1. Newton’s Laws of Motion Upper-Air Maps and Winds NATS 101 Lecture 12 Newton’s Laws of Motion Upper-Air Maps and Winds

2. Isobaric Maps Weather maps at upper levels are analyzed on isobaric (constant pressure) surfaces. (Isobaric surfaces are used for mathematical reasons that are too advanced to include in this course!) Isobaric maps provide the same information as constant height maps, such as: Low heights on isobaric surfaces correspond to low pressures on constant height surfaces! Cold temps on isobaric surfaces correspond to cold temperatures on constant height surfaces!

3. Isobaric Maps Ahrens, Fig. 2, p141 504 mb 496 mb PGF Downhill (Constant height) Some generalities: 1) High/Low heights on an isobar surface correspond to High/Low pressures on a constant height surface 2) Warm/Cold temps on an isobaric surface correspond to Warm/Cold temps on a constant height surface 3) The PGF on an isobaric surface corresponds to the downhill direction

4. Contour Maps How can we portray undulations of a 3D isobaric surface on a 2D plane without loss of information?

5. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Consider the terrain height of an island.

6. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Denote the shoreline by a line. Labeled the line 0’ for zero feet above mean-sea-level.

7. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Raise the water level by 500’. Denote the new shoreline by another line. Labeled that line 500’ for five-hundred feet above mean-sea-level.

8. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Raise the water level by another 500’ to 1,000’. Labeled that line 1000’ for one thousand feet above mean-sea-level.

9. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Labeled another line 1500’ above mean-sea-level.

10. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html 2000’ above mean-sea-level.

11. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html 2500’ above mean-sea-level.

12. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html 3000’ above mean-sea-level.

13. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html 3500’ above mean-sea-level.

14. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html A 4000’ line is not needed since the island is completely submerged.

15. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Lower the water level back to 0’. We are left with lines every 500’ at 0’, 500’, 1000’,... above MSL

16. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/elevation.html Rotate to a top-down perspective. We can see the entire island.

17. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/contourlabel.html Extra precision could be of value, but the map starts to get busy. If lines every 500’ is good, would lines every 250’ be better?

18. Contour Maps http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/contourlabel.html Contours every 250’; labeled and thickened every 1250’ Map can be clarified by accentuating every few contour lines

19. Contour Spacing and Gradient http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/contourspacing.html Contours every 500’. Note differences in the steepness of the mountain slopes.

20. Contour Spacing and Gradient http://academic.brooklyn.cuny.edu/geology/leveson/core/linksa/contourspacing.html Contours every 500’. Note that tight spacing of contours corresponds to steep slopes.

21. Topographic Map Google maps Grand Canyon Village

22. 570 dam contour

23. 576 dam contour

24. 570 and 576 dam contours

25. All contours at 6 dam spacing

27. -20 C and –15 C Temp contours

28. -20 C, –15 C, -10 C Temp contours

29. All contours at 5 o C spacing

30. Height contours Temps shaded Region of High Heights  RIDGE  and Warmth Region of Low Heights  TROUGH  and Cold

31. PGF Wind Wind doesn’t blow downhill!

32. Do Rocks Always Roll Downhill? Gedzelman, p 247 Upper-Level Winds PGF Begs the Question….

33. The Empirical Evidence Shows Wind Direction and PGF Relationship Winds more than 1 to 2 km above the ground are perpendicular to PGF! Analogous a marble rolling not downhill, but at a constant elevation with lower altitudes to the left of the marble’s direction How can we explain observations?

34. Why does the wind blow? To begin the answer to this question we first have to revisit Sir Isaac Newton

35. Newton’s Laws of Motion Newton’s 1st Law An object at rest will remain at rest and an object in motion will remain at a constant velocity (same speed and same direction) if the net force exerted on it is zero An external force is required to speed up, slow down, or change the direction of air

36. Newton’s Laws of Motion Newton’s 2nd Law The net force exerted on an object equals its mass times its acceleration Sum of All Forces = Mass  Acceleration Acceleration = Velocity Change / Time Acceleration = Change in Either Speed or Direction

37. Velocity, Acceleration and Force are Vectors Speed/Size Change Original Velocity New Velocity Original Velocity New Velocity Acceleration and Force Original Velocity New Velocity Acceleration and Force Direction Change

