1. Air Pressure NATS 101-06 Lecture 11 Air Pressure

2. Review ELR-Environmental Lapse Rate Temp change w/height measured by a thermometer hanging from a balloon DAR and MAR are Temp change w/height for an air parcel (i.e. the air inside balloon) Why Do Supercooled Water Droplets Exist? Freezing needs embryo ice crystal First one, in pure water, is difficult to make

3. Review Updraft velocity and raindrop size Modulates time a raindrop suspended in cloud Ice Crystal Process SVP over ice is less than over SC water droplets Accretion-Splintering-Aggregation Accretion-supercooled droplets freeze on contact with ice crystals Splintering-big ice crystals fragment into many smaller ones Aggregation-ice crystals adhere on snowflakes, which upon melting, become raindrops!

4. Warm Cloud Precipitation As cloud droplet ascends, it grows larger by collision-coalescence Cloud droplet reaches the height where the updraft speed equals terminal fall speed As drop falls, it grows by collision-coalescence to size of a large raindrop Ahrens, Fig. 5.16 Updraft (5 m/s) Terminal Fall Speed (5 m/s)

5. Ice Crystal Process Since SVP for a water droplet is higher than for ice crystal, vapor next to droplet will diffuse towards ice Ice crystals grow at the expense of water drops, which freeze on contact As the ice crystals grow, they begin to fall Ahrens, Fig. 5.19 Effect maximized around -15 o C

6. Accretion-Aggregation Process Accretion (Riming) Aggregation Supercooled water droplets will freeze on contact with ice ice crystal Small ice particles will adhere to ice crystals snowflake Splintering Ahrens, Fig. 5.17 Also known as the Bergeron Process after the meteorologist who first recognized the importance of ice in the precipitation process

7. 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

8. 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

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

10. 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

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

12. Ideal Gas Law Ideal Gas Law describes relation between 3 variables: temperature, density and pressure P(mb) = constant   (kg/m 3 )  T(K) P(mb) = 2.87   (kg/m 3 )  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

13. Ideal Gas Law P = constant    T (constant) With T constant, Ideal Gas Law reduces to  P varies with   Denser air has a higher pressure than less dense air at the same temperature Why? You give the physical reason!

14. Ideal Gas Law P = constant   (constant)  T With  constant, Ideal Gas Law reduces to  P varies with T  Warmer air has a higher pressure than colder air at the same density Why? You should be able to answer the underlying physics!

15. Ideal Gas Law P (constant) = constant    T With P constant, Ideal Gas Law reduces to  T varies with 1/   Colder air is more dense (  big, 1/  small) than warmer air at the same pressure Why? Again, you reason the mechanism!

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

17. 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 Isobaric Surfaces Slopes are horizontal

18. 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 height to tropopause, near 300 mb in winter 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

19. 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

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

21. Review: Pressure-Height Remember Pressure falls very rapidly with height near sea-level 3,000 m 701 mb 2,500 m747 mb 2,000 m 795 mb 1,500 m846 mb 1,000 m899 mb 500 m955 mb 0 m1013 mb 1 mb per 10 m height Consequently………. Vertical pressure changes from differences in station elevation dominate horizontal changes

22. Station Pressure Pressure is recorded at stations with different altitudes Station pressure differences reflect altitude differences Wind is forced by horizontal pressure differences Horizontal pressure variations are 1 mb per 100 km Adjust station pressures to one standard level: Mean Sea Level Ahrens, Fig. 6.7

23. Reduction to Sea-Level-Pressure Sea Level Pressure Station pressures are adjusted to Sea Level Pressure Make altitude correction of 1 mb per 10 m elevation Ahrens, Fig. 6.7

24. Correction for Tucson Elevation of Tucson AZ is ~800 m Station pressure at Tucson runs ~930 mb So SLP for Tucson would be SLP = 930 mb + (1 mb / 10 m)  800 m SLP = 930 mb + 80 mb = 1010 mb

25. Correction for Denver Elevation of Denver CO is ~1600 m Station pressure at Denver runs ~850 mb So SLP for Denver would be SLP = 850 mb + (1 mb / 10 m)  1600 m SLP = 850 mb + 160 mb = 1010 mb Actual pressure corrections take into account temperature and pressure-height variations, but 1 mb / 10 m is a good approximation

26. You Try at Home for Phoenix Elevation of Phoenix AZ is ~340 m Assume the station pressure at Phoenix was ~977 mb at 3pm yesterday So SLP for Phoenix would be?

