1. 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
Terminal Fall Speed (5 m/s)
Updraft (5 m/s)
Ahrens, Fig. 5.16

5. Effect maximized around -15oC
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
High vapor levels around droplets and lower concentrations over ice will tend to homogenize by random molecular motions…DIFFUSION.
Thus water vapor molecules over liquid will move towards ice crystals.
Vapor pressure over ice becomes larger than SVP over ice, smaller than SVP over liquid droplet.
Droplets will shrink as liquid evaporates to replace evacuated vapor molecules.
Supercooled water droplets will be attracted to ice crystal, where they freeze/adhere on contact.
Effect maximized around -15oC
Ahrens, Fig. 5.19

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

7. 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
Recoil Force

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

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

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/m3)  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/m3)  T(K)
P(mb) = 2.87  (kg/m3)  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. P = constant    T (constant)
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. P = constant   (constant)  T
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. P (constant) = constant    T
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
Decreases with height at same rate in air of same temperature
Isobaric Surfaces
Slopes are horizontal
300 mb
400 mb
500 mb
9.0 km
9.0 km
600 mb
700 mb
800 mb
900 mb
1000 mb
Minneapolis
Houston

18. Pressure-Temperature-Density
WARM
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
300 mb
COLD
400 mb
500 mb
9.5 km
600 mb
8.5 km
700 mb
800 mb
900 mb
1000 mb
Minneapolis
Houston

19. Pressure-Temperature-Density
WARM
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
300 mb
COLD
400 mb L
500 mb H
PGF
9.5 km
600 mb
8.5 km
700 mb
800 mb
900 mb H
1000 mb L
PGF
Minneapolis
Houston
SFC pressure rises
SFC pressure falls

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 m 747 mb
2,000 m 795 mb
1,500 m 846 mb
1,000 m 899 mb
500 m 955 mb
0 m mb
1 mb per 10 m height
Consequently……… Vertical pressure changes from differences in station elevation dominate horizontal changes

22. Station Pressure
Ahrens, Fig. 6.7
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

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

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 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
882 mb Hurricane Wilma October 2005
Ahrens, Fig. 6.3

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. PGF
Ahrens, Fig. 6.7

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. 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!

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

33. 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

34. 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.”

35. 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.”
Click “interactive exercise”
Click “interactive isotherm map”
From

36. 570 dam contour

37. 576 dam contour

38. 570 and 576 dam contours

39. All contours at 6 dam spacing

40. All contours at 6 dam spacing

41. -20 C and –15 C Temp contours

42. -20 C, –15 C, -10 C Temp contours

43. All contours at 5o C spacing

44. Height contours Temp shading

45. PGF
Wind

46. 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

47. 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

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

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