38. Uniform, Circular Motion Requires Acceleration Original Velocity New Velocity Acceleration directed toward center of circle Centripetal Original Velocity New Velocity Circular Path

39. CENTRIPETALFORCE You experience acceleration without a change in speed, for example, on a tilt-a-whirl carnival ride. The force is directed toward the center of the wheel. An equal an opposite (fictitious) centrifugal force is exerted by the inertia of your body on the wheel—so you stay put and don’t fall off even when upside down. Important when considering curved flows, as well see later… CENTRIFUGAL FORCE Centripetal Force

40. Newton’s 2nd law can be used to derive a governing equation for atmospheric motion The simplified form in the horizontal that we’ll consider has four terms. By understanding how each of these terms works, we’ll be able to explain why the wind blows.

41. Simplified equation of horizontal atmospheric motion (1)(2)(3)(4) TermForceCause 1Pressure gradient forceSpatial differences in pressure 2Coriolis forceRotation of the Earth 3Centripetal forceCurvature of the flow 4Friction forceActs against direction of motion due to interaction with surface FOCUS ON FIRST TWO TODAY…

42. Force Balance What we’re looking for in the equation of motion is the condition where the forces exactly balance—or the sum of the forces is equal to zero. When this happens, there is no net acceleration and the wind speed is constant, by Newton’s first law. 0 = Pressure gradient force + Coriolis force + Centripetal Force + Friction 0 = Pressure gradient force + Coriolis force Geostrophic Balance

43. Pressure gradient force Definition: Force to the difference in pressure (Δp) over a distance (d). (In the equation ρ is the density of air) The pressure gradient force is directed perpendicular to lines of constant pressure (isobars), toward lower pressure.

44. Strength of the pressure gradient force How strong the pressure gradient is depends on distance between the areas of high and low pressure, or how close the lines of constant pressure are spaced. Strong pressure gradient: Isobars are close together Weak pressure gradient: Isobars are far apart. WEAKPRESSUREGRADIENT STRONGPRESSUREGRADIENT

45. The pressure gradient force is why the wind blows, but you need the other terms to complete the picture…

46. Upper Level Chart for Surface Arctic Air Outbreak (300-mb)

47. PRESSURE GRADIENT AT DENVER LOW HIGH Observations for upper level winds: Wind DOES NOT follow the pressure gradient. Wind runs parallel to the lines of constant height (i.e. isobars). Strength of the wind IS related to the closeness, or packing, of the isobars. For example, compare the wind speed at Denver (105 knots) to some of the surrounding upper air observations, like Albuquerque. NEED AT LEAST ONE OF THE OTHER THREE FACTORS TO ACCOUNT FOR WIND MOTION DENVER 105 knots ALBUQUERQUE 90 knots

48. Coriolis Force Definition: Apparent force due to rotation of the Earth (Ω). Depends on the speed (V) and the latitude (Φ). Causes apparent deflection in reference of an observer at a fixed point on Earth Gaspard Coriolis

49. Coriolis force on a merry-go-round From perspective of person NOT on the merry-go-round, path of ball is straight. From perspective of person on merry-go-round, path of ball deflects. It accelerates. This is an apparent (fictitious) force.

50. Life on a Rotating Platform From perspective of person not on merry- go-round, path of ball is straight. From perspective of person on merry-go- round, path of ball deflects to left. There is an apparent force. (left click picture for animation) World Weather Project 2010 Courtesy of M. Ramamurthy U of Illinois, Urbana-Champaign Merry Go Round Link

51. Rotation of the Earth (from the polar perspective) NORTHERN HEMISPHERESOUTHERN HEMISPHERE COUNTERCLOCKWISE ROTATION Deflection to the right CLOCKWISE ROTATION Deflection to the left (Getzelman) SAME IDEA AS THE MERRY-GO-ROUND! deflection

52. Coriolis Effect: An Apparent Force Cannonball follows a straight path to an observer in space Earth rotates counter-clockwise underneath cannonball (in Northern Hemisphere) Cannonball appears to deflect to the right to an observer on earth Shot misses Paris to the right

53. Coriolis Force and Latitude All three airplanes travel in a straight line with respect to an outside observer (from space). The largest deviation, or deflection to the right, with respect to an observer on Earth occurs for the one traveling closest to the pole. The higher the latitude, the greater the Coriolis force. Accounted for by the sine term in the mathematical expression. Zero at equator (sin 0° = 0) Maximum at poles (sin 90° = 1)

54. Coriolis force and speed The Coriolis force is proportional to the wind speed. The faster the speed (or velocity), the greater the amount of Coriolis force. Note also the dependence on latitude here.

