Atmospheric Motion

1. Atmospheric Motion Leila M. V. Carvalho

2. What is wind? Well, wind is air in movement. We can feel the wind and we notice its presence, we can fear, and we can even use its energy to move and generate power

3. Isaac Newton (1642-1727) first law of motion states that “an object at rest will remain at rest and object in motion will remain in motion (and travel at a constant velocity along a straight line) as long as no force is exerted in the object” So, if wind is air in movement, a force must exist to move air from rest to movement. Let’s examine the forces that act upon the atmosphere Imagine a volume with molecules at a given temperature. They are randomly vibrating and colliding with each other, depending on the temperature Wind is therefore the movement of a given volume of air. F = ma (mass x accelaration) , and F=F1+ F2 +…+ Fn Horizontal Wind

4. In this condition, what should be the direction of the wind? High Pressure Low Pressure Here, we observe an horizontal pressure change or horizontal pressure gradient. Gradient measures the spatial variation of a scalar (pressure, temperature, density, etc). Pressure gradient = difference in pressure/distance, PG=Δp/d

5. REMEMBER THAT A “GRADIENT” ALWAYS POINT TOWARD THE HIGHEST MAGNITUDES OF THE SCALAR. wind direction Pressure Gradient Force Pressure Gradient According with Newton second law, a force must act upon an object to change its speed (from rest to a speed V). This force, in this case is the Gradient Pressure Force High Pressure p1 Low Pressure p2 W E THE PRESSURE GRADIENT FORCE POINTS FROM HIGH TOWARDS LOW PRESSURE Pressure gradient = difference in pressure/distance, PG=Δp/d The Pressure Gradient Force per unity of mass (PGF) is proportional to - Δp/d, Where Δp=p2-p1 In mathematical terms: , where ρ is the atmosphere density at a given level

6. Let’s recall the definition of air pressure • Air pressure is simply the weight of mass of air above a given level, the force per unit area exerted against a surface by the weight of the air molecules above that surface. P1>P2 P2 P1

7. Pressure measurements (pg. 100 text book) Mercury barometer Aneroid barometer Barograph Pressure is measured based on the compression of chambers Cylinder moves and pressure is registered along the days Inches or millimeters of mercury Barometer: literally means measure ‘Bar’, which is one unity of pressure. Bar is a relatively large unity, and because surface pressure changes are normally small, the common unity in Meteorology: millibar (mb), 1mb=1/1000 bar (1mb = hecto Pascal (100 Pa), where Pa=N/m2) STANDARD PRESSURE AT SEA LEVEL: 1013.25mb = 29.92 in Hg = 76cm

8. We also learned that pressure and density decrease exponentially with height : rapidly at first and slowly at higher altitudes P1>P2 P2 P1

9. 4,322m 1000m Δp/ Δz = 100mb/km If you are climbing a mountain from the sea level to about 1000m, you will notice that pressure will decrease about 100mb/km = 10mb/100m (10mb/328 ft)

10. Δp/ Δz = 50mb/km Δz=1000m If we were to climb between 9-10km (a little bit above the Everest), pressure fall would be only 50mb/km (Notice that a mountain at this height should have much more snow than this one)

11. Of course there is a relationship between variation of pressure with height and density with height. Both decrease exponentially with height

12. Surface pressure: • It is clear that the terrain varies considerably in most regions of our planet • It is important to compare surface pressure from place to place • This is because differences in pressure in a given level are essential for the horizontal movement of the air (wind) • For this purpose, we apply equations (we will see later) to know what should be the pressure if a particular location was at sea level. • When we look at a map with sea level pressure we can then compare pressure among locations. P2<P1 P2 P1 It is possible that when reduced to sea level, P1~P2

13. Note that some isobars in the sea level pressure (slp) charts (lines with same slp) do not necessarily follow topography

14. Pressure, density (mass of air in a given volume), and air temperature are all related. The relationships among these variables is expressed by the gas law (or equation of state) where pis pressure expressed in Pascal, ρ(rho)is density in kilograms (m/V), R is a constant equal to 287 joules per kilogram per kelvin, Tis temperature in Kelvin. For example: Keep constant temperature; if density increases it will imply that the number of molecules increased. Therefore, pressure must increase!

15. Likewise, if density is maintained and temperature increases, pressure increases

16. Surface air pressure: lines indicate regions with the same pressure (ISOBARS). L means ‘Low’ and ‘H’ means high. Blue line indicates a frontal system. Where do you see the highest and lowest pressure gradient in this figure? Since isobars are plotted here every 4 millibars, high pressure gradients can be identified where isobars are very close (packed) to each other. Grad P FGP

17. Relationship between density and pressure : simple model • Imagine a simple atmospheric model where density remains constant with height. The air pressure at the surface is related to the number of molecules above. When air of the same temperature is stuffed into the column, the surface air pressure rises. When air is removed from the column, the surface pressure falls.