27. Sea Level Pressure Values Ahrens, Fig. 6.3 882 mb Hurricane Wilma October 2005

28. Summary Because horizontal pressure differences are the force that drives the wind Station pressures are adjusted to one standard level…Mean Sea Level…to remove the dominating impact of different elevations on pressure change

29. Ahrens, Fig. 6.7 PGF

30. Key Points for Today Air Pressure Force / Area (Recorded with Barometer) Ideal Gas Law Relates Temperature, Density and Pressure Pressure Changes with Height Decreases more rapidly in cold air than warm Station Pressure Reduced to Sea Level Pressure

31. Pressure in Warm and Cold Air Ahrens, Fig. 6.2

32. Pressure-Temperature-Density 300 mb Less Dense 300 mb More Dense Same Density 9.5 km 8.5 km Minneapolis Houston 1000 mb Ahrens, Fig. 6.2 Minneapolis Houston

33. Pressure-Temperature-Density Pressure Decreases with height at same rate in air of same temperature 300 mb Level Slope is horizontal Minneapolis Houston 300 mb 1000 mb 9.0 km Same Density Ahrens, Fig. 6.2

34. Pressure-Temperature-Density Pressure Decreases more rapidly with height in cold air than in warm air 300 mb Level Slopes downward from warm air to cold air Minneapolis Houston 300 mb 1000 mb 9.5 km 8.5 km More Dense Less Dense Ahrens, Fig. 6.2

35. Pressure-Temperature-Density Pressure Decreases more rapidly with height in cold air than in warm air 300 mb Level Slopes downward from warm air to cold air Minneapolis Houston 300 mb 1000 mb 9.5 km 8.5 km More Dense Less Dense Ahrens, Fig. 6.2

36. Horizontal Pressure Differences 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 accelerates from column 2 towards 1 Pressure falls at bottom of column 2, rises at 1 1000 mb 300 mb H L 9.5 km 8.5 km Ahrens, Fig. 6.2 PGF

37. 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 height to tropopause, near 300 mb in winter 8.5 km COLD 9.5 km WARM 300 mb 1000 mb 400 mb 500 mb 600 mb 700 mb 800 mb 900 mb 200 mb 100 mb MinneapolisHouston

38. Pressure-Temperature-Density 8.5 km COLD 9.5 km WARM 300 mb 1000 mb 400 mb 500 mb 600 mb 700 mb 800 mb 900 mb MinneapolisHouston 200 mb 100 mb 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

39. Measuring Air Pressure Mercury Barometer Air pressure at sea level can support nearly 30 inches of Hg Hg level responds to changes in pressure Pressure can support nearly 30 feet of water Ahrens, Fig. 6.4

40. Recording Aneroid Barometer Aneroid cell is partially evacuated Contracts as pressure rises Expands as pressure falls Changes recorded by revolving drum Ahrens, Fig. 6.6

41. Isobaric Maps Ahrens, Fig. 2, p141

42. Isobaric Maps Weather maps at upper levels are analyzed on isobaric (constant pressure) surfaces. (Isobaric surfaces are used for mathematical reasons that are too complex to explain 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!

43. 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

44. Contour Maps Display 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

45. 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.”

46. 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://www.e-education.psu.edu/gened/meteo101/Examples/Section2p02.html Click “interactive exercise” https://www.e-education.psu.edu/gened/meteo101/Examples/Section2p03.html https://www.e-education.psu.edu/gened/meteo101/Examples/Section2p04.html Click “interactive isotherm map” From

47. 570 dam contour

48. 576 dam contour

49. 570 and 576 dam contours

50. All contours at 6 dam spacing

52. -20 C and –15 C Temp contours

53. -20 C, –15 C, -10 C Temp contours

54. All contours at 5 o C spacing

55. Height contours Temp shading

56. PGF Wind

57. Key Concepts for Today Station Pressure and Surface Analyses 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 Upper Air Maps-Analyze Height Contours

58. Key Concepts for Today 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

59. Assignment Reading - Ahrens pg 148-149 include Focus on Special Topic: Isobaric Maps Problems - 6.9, 6.10

60. Assignment Topic – Newton’s Laws Reading - Ahrens pg 150-157 Problems - 6.12, 6.13, 6.17, 6.19, 6.22

61. Example: Ideal Gas Law If Pressure at Sea Level averages 1013 mb and Temperature at Sea Level averages 288 K, what is the average Density at Sea Level? Answer can be found using the Ideal Gas Law P(mb) = 2.87   (kg/m 3 )  T(K)  (kg/m 3 ) = P(mb) / {2.87  T(K)}  (kg/m 3 ) = (1013 mb) / (2.87  288 K)  (kg/m 3 ) = 1.23 kg/m 3  2.00 lbs/yard 3

62. 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 height to tropopause, near 300 mb in winter COLD 8.5 km COLD 9.5 km WARM 300 mb 1000 mb 400 mb 500 mb 600 mb 700 mb 800 mb 900 mb Minneapolis Same pressure Houston Same pressure 200 mb 100 mb

63. Pressure-Temperature-Density 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 COLD 8.5 km COLD 9.5 km WARM 300 mb 1000 mb 400 mb 500 mb 600 mb 700 mb 800 mb 900 mb H L LH PGF 200 mb 100 mb

64. Measuring Air Pressure Mercury Barometer Air pressure at sea level can support nearly 30 inches of Hg Hg level responds to changes in pressure Pressure can support nearly 30 feet of water Ahrens, Fig. 6.4

65. Recording Aneroid Barometer Aneroid cell is partially evacuated Contracts as pressure rises Expands as pressure falls Changes recorded by revolving drum Ahrens, Fig. 6.6

66. Pop Quiz #2 Elevation of Phoenix AZ is ~340 m Elevation of Tucson AZ is ~800 m The station pressure at Phoenix was ~976 mb at 8 am today The station pressure at Tucson was ~932 mb at 8 am today Which station had the highest SLP?