6 - Air Pressure and Winds PDF

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Eleazar Horta...

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Air Pressure and Winds What makes the wind blow? This is a fundamental question and there is a simple answer: horizontal differences in air pressure are what caused the wind to blow. There are other forces that will modify the speed and direction of the wind, and we will discuss these in detail. However, horizontal pressure differences are the only force that can cause the wind to blow. In science, the term “pressure” refers to a force acting over a given surface area. With respect to air pressure, the force is due to the weight of the air above a particular location all the way up to the top of the atmosphere. For example, assume we have a square area on the surface at sea level that measures one inch on each side. Also assume that the square area is at the bottom of a column with vertical sides that go straight up to the top of the atmosphere. If we could measure the weight of the air in this column, we would find that it weighs approximately 14.7 pounds. The air pressure at the surface would therefore be 14.7 pounds per square inch. This pressure of 14.7 pounds per square inch is approximately equal to 1013.25 millibars, or 1013.25 hectopascals. Consider a box of air. The air molecules inside the box are continually moving around, colliding with the sides of the box and with each other. As the air molecules collide with the walls of the box, they are exerting a force on those walls. This force will increase if the number of air molecules goes up, which means there will be more collisions with the walls. This force will also increase if the temperature of the air goes up, which means that the air molecules are moving more quickly and therefore collide with the wall more energetically. Therefore, the air pressure will go up inside the box if either the mass of air increases, or if the temperature of the air inside the box increases. If we could make the box smaller with the same amount of air inside, there would be more collisions with the box walls and the pressure would increase. Ideal Gas Law The ideal gas law is the equation that relates the pressure, the temperature and the density of the gas to each other. The ideal gas law equation, which is also known as the equation of state, is: Pressure = (temperature) * (density) * (the gas constant)

(Gas Law)

Since the gas constant never changes, this can also be expressed as: Pressure ~ (temperature) * (density) This equation says that the pressure is proportional to the product of the temperature times the density. Note that for the purposes of this equation, the temperature must be

the absolute temperature, expressed in degrees Kelvin. Since the density is equal to the mass divided by the volume, the ideal gas law can also be expressed as: Pressure = (temperature) * (mass) * (the gas constant) (volume)

(Equation 1)

Or: Pressure ~ (temperature) * (mass) (volume)

(Equation 2)

Okay, you can relax. Although I am using equations here, you will not need to do any mathematical calculations with these equation. However, it is critically important to understand the insights that we can gain from the gas law. Consider Equation 1 above. Since the gas constant by definition does not change, we can ignore it from this analysis. Assume the temperature of a sample of air goes up. If the other quantities on the right side of the equation (mass and volume) remained constant, then the pressure must go up to keep the equation balanced. As we discussed previously, the pressure will increase because the air molecules are colliding with the sides of the box with more energy. What would happen if the volume increases while keeping the temperature and mass constant? The volume is in the denominator of the equation. If the volume gets bigger the fraction on the right side of the equation will get smaller. Therefore the pressure will go down. This should help you understand why the pressure of an air parcel will go down as it expands. In the real atmosphere, of course, is not possible for only one quantity to change at a time. Usually the temperature, volume and pressure all vary at the same time for a given mass of air. We will not be delving into the details of this equation, but this equation explains why air warms as it is compressed, such as while the air is sinking. This equation also explains why air cools as it rises and expands. Why The Wind Blows B A cold

