Objectives:

Although the atmosphere is almost entirely a gaseous fluid, it is a system with physical mass that responds to gravity and other forces such as those arising from pressure differences over distance (gradients). Gravity holds the atmospheric shell to Earth as a thin layer over the solid and liquid surfaces of the planet. Frictional coupling with the planetary surface causes the atmosphere to rotate with the planet. By isolating the forces that act on a parcel of air, we can explain observed air motions and the various scales of atmospheric circulation.

After completing this investigation, you should be able to:

• Describe the horizontal forces that act on air parcels.
• Show the directions toward which these atmospheric forces act.
• Relate these horizontal forces to the winds reported on weather maps.

Materials: Two “3x5” cards (or two cards 3 inches by 5 inches cut from stiff paper), scissors, tape, and pen or pencil.

Introduction:

Pressure Gradient Force

An air pressure gradient exists wherever air pressure varies from one place to another. This change in pressure over distance results in a force that puts air into motion.

1. Figure 1 to the right represents a portion of a surface weather map on which are plotted three straight, parallel isobars. Pressure is in mb units, and isobars are uniformly spaced and drawn with a 4-mb interval. [(High)(Low)] pressure is located across the top of the diagram.

Figure 1. Surface weather map section.

2. The diagram shows a pattern of air pressure changing over distance. Assuming that the atmosphere is initially calm, the only force acting horizontally on a parcel of air represented on the diagram at Point A is a pressure gradient force. Draw an arrow about a centimeter in length starting at Point A and aimed directly towards the top of the diagram that depicts the direction the pressure gradient force would act. Your arrow shows the pressure gradient force acting directly towards [(highest)(lowest)] pressure. This force is directed perpendicular to the isobar lines. The horizontal pressure gradient has given rise to a force that causes the air parcel at A to begin moving in the direction towards which the force is acting.

Coriolis Effect

Everywhere on Earth, except at the equator, objects moving freely across Earth’s surface travel along curved paths. This turning is produced by Earth’s rotation and is called the Coriolis Effect. The following demonstrates the impact of Earth’s rotation on horizontally-moving objects.

Directions: First construct a rotating card device with two 3x5 file cards (or two cards 3 inches by 5 inches made from stiff paper). Following Figure 2 below, (i) cut an approximately two and one-half inch straight slit down the middle of one card (A), and (ii) cut a slit about one and one-half inch long in the middle of the other card (B). Fit the cards together as shown (iii), and lay them flat on the desk or table in front of you. Tape card (A) to the table with the long slit as shown (tape is dotted rectangles). Bend up the lower left and right corners of the loose card (B) to use as tabs. Pull the loose card horizontally towards you until the ends of the cuts meet to form a point of rotation. Be sure the moving card (B) can turn clockwise and counterclockwise around the point of contact. Make an X to mark the spot around which the card rotates.

Figure 2. Construction of a rotating card device to study the Coriolis Effect.

3. Orient the cards in the “cross” position as shown in the drawing (iii). Place your pencil point at X. With the cards motionless, carefully draw a line on the loose card (B) along the cut-edge and directly away from you. The line you drew represents a path that is [(straight)(curved)].

4. Now investigate how rotation affects the path of your pencil line. Again, begin with the cards in the “cross” position and your pencil point at X. As you slowly pull the lower left tab of the loose card (B) towards you, slowly move your pencil point away from you along the cut-edge while drawing its path on (B). The loose card is rotating counterclockwise as you do this. The line you drew is [(straight)(curved)].

5. You actually moved the pencil point along a path that was both straight and curved at the same time! This is possible because motion is measured relative to a frame of reference. In this investigation, there are two different frames of reference; one fixed and the other rotating. When the pencil-point motion was observed relative to the fixed card (A) and its cut-edge, its path was [(straight)(curved)].

6. When the pencil motion was measured relative to the rotating card (B), its path was [(straight)(curved)]. This apparent deflection of motion from a straight line in a rotating system is called the Coriolis Effect for Gaspard Gustave de Coriolis (1792-1843), who first explained it mathematically. Because Earth is a rotating system, objects moving freely across its surface exhibit curved paths, except at the equator. This includes air parcels moving horizontally.

