1. ATMO 336 Weather, Climate and Society Upper Air Maps

2. Temperature (T) Profile More complex than pressure or density Layers based on the Environmental Lapse Rate (ELR), the rate at which temperature decreases with height. inversion isothermal 6.5 o C/km Ahrens, Fig. 1.7

3. Higher Atmosphere Molecular Composition Homosphere- gases are well mixed. Below 80 km. Emphasis of Course. Heterosphere- gases separate by molecular weight, with heaviest near bottom. Lighter gases (H, He) escape. Ahrens, Fig. 1.8

4. Atmospheric Layers Essentials Thermosphere-above 85 km Temps warm w/height Gases settle by molecular weight (Heterosphere) Mesosphere-50 to 85 km Temps cool w/height Stratosphere-10 to 50 km Temps warm w/height, very dry Troposphere-0 to 10 km (to the nearest 5 km) Temps cool with height Contains “all” H 2 O vapor, weather of public interest

5. Take Home Points Many gases make up air N 2 and O 2 account for ~99% Trace gases: CO 2, H 2 O, O 3, etc. Can be very important…more later Pressure and Density Profiles Decrease rapidly with height Temperature Profile Complex vertical structure

6. Recoil Force What is Air Pressure? Pressure = Force/Area What is a Force? It’s like a push/shove In an air filled container, pressure is due to molecules pushing the sides outward by recoiling off them

7. Air Pressure Concept applies to an “air parcel” surrounded by more air parcels, but molecules create pressure through rebounding off air molecules in other neighboring parcels Recoil Force

8. Air Pressure At any point, pressure is the same in all directions But pressure can vary from one point to another point Recoil Force

9. Higher density at the same temperature creates higher pressure by more collisions among molecules of average same speed Higher temperatures at the same density creates higher pressure by collisions amongst faster moving molecules

10. Ideal Gas Law Relation between pressure, temperature and density is quantified by the Ideal Gas Law P(mb) = constant x d(kg/m 3 ) x T(K) Where P is pressure in millibars Where d is density in kilograms/(meter) 3 Where T is temperature in Kelvin

11. Ideal Gas Law Ideal Gas Law is complex P(mb) = constant x d(kg/m 3 ) x T(K) P(mb) = 2.87 x d(kg/m 3 ) x T(K) If you change one variable, the other two will change. It is easiest to understand the concept if one variable is held constant while varying the other two

12. Ideal Gas Law P = constant x d x T (constant) With T constant, Ideal Gas Law reduces to Law reduces to  P varies with d  Boyle's Law Denser air has a higher pressure than less dense air at the same temperature

13. Ideal Gas Law P = constant x d (constant) x T With d constant, Ideal Gas Law reduces to  P varies with T  Charles's Law Warmer air has a higher pressure than colder air at the same density

14. Ideal Gas Law P (constant) = constant x d x T With P constant, Ideal Gas Law reduces to  T varies with 1/d  Colder air is more dense (d big, 1/d small) than warmer air at the same pressure

15. Summary Ideal Gas Law Relates Temperature-Density-Pressure

16. Pressure-Temperature-Density 9.0 km 300 mb 1000 mb 400 mb 500 mb 600 mb 700 mb 800 mb 900 mb MinneapolisHouston 9.0 km Pressure Decreases with height at same rate in air of same temperature Constant Pressure (Isobaric) Surfaces Slopes are horizontal

17. Pressure-Temperature-Density Pressure (vertical scale highly distorted) Decreases more rapidly with height in cold air than in warm air Isobaric surfaces will slope downward toward cold air Slope increases with increasing height Animation 8.5 km 9.5 km 300 mb 1000 mb 400 mb 500 mb 600 mb 700 mb 800 mb 900 mb MinneapolisHouston COLD WARM

18. Pressure-Temperature-Density 8.5 km 9.5 km 300 mb 1000 mb 400 mb 500 mb 600 mb 700 mb 800 mb 900 mb MinneapolisHouston H L LH Pressure Higher along horizontal red line in warm air than in cold air Pressure difference is a non-zero force Pressure Gradient Force or PGF (red arrow) Air will accelerate from column 2 towards 1 Pressure falls at bottom of column 2, rises at 1 Animation SFC pressure risesSFC pressure falls PGF COLD WARM

19. Summary Ideal Gas Law Implies Pressure decreases more rapidly with height in cold air than in warm air. Consequently….. Horizontal temperature differences lead to sloping constant pressure surfaces, or horizontal pressure differences! (And horizontal pressure differences lead to air motion…or the wind!)

20. 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!

21. 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

22. 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

23. Contour Maps How we display atmospheric fields Portray undulations of 3D surface on 2D map A familiar example is a USGS Topographic Map It’s a useful way to display atmospheric quantities such as temperatures, dew points, pressures, wind speeds, etc. Gedlezman, p15

24. Rules of Contouring (Gedzelman, p15-16) “ Every point on a given contour line has the same value of height above sea level.” “Every contour line separates regions with greater values than on the line itself from regions with smaller values than on the line itself.” “The closer the contour lines, the steeper the slope or larger the gradient.” “The shape of the contours indicates the shape of the map features.”