warm

Consider the two columns of air illustrated above. Assume that the surface area in each column is the same, and that each column has exactly the same mass of air. The force exerted on the surface will be equal to the weight of the air in each column. Since the two columns have the same mass, they will exert the same amount of force on the surface. Since the two forces are acting on equal surface areas, the result will be that each column has the same surface air pressure. However, look at what happens above the surface, at the elevation of the red arrow. The warm column of air is taller than the cold column of air, because it is less dense and they have the same mass. The warm column of air extends much farther above the arrow than the cold column of air, so the mass of warm air above the arrow in Column B will be greater than the mass of cold air above the arrow in Column A. Therefore, at the elevation of the red arrow, the air pressure in Column B is higher than the air pressure in Column A. This is an important concept to understand. It illustrates how differences in temperature can result in horizontal differences in pressure. For this reason, warm air aloft is associated with high atmospheric pressure and cold air aloft is associated with low atmospheric pressure. As a gas, the air is normally free to flow wherever it is pushed. This “push” is due to horizontal differences in pressure. We will be discussing this concept in much more detail soon. In this situation illustrated in the figure above, the air will tend to blow from the region of higher pressure (Column B) toward the region of lower pressure (Column A). This is why the wind blows. The movement of the air will result in a reduction of the mass in Column B and an associated increase in the mass in Column A. This shift in the mass distribution will tend to even out the difference in pressure.

Pressure Gradient Force The pressure gradient force is the force that causes the wind to blow. The pressure gradient force depends on the difference in the air pressure between two locations at the same elevation, and the horizontal distance between those locations. Mathematically, the pressure gradient is equal to the difference in pressure divided by the distance between the two locations. If the distance remains the same, a larger difference in pressure will result in a greater pressure gradient force, and therefore stronger winds. If the difference in pressure remains the same and the distance between the two locations gets smaller, the pressure gradient will increase and the winds will get stronger.

The wind speed is directly related to the pressure gradient force. Stronger pressure gradients result in higher wind speeds. Weaker pressure gradients result in lower wind speeds. Measuring And Reporting Air Pressure The instrument that we use to measure air pressure is called a barometer. The original barometer was a mercury barometer invented by Torricelli. In the mercury barometer, the height of the column of mercury is proportional to the air pressure. In the metric system, the Newton is the unit of force and the square meter is the standard unit of area. The main unit of pressure in the metric system is the Pascal, which is equal to one Newton per square meter. One hectopascal is equal to 100 Pascals. The standard sea level atmospheric pressure is equal to 1013.25 millibars, or 1013.25 hectopascals, or 29.92 inches of mercury. In the United States, millibars and inches of mercury are the most commonly used units used to express air pressure. Mercury is a hazardous liquid, and mercury barometers are large and unwieldy instruments. For this reason, most home barometers are classified as aneroid barometers, which means they contain no fluid. The key component of an aneroid barometer is a small, flexible metal box. As the external air pressure goes up, the box is compressed. As the box compresses it moves a pointer to indicate that the air pressure has gone up. As a liquid, mercury will expand and contract as the temperature changes. Therefore, mercury barometer readings must be corrected to account for the actual air temperature. The force of gravity around the world is not constant, and variations in the force of gravity will affect the height of the mercury column, so mercury barometers must be corrected for these differences in the gravitational force. No instrument is perfect, and therefore every instrument has some built-in errors associated with it. Fortunately, these errors can usually be estimated fairly closely. After a mercury barometer reading is corrected for temperature, gravity and instrument error, this reading is referred to as the station pressure at that particular location and elevation. Some weather stations are on the ground at sea level, while other weather stations are far above sea level in the mountains. We have already learned that the atmospheric pressure decreases with altitude. To make it easier to compare the pressure readings between stations, barometer readings are also corrected for altitude. After the station pressure is corrected for altitude, the result is called the sea level pressure. When the air temperature decreases at the standard lapse rate of about 6.5 degrees Celsius per thousand meters, the atmospheric pressure will drop by approximately 10 millibars for every hundred meters of altitude change in the lower troposphere.