7. Now imagine yourself far above the North Pole and looking down on the Earth below. Think of the loose card (B) as being part of Earth’s surface and that X represents the North Pole. From this perspective, Earth appears to rotate counterclockwise. You can observe the pencil point’s motion relative to the Earth’s surface (B). You see that as the pencil point moves along the cut-edge and away from the X, it draws a path on the rotating surface that [(is straight)(curves to the right)(curves to the left)].

8. Now imagine yourself far above the South Pole and looking down on the Earth below. Again, think of the loose card (B) as being part of the Earth’s surface and that X represents the South Pole. From this perspective, Earth appears to rotate clockwise. Rotate the loose card clockwise by pulling on the lower-right tab as you draw a line along the cut edge. You can observe that as the pencil point moves along the cut-edge and away from the X, it draws a path on the rotating card that [(is straight)(curves to the right)(curves to the left)].

9. The effect of Earth’s rotation on the path of objects moving across its surface is greatest at the poles, and diminishes to zero at the Equator. In summary, the Coriolis Effect causes objects freely moving horizontally over the Earth’s surface in the Northern Hemisphere to appear to curve to the [(right)(left)].

10. The Coriolis Effect causes objects in the Southern Hemisphere to appear to curve to the [(right)(left)] as they move freely across Earth’s surface.

When investigating atmospheric motions, it is informative to analyze the forces acting on the air. However, the rotating-card activity you just completed shows that the observed curved motions are due to a rotating frame of reference and not due to a force. Consequently, an imaginary Coriolis “force” is invented to be applied along with real forces to describe motions of objects. The Coriolis force producing such curved motion is defined as always acting perpendicular to the direction of motion, to the right in the Northern Hemisphere to explain rightward turning, and to the left in the Southern Hemisphere to describe leftward turning.

Pressure Gradient Force, Coriolis Effect, Friction, and Weather Maps

11. On the Figure 3 weather map segment, consider an air parcel at rest at Point A. An initial horizontal pressure gradient force [(is)(is not)] acting on the parcel.

12. Once horizontal motion has begun at this Northern Hemisphere location, the air parcel’s path will be deflected to the [(right)(left)] of its direction of motion.

Figure 3. Segment of surface weather map showing horizontal forces acting on an air parcel.

13. The moving air parcel follows the dashed curved path shown on the map. The thick black arrow at Point B shows the parcel’s direction of motion at that location. At that instant, the longer thin red arrow represents the [(Coriolis)(Pressure Gradient)(Frictional)] force.

14. The shorter thin blue arrow represents the [(Coriolis)(Pressure Gradient)(Frictional)] force, which is acting at a right angle and to the right of the direction of motion.

15. As the air parcel speeds up, the Coriolis Effect increases and the parcel’s motion continues to be deflected to its right. This continues until the parcel reaches Point C where the magnitude of the Coriolis Effect finally equals that of the pressure gradient force (which continues to act toward lowest pressure). At Point C the Coriolis Effect will be acting directly opposite to the pressure gradient force. The two forces are then in balance. From Point C and onward, the air parcel will flow [(perpendicular)(parallel)] to the isobars. This flow is known as the geostrophic wind.

16. Point D shows the effect of friction on moving air. The force of friction, represented by the small green arrow drawn from Point D, always acts opposite to the direction of motion and slows the moving object. The slowing causes the Coriolis Effect to decrease. As shown by the thick arrow at Point D, the direction of airflow changes and air flows obliquely across isobars towards [(lower)(higher)] pressure.

17. It is the presence of the frictional force added to the pressure gradient force and the Coriolis Effect that causes air to spiral [(inward)(outward)] in surface-map Lows and outward in Highs.

An additional force acts on horizontally moving air if the isobars are curved. That force, called the centripetal force, is not treated in this investigation.

Figure 4 is the surface weather map (Isobars, Fronts, Radar & Data) for 00Z 26 OCT 2013, Friday evening. At map time a “clipper-type” low-pressure system with fronts was moving quickly eastward along the northern U.S. border. A high-pressure system centered over the Kentucky/Tennessee border marked a cool air mass that was drifting slowly southeastward.

Figure 4. Surface weather map for 00Z 26 OCT 2013.