18. Let’s compare these two cities. In this slide, they show they have the same pressure at the surface and in any other level. Both also have the same temperature in all levels P1 = P2 P2 P1 CITY 2 Same surface pressure CITY 1 Same surface pressure

19. warm Let’s examine pressure aloft cold Low pressure High pressure CITY 1 Same Surface pressure CITY 1 Same Surface pressure

20. It takes a shorter column of cold air to exert the same pressure as a taller column of warm air. Because of this fact, aloft, cold air is associated with low pressure and warm air with high pressure. The pressure differences aloft create a force that causes the air to move from a region of higher pressure toward a region of lower pressure. The removal of air from column 2 causes its surface pressure to drop, whereas the addition of air into column 1 causes its surface pressure to rise. (differences are exaggerated) CITY 2 Same surface pressure CITY 1 Same surface pressure

21. Vertical Pressure Gradient Let’s assume that initially you have two columns of air with equal temperatures, pressures, and densities. Let’s say now that the right column heats more than column on the left side 5700m 5640m It still contains the same amount of mass, but it has lower density to compensate for its greater height. The pressure drops 500mb over 5640m within the cold air but it is necessary to be at 5700m of ascent for the pressure drop the same amount in the warm air; Of course, these numbers are examples and depend on the difference of temperature

22. Hydrostatic Equilibrium • Now that you understood that pressure gradient force is fundamental to generate winds, you may ask to yourself: if pressure decreases with height, there is a gradient force pointing outside the earth. Why the atmosphere does not blow away??? FGF P2<P1 P2 P1

23. Hydrostatic equilibrium z • The answer is that gravity pulls the atmosphere downward. • And, in this case, why it does not collapses the atmosphere near the surface? • The answer is that the vertical gradient force are normally nearly equal value and operate in opposite direction: This is what we call Hydrostatic Equilibrium or g is the acceleration of the gravity ~ 9.8m/s2 near the surface and around the Equator

24. Forces affecting the speed and direction of the wind Northern Hemisphere • Differences in temperature result in unequal distribution of air around the globe that causes difference in pressure and pressure gradient forces. If no other forces were involved, the wind would always flow in the direction of the gradient force, which is not true • There are two other important forces: Coriolis force and friction

25. The Coriolis Force Suppose that the girl is at rest and a bullet is launched towards her. In this situation she is reached by the bullet Now, suppose she rotates when the bullet is launched

26. This is what WE see from our referential that is not rotating. We see the girl rotating while the bullet is moving straightforward This is what she sees from her referential. In her referential, she is at rest and the ball is deflecting to the right of the original trajectory

27. This is what she sees from her referential. In her referential, she is at rest and the bullet is deflecting to the right of the original trajectory To apply the Newton’s second law , F1+F2+…+ = m. a (mass x acceleration) F F The ‘apparent’ force deflecting the trajectory is named Coriolis force

28. Mathematical definition Magnitude proportional to speed of motion and sine of latitude Oriented perpendicular to direction of motion Always to right of direction of motion in Northern Hemisphere Always to left of direction of motion in Southern Hemisphere Fg North Pole Equator Fc Force/mass (acceleration) = 2 x angular velocity of earth (1 revolution/day) x velocity x sine of latitude f=2ΩsinφCoriolis parameter

29. Southern Hemisphere Always to left of direction of motion in Southern Hemisphere f=2ΩsinφCoriolis parameter < 0 Southern Hemisphere Fc Fg Equator South Pole

30. Not only Coriolis and Gradient force are important to balance the wind Northern Hemisphere The other factor that influences the movement of air is friction. Air in contact with the surface experiences frictional drag, which decreases wind speed. Friction is important within the lowest 1.5 km of the atmosphere (planetary boundary layer). Air in the free atmosphere, above 1.5 km, experiences negligible friction.

31. The Equation of Motion Δv / Δt = Fp + Fc + Ff where Fp stands for pressure gradient, Fc stands for the Coriolis effect, and Ff stands for friction. The equation of motion says the acceleration of a mass of air is the sum of the accelerations of these three forces.