Surface Weather Maps Once the sea level pressure is calculated for each station, each of these pressure measurements can be plotted on a large scale chart. To help visualize the pressure distribution, lines are drawn on the chart that connect regions where the air pressure is the same. These lines are called isobars. Isobars are typically drawn where the air pressure is 1000 millibars, and at intervals of four millibars both higher and lower than this base. Once the isobars are plotted on the weather map, regions of high pressure and low pressure can be easily identified. If desired, arrows can be added to these weather maps to indicate the direction of the wind. At the surface, the wind will blow across the isobars at an angle of about 30 degrees toward the direction of lower pressure. Aloft, above the layer of friction, the wind will blow more closely parallel to the isobars. Although surface weather maps usually show the isobar pattern and therefore the pressure distribution, upper air maps are constructed differently. Instead of showing how the pressure varies as we move horizontally, upper air maps show how the altitude of a particular pressure level varies. For example, if we create a weather chart that shows the conditions at the 500 millibar level, this weather map will actually show lines that indicate how the altitude at which the air pressure is 500 millibars varies. The lines on this chart are called contour lines, and they represent points of equal altitude above sea level. The contour lines on an upper level chart are exactly analogous to isobars on a surface chart. Higher heights represent higher surface pressures. Low contour heights represent low surface pressures. The altimeter on an aircraft is essentially an aneroid barometer that is calibrated to indicate altitude instead of air pressure. When the pilot is flying with a constant altimeter reading, the plane is actually varying in altitude as it moves along a surface of constant air pressure. This does not create a safety hazard because all aircraft are affected equally. Sometimes the meteorologist is interested in the distribution of temperatures across a region. In this case, isotherms can be plotted on the weather map. An isotherm is a line that collects points of equal temperature. Newton’s Laws of Motion Sir Isaac Newton was one of the greatest scientists and mathematicians that ever lived. His laws of motion were developed about 300 years ago and they are still used today by scientists and engineers. Two of them are important to understanding the wind.

Newton’s first law states that an object at rest will remain at rest, and an object in motion will remain in motion at a constant speed along a straight line, as long as no net force is exerted on the object. For example, consider a book sitting motionless on a table. There are two forces acting on this book. The force of gravity is pulling the book down towards the floor. Since the book is not moving, this gravitational force must be balanced by a force that the table is exerting on the book, holding the book up. These forces are equal in magnitude and opposite in direction and they therefore cancel each other out. Since there is no net force acting on the book, the book will remain motionless. Newton’s second law states that the force exerted on an object is equal to its mass times the acceleration that results from that force. For example, consider a bowling ball. When the bowler throws the ball down the lane, the ball will experience a faster acceleration when it is thrown with more force. Or, if the bowler uses a lighter ball and throws it with the same force, the lighter ball will go faster because it has a smaller mass. Most people think of acceleration (or deceleration) as a change in the speed of an object. However, acceleration can also refer to a change in the direction of motion as well as the speed.

Newton and the Wind - Pressure Gradient Force Newton’s laws apply to the wind. If the atmosphere is initially still, the wind will not start to blow until there is a horizontal pressure gradient force that forces it to move. For the wind to change speed or change direction, there must be a net force acting on each small air parcel. We have already talked about the pressure gradient force, which is equal to the difference in atmospheric pressure divided by the distance over which that pressure difference is operating. The pressure gradient force is the only force that can cause the air to start moving. The pressure gradient force can be indicated on the weather map by looking at the spacing of isobars or the spacing of contour lines. When isobars or contour lines are closer together, this indicates a stronger pressure gradient and therefore faster winds. The pressure gradient force always acts directly from the higher pressure toward the lower pressure, at a 90 degree angle to the isobars. To illustrate: High Pressure 1008 mb isobar PGF

50 km 1000 mb isobar

Low Pressure

The pressure gradient force is illustrated by the red arrow in the figure above. In this example, the pressure gradient is equal to 8 millibars per 50 kilometers. If the pressure gradient force was the only force influencing the wind, the wind would always blow directly from a high-pressure region toward the nearest low-pressure region. However, once the wind starts to blow it is influenced by the Coriolis force.