18. The wind at Minneapolis, in southeastern Minnesota, where the pressure was “094” (partially obscured), meaning 1009.4 mb, showed the air was moving generally toward the [(northwest)(northeast)(southeast)(southwest)] at about 10 knots. (It may help to imagine the wind arrow extended through the station circle in the direction the air is flowing and an arrowhead added.)

19. Draw a thin, short, straight line about 1 cm long from the Minneapolis station circle that is perpendicular to the 1008-mb and 1012-mb isobars above and below Minneapolis. Bold the portion of the line from the station circle toward lower pressure and add an arrowhead to form an arrow pointing toward lowest pressure. The arrow you just drew represents the direction of the [(Coriolis)(horizontal pressure gradient)(friction)] force acting on the air at Minneapolis.

20. This force acting on the wind flow at Minneapolis was directed generally toward the [(south)(north)(east)(west)].

21. The observed wind direction at Minneapolis was [(parallel)(at an angle)] to the force arrow you drew perpendicular to the isobars in item 19.

22. Draw a small arrow from the station circle center at a 90-degree angle to the right of the wind arrow that represents the Coriolis Effect acting on the wind at Minneapolis. Your Coriolis force arrow is directed generally toward the [(northwest)(northeast)(southeast)(southwest)].

23. Because these are surface winds, another force acting on the air in the direction opposite to the air flow, was the local [(Coriolis)(pressure gradient)(friction)] force. At map time, this force at Minneapolis was acting generally toward the southwest.

24. Considering the Minneapolis conditions as part of the circulation about the Low, the horizontal pressure gradient, Coriolis and friction forces combine to direct surface air flow around Northern Hemisphere low-pressure centers that is [(clockwise and outward)(counterclockwise and inward)], consistent with the hand-twist model.

25. Next focus on Oklahoma City, OK under the influence of the High. The pressure at Oklahoma City was 1023.8 mb. Oklahoma City’s pressure gradient force (perpendicular to the 1024-mb isobar) was directed generally toward the [(south)(west)(north)(east)].

26. The observed wind direction at Oklahoma City was [(parallel)(at an angle)] to the pressure gradient force.

27. The Coriolis force at Oklahoma City was directed generally toward the [(southwest)(northwest)(northeast)(southeast)].

28. The friction force at Oklahoma City was toward the general direction of [(southwest)(northwest)(northeast)(southeast)].

29. The air flow at Oklahoma City demonstrates that the horizontal pressure gradient, Coriolis and friction forces combine to direct surface air flow around Northern Hemisphere high-pressure centers that is [(clockwise and outward)(counterclockwise and inward)], consistent with the hand-twist model.

30. Now consider Jacksonville, FL also near the 1024-mb isobar, with a generally north-northeast wind of 5 knots and a coded pressure of “244”. Jacksonville is in a different position relative to the center of the high-pressure system. Draw a short arrow from the station circle at Jacksonville to represent the horizontal pressure gradient force as you did in item 19. Consider the orientation of the other forces at Jacksonville as you determined for Oklahoma City. The combination of forces will still have the same orientation to each other at a station although differing in actual directions. In this case, the direction of the Jacksonville pressure gradient force is generally toward the south-southeast. Note though that the horizontal pressure gradient force at Jacksonville is still perpendicular to the isobar directed toward [(highest)(lowest)] pressure.

31. The spacing of isobars on the map correlates to the strength of the pressure gradient with closer isobar spacings associated with stronger gradients. Compare the pressure gradients inferred by the isobar spacings associated with the Low across northern Illinois and southern Wisconsin to those associated with the High across Georgia. The stronger horizontal pressure gradients were located in [(Illinois/Wisconsin)(Georgia)].

32. The horizontal pressure gradient force is the primary determiner of wind speed. Generally, the higher wind speeds reported at stations in [(Illinois/Wisconsin)(Georgia)] were associated with stronger pressure gradients.

The pressure patterns, including the pressure gradients they produce, are major determiners of local weather conditions including wind speeds and directions. However, local conditions can also influence winds. For example, wind may be channeled by local terrain independently of isobar orientations. Mountainous regions in the West with greater friction may hinder winds from reaching a balance with large-scale pressure gradients.