25. Contour Maps “To successfully isopleth the 50- degree isotherm, imagine that you're a competitor in a roller- blading contest and that you're wearing number "50". You can win the contest only if you roller-blade through gates marked by a flag numbered slightly less than than 50 and a flag numbered slightly greater than 50.” https://courseware.e-education.psu.edu/public/meteo/meteo101demo/Examples/Section2p02.html Click “interactive exercise” https://courseware.e-education.psu.edu/public/meteo/meteo101demo/Examples/Section2p03.html Click first “here” https://courseware.e-education.psu.edu/public/meteo/meteo101demo/Examples/Section2p04.html Click “interactive isotherm map” From

26. Upper-Air Model Conditions at specific pressure level Wind Temperature (  C) Moisture (Later) Height above MSL UA 500mb Analysis Ahrens, p 427 Ahrens, p 431 Responsible for boxed parameters

27. 570 dam contour

28. 576 dam contour

29. 570 and 576 dam contours

30. All contours at 6 dam spacing

32. -20 C and –15 C Temp contours

33. -20 C, –15 C, -10 C Temp contours

34. All contours at 5 o C spacing

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

36. PGF Wind

37. Do Rocks Always Roll Downhill? Gedzelman, p 247 Upper-Level Winds PGF Today’s Question….

38. Take Home Points Station Pressure and Surface Analyses (later) Reduced to Mean Sea Level Pressure (SLP) PGF Corresponds to Pressure Differences Upper-Air Maps On Isobaric (Constant Pressure) Surfaces PGF Corresponds to Height Sloping Downhill Contour Analysis Surface Maps-Analyze Isobars of SLP (later) Upper Air Maps-Analyze Height Contours

39. Take Home Points Wind Direction and PGF 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 that be?

40. Weather, Climate and Society Newton’s Laws of Motion Upper-Air Winds

41. Supplemental References for Today’s Lecture Gedzelman, S. D., 1980: The Science and Wonders of the Atmosphere. 535 pp. John-Wiley & Sons. (ISBN 0-471-02972-6)

42. Do Rocks Always Roll Downhill? Gedzelman, p 247 Upper-Level Winds PGF Today’s Question….

43. 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

44. 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 x Acceleration Acceleration = Velocity Change / Time Acceleration = Change in Either Speed or Direction

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

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

47. Accelerated Frame of Reference You are glued to car’s floor and drop an egg. What happens if the car begins to accelerate? Inside the car, it looks a mystery force is attracting the egg to the back of the car. Your frame of reference is accelerating. Someone outside the car sees that the egg is just accelerating to the floor, you are accelerating with the box car. A force is accelerating the car. Their frame of reference is not accelerating. Splat! (rest) time

48. 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

49. Earth’s Rotation If viewed from space, earth is like a carousel! Northern Hemisphere rotates counterclockwise Southern Hemisphere rotates clockwise Gedzelman, p 240

50. Refinements Simple, right? But there are a couple of nuances We will consider both… Coriolis “force” varies with wind speed. The earth is a sphere, not flat like a carousel.

51. Ball Appears to Deflect to the Right of the Observer Gedzelman, p 242 Deflection increases if: Rotation rate increases Speed of ball increases

52. Ball Appears to Deflect to the Right of the Observer Gedzelman, p 242 Deflection increases if: Speed of ball increases slow fast

53. Ball Appears to Go Straight Gedzelman, p 242 If the ball is thrown parallel to the axis of rotation, there is no apparent deflection

54. Deflection Depends on Orientation of Axis of Rotation and Velocity Gedzelman, p 242 velocity Apparent Deflection No Deflection

55. Coriolis Force Varies with Latitude Gedzelman, p 243 Airplane Link

56. 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

57. Geostrophic Balance Pressure Gradient Force Coriolis Force Geostrophic Wind 5640 m 5700 m Geostrophic Wind Arises from a Balance Between the PGF and the Coriolis Force. PGF + Coriolis Force = 0 (Technically, it can only exist for East-West flow and for straight contours, but we will ignore that technicality.)

58. Geostrophic Balance Pressure Gradient Force Coriolis Force Geostrophic Wind 5640 m 5700 m The Balance Leads to the Wind Blowing Parallel to the Height Contours, with Lower Heights to the Left of the Wind Direction in the NH. Closer the Spacing Between the Height Contours- The Faster the Geostrophic Wind Speed.

59. PGFCor Geo

60. Take Home Points Rotation of Earth 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

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

62. Assignment for Next Lecture Topic – Centripetal force due to curved flow Frictional force near the ground Reading - Ahrens pg 155-158 Problems - 6.23, 24