should form in each situation; either over the water or over the land.

Consider the image below showing a valley region in the mountains. Again, you know that land will warm during the day and cool at night. As air warms, it becomes less dense and will rise. As air cools, it becomes more dense and sinks.

Problem 8.

On your answer sheet, draw arrows to indicate air movement for each situation. Draw clouds where you would expect clouds to form in each situation.

DAYTIME - AFTERNOON

NIGHTTIME - JUST BEFORE SUNRISE

This concludes this exercise. Please close Netscape and sign off.

		Air is moving (wind) from the region of high pressure (for example: 600 hPa) at upper levels in the warmer column of air (such as exists near the equator) toward the lower pressure (for example: 400 hPa) at upper levels in the cooler columns of air (such as exists near the polar regions).
		Near sea level air is moving from the high pressure (for example: 1004 hPa) in the cooler column toward the lower pressure (for example: 996 hPa) in the warmer column. Notice the pressure at the bottom of the column change as molecules leave the warm column at upper levels and are added to the cold column. Again, the top of the columns are representing the level of the troposphere. This difference in temperature results in a difference in pressure which initiates the movement of air from one location to another.