55. Coriolis Force vs. Wind Direction NORTHERN HEMISPHERESOUTHERN HEMISPHERE WIND CORIOLIS FORCE (TO RIGHT) WIND CORIOLIS FORCE (TO LEFT) Coriolis forcewind direction Coriolis force acts perpendicular (at a right angle) to the wind direction, to the right or left depending on which hemisphere.

56. Key Points: Coriolis Force Introduced to account for the earth’s rotation. Only deflects a moving object. Never changes the speed of an object. Zero if the velocity of an object relative to the earth’s surface is zero. Zero at the equator. For given speed, it is maximum at the poles.

57. Geostrophic Adjustment A.Parcel at rest initially accelerates toward lower pressure. B.Coriolis Force rotates parcel to right in NH. C.As parcel speeds up, Coriolis Force increases. D.Eventually (about a day), PGF equals CF and flow is parallel to isobars. (left click picture to animate) World Weather Project 2010 Courtesy of M. Ramamurthy U of Illinois, Urbana-Champaign Animate Picture

58. Geostrophic Wind Positions 1 and 2: Pressure gradient force Pressure gradient force accelerates the parcel towards the low pressure. Coriolis forcevelocity of the parcel Coriolis force acts to the right of the velocity of the parcel, making it curve to the right. PARCEL RELEASED

59. Positions 3 and 4: Pressure gradient force continues to accelerate the parcel towards the low pressure. velocity of the parcelCoriolis force As the velocity of the parcel increases, the Coriolis force increases, making the parcel continue to curve to the right. Geostrophic Wind

60. Position 5: FINAL STATE Pressure gradient forceCoriolis force Pressure gradient force is balanced by the Coriolis force. Velocity of the parcel Velocity of the parcel is constant (no acceleration). Direction is parallel to the isobars. FINAL STATE is called geostrophic balance. Geostrophic Wind

61. Pressure gradient forceCoriolis force Pressure gradient force is equally balanced by the Coriolis force, so net force is zero. Wind speed and direction (velocity) Wind speed and direction (velocity) is constant (no acceleration). Direction of wind is parallel to the isobars, or lines of constant pressure. WIND CORIOLIS FORCE PRESSURE GRADIENT FORCE Isobar 1 Isobar 2

62. WIND CORIOLIS FORCE PRESSURE GRADIENT FORCE Isobar 1 Isobar 2 WIND PRESSURE GRADIENT FORCE Isobar 2 Isobar 1 WEAK GEOSTROPHIC WIND Isobars far apart STRONG GEOSTROPHIC WIND Isobars close together CORIOLIS FORCE

63. PRESSURE GRADIENT FORCE Geostrophic Wind and Upper Level Charts CORIOLIS FORCE GEOSTROPHICWIND Winds at upper levels are pretty close to being geostrophic: Wind is parallel to isobars Wind strength dependents on how close together isobars are

64. GEOSTROPHY: No centripetal force or friction Simplified equation of horizontal atmospheric motion TermForceCause 1Pressure gradient forceSpatial differences in pressure 2Coriolis forceRotation of the Earth 3Centripetal forceCurvature of the flow 4Friction forceActs against direction of motion due to interaction with surface (1)(2)(3)(4) X

65. Do Rocks Always Roll Downhill? Gedzelman, p 247 Upper-Level Winds PGF Not if the Hill is Big Enough!

66. Fundamental Concepts for Today Rotation of Earth Geocentric =Accelerated Frame of Reference Introduce Coriolis “Force” Apparent Force to Account for Deflection Depends on Rotation, Latitude, Wind Speed Geostrophic Balance and Wind Balance Between PGF and Coriolis Force Geostrophic Wind Blows Parallel to Contours About One Day Required to Reach Balance

67. Assignment Next Lecture Surface Wind,Vertical Air Motions Reading - Ahrens 3rd: 155-162 4th: 157-164 5th: 158-164 Problems - HW05 D2L (Due Wed. Mar. 3) 3rd-Pg 162: 6.23, 6.24 4th-Pg 164: 6.23, 6.24 5th-Pg 165: 6.24, 6.25