Coriolis Effect (Coriolis Force) The Coriolis Effect occurs because we look at freely moving objects from a rotating reference frame - the rotating surface of the earth. The easiest example to visualize is to picture a missile being fired from the North Pole due south toward the equator along a line of longitude. IF THE EARTH WAS NOT ROTATING: An observer on the earth would see the missile traveling along a straight path, from north to south. An observer in outer space drinking Starbucks Coffee at an Intergalactic Truck Stop would also see the missile moving on a straight path. If the observer on earth were standing on the same longitude line along which the missile is flying, the missile would fly directly overhead. NOW LET EARTH ROTATE: The folks at the Intergalactic Truck Stop would still see the missile traveling along a straight line, due south. However, the observer on the earth’s surface is now moving. By the time the missile travels to the latitude where the observer is, the earth has rotated the observer away to the east. The observer would actually see the missile curving to the west (to the right of the missile path), even though the missile’s path was actually straight and due south. This is not due to the missile itself. This is because the earth is rotating under the missile, carrying the observer away from the missile path. This is a greatly simplified explanation, but it illustrates the major points. The Coriolis effect influences an object moving in any direction. The magnitude of the Coriolis effect is much smaller for vertical motion than for horizontal motion. Here is an illustration to demonstrate why Coriolis changes with latitude: If you are standing on the equator, facing east, the earth’s rotation will cause you to move forward, without any rotation at all. If you start moving to the left (north) while still facing east, you will begin to experience rotation as well as forward movement. By the time you are standing on the pole, your motion has become entirely rotation and the earth’s rotation will cause you to spin in place. You will experience no forward motion at all.

Mathematically, the Coriolis effect varies with the sine of latitude. At the equator, latitude = zero, and the sine of 0 degrees is 0. Therefore, there is no Coriolis effect on the equator. At the pole, the sine of 90 degrees is 1 (its maximum value), and the Coriolis effect is at its maximum. Key point: Coriolis is NOT a real force like gravity. It is an apparent force, due to observing a moving body from another moving body instead of from a stationary position. Key point: Although the Coriolis effect influences any moving object, the magnitude of the Coriolis effect is very small. For this reason, it is only noticeable on a freely moving object (such as the wind or an ocean current) over long distances. We would never notice the Coriolis effect influencing our car, because the frictional force between the road and the tires is much greater than the Coriolis effect. For the same reason, the Coriolis effect has nothing to do with the direction in which water spirals down a drain. In the northern hemisphere, the Coriolis effect will always be directed 90 degrees to the right of the direction of motion. In the southern hemisphere, the Coriolis effect will always be directed 90 degrees to the left of the direction of motion. If an object is not moving at all, the Coriolis effect will be zero. The Coriolis effect will increase as the object’s speed increases. For this reason, the Coriolis effect cannot cause the wind to blow, nor can it cause the speed of the wind to change. However, once the wind is already moving, the Coriolis effect can influence the direction in which the wind is moving. Friction The friction layer is the lower part of the atmosphere in which friction with the surface influences the moving wind. The friction layer is typically about 1000 meters, or 3300 feet, thick. It will be thinner if the surface is smooth (like over the ocean) and thicker if the surface is rough (like in a mountainous region). Geostrophic Wind Approximation Let’s look at what happens above the friction layer when the isobars are straight. Initially, the wind will be blowing directly from the high-pressure area to the low-pressure area, perpendicular to the isobars. In the diagram below, the wind will initially be blowing down the page. This is indicated by the black arrow and the letter “A”. Once the wind begins to move it will be influenced by the Coriolis effect. In the northern hemisphere, the Coriolis effect is always in a direction 90 degrees to the right of the motion, and it will tend to turn the wind to the right. The pressure gradient is still working to increase the speed of the wind. The Coriolis force is indicated by the blue

arrow. The diagram next to the letter B illustrates that the wind has turned to its right, and shows the directions of the Coriolis and pressure gradient forces. High Pressure 1008 mb isobar PGF
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