32. Let’s see what happens with a parcel as it moves from high to low pressure with no friction L 900mb FGP FGP FGP wind FGP FGP 904mb CF CF CF 908mb CF H Winds with direction determined by the balance between Coriolis force and Force of Gradient Pressure are known as Geostrophic winds Force/mass (acceleration) = 2 x angular velocity of earth (1 revolution/day) x velocity x sine of latitude Coriolis force only appear when there is movement (V≠0)

33. Important facts about Coriolis force: • Remember: Coriolis force is ALWAYS perpendicular (90 degrees) to the direction of the movement. • For this reason, it does not change the speed intensity (i.e., does not accelerate an object or an air mass). It only changes its direction!!! (to the right in the NH and to the left in the SH)

34. Let’s see what happens with a parcel as it moves from high to low pressure with no friction L 900mb FGP FGP FGP wind FGP FGP 904mb CF CF CF 908mb CF H Winds with direction determined by the balance between Coriolis force and Force of Gradient Pressure are known as Geostrophic winds Force/mass (acceleration) = 2 x angular velocity of earth (1 revolution/day) x velocity x sine of latitude Coriolis force only appear when there is movement (V≠0)

35. Surface Winds and Friction (Ff) What does Friction cause to the movement? It reduces speed or the magnitude of the wind (V) Which force will be affected by friction, Pressure gradient force or Coriolis force?

36. Surface Winds and Friction (Ff) (NH) 1012 mb Wind 1016 mb If Friction decreases the wind speed, so which force will be weaker (relative to the other) (FGP or Fc)? In other words, FGP > Fc and the result is: 1012 mb Wind 1016 mb

37. NH LOW 1012 mb Wind 1016 mb HIGH With Friction SH LOW SH LOW No Friction 1012 mb Wind Wind 1016 mb HIGH HIGH

38. GEOSTROPHIC WINDS A) south-to-north pressure gradient force B) The horizontal pressure gradient accelerates the parcel northward Initially, when the wind speed is low, the Coriolis force is small. C) As the parcel speeds up, the strength of the Coriolis force increases and causes greater displacement to the right The wind speed increases the Coriolis force sufficiently to cause the air to flow perpendicular to the pressure gradient force. The air flow becomes unaccelerated, with unchanging speed and direction known as geostrophic flow (or geostrophic wind).

39. Geostrophic wind Ω= 2π/day= 2π/(86,000 sec)7.27x10-5 radians/sec 2π radians = 360o Dry air at standard temperature and pressure (273.15 K, 1000mb) Density ~ 1.25 kg/m3

40. Northern Hemisphere Geostrophic flow cannot exist near the surface. Friction slows the wind, so that the Coriolis force is less than the pressure gradient force. The air flows at an angle to the right of the pressure gradient force in the Northern Hemisphere (a) and to the left in The Southern Hemisphere (b). CF Southern Hemisphere CF

41. ESTIMATING WIND DIRECTION BY LOOKING AT CLOUDS ~ 3000m (10kft) • Stand with your backs to the direction from which the clouds are moving • Lower pressure aloft will always be to your left and higher pressure to your right • Near surface, friction will decrease wind speed and FGP will dominate. So the wind will be ‘bending’ towards low pressure

42. Super geostrophic Flows Supergeostropic flow(a) occurs in the upper atmosphere around high-pressure systems. As the air flows, it is constantly turning to its right. This turning motion occurs because the Coriolis force has a greater magnitude than the pressure gradient force (as represented by the length of the dashed arrows). Observe the changing direction of the four solid arrows 1 through 4. Subgeostrophic flow(b) occurs in the upper atmosphere around low-pressure systems. The pressure gradient force is greater than the Coriolis force and the air turns to its left in the Northern Hemisphere. Sub Geostrophic flows

43. Enclosed areas of high pressure marked by roughly circular isobars or height contours are called anticyclones. The wind rotates clockwise around anticyclones in the Northern Hemisphere, as the Coriolis force deflects the air to the right and the pressure gradient force directs it outward. In the boundary layer, the air spirals out of anticyclones (a), while in the upper atmosphere it flows parallel to the height contours (b). In the Southern Hemisphere, the flow is counterclockwise (c) and (d).

44. Closed low-pressure systems are called cyclones. Air spirals counterclockwise into surface cyclones in the Northern Hemisphere (a) and rotates counterclockwise around an upper-level low (b). The flow is reversed in the Southern Hemisphere (c) and (d).

45. Tridimensional view Northern Hemisphere

46. Troughs and Ridges: relationships with warming and cooling of the atmosphere underneath Elongated zones of high and low pressure are called ridges (a) and troughs (b), respectively.

47. Can we identify ridges and troughs in this Water Vapor image?

48. Winds aloft:

49. Now that we understand forces that cause wind we observe, another important question is: how does temperature affects pressure gradients?

50. Does temperature modify vertical pressure gradient? Z Hydrostatic balance in terms of density From equation of state: Rate of decrease in pressure inversely proportional to temperature: cold air pressure falls faster with height than warm air Thickness of layer between two pressures closely related to temperature