NATS 101-06 Lecture 11 Air Pressure

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NATS 101-06Lecture 11Air Pressure

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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

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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!

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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
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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

Effect maximized around -15oC
Ahrens, Fig. 5.19
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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)
Aggregation
Splintering
Also known as the Bergeron Process after the
meteorologist who first recognized the importance
of ice in the precipitation process
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What is Air Pressure?

• Pressure Force/Area
• What is a Force? Its like a push/shove
• In an air filled container, pressure is due to
  molecules pushing the sides outward by recoiling
  off them

Recoil Force
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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

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Air Pressure

• At any point, pressure is the same in all
  directions
• But pressure can vary from one point to another
  point

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• 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
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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

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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

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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!

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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!

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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!

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Summary

• Ideal Gas Law Relates
• Temperature-Density-Pressure

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Pressure-Temperature-Density

• Pressure
• 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
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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
700 mb
8.5 km
800 mb
900 mb
1000 mb
Minneapolis
Houston
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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
500 mb
H
L
PGF
9.5 km
600 mb
700 mb
8.5 km
800 mb
900 mb
1000 mb
L
H
PGF
Minneapolis
Houston
SFC pressure rises
SFC pressure falls
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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 motionor the wind!

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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 1013 mb
• 1 mb per 10 m height

Consequently. Vertical pressure changes
from differences in station elevation dominate
horizontal changes
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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
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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
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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

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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

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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?

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

• Because horizontal pressure differences are the
  force that drives the wind
• Station pressures are adjusted to one standard
  levelMean Sea Levelto remove the dominating
  impact of different elevations on pressure change

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PGF
Ahrens, Fig. 6.7
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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

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Pressure in Warm and Cold Air
Ahrens, Fig. 6.2
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Pressure-Temperature-Density
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Pressure-Temperature-Density
Ahrens, Fig. 6.2

• Pressure
• Decreases with height at same rate in air of same
  temperature
• 300 mb Level
• Slope is horizontal

300 mb
9.0 km
Same Density
Same Density
1000 mb
Minneapolis Houston
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Pressure-Temperature-Density
Ahrens, Fig. 6.2

• Pressure
• Decreases more rapidly with height in cold air
  than in warm air
• 300 mb Level
• Slopes downward from warm air to cold air

300 mb
9.5 km
8.5 km
Less Dense
MoreDense
1000 mb
Minneapolis Houston
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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

Ahrens, Fig. 6.2
300 mb
9.5 km
8.5 km
Less Dense
MoreDense
1000 mb
Minneapolis Houston
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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

Ahrens, Fig. 6.2
300 mb
9.5 km
PGF
8.5 km
H
L
1000 mb
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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

100 mb
200 mb
300 mb
400 mb
500 mb
9.5 km WARM
600 mb
700 mb
8.5 km COLD
800 mb
900 mb
1000 mb
Minneapolis
Houston
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Pressure-Temperature-Density
100 mb
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
200 mb
300 mb
400 mb
500 mb
H
L
PGF
9.5 km WARM
600 mb
700 mb
8.5 km COLD
800 mb
900 mb
1000 mb
L
H
PGF
Minneapolis
Houston
SFC pressure rises
SFC pressure falls
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Measuring Air Pressure
Ahrens, Fig. 6.4

• 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

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Recording Aneroid Barometer
Ahrens, Fig. 6.6

• Aneroid cell is partially evacuated
• Contracts as pressure rises
• Expands as pressure falls
• Changes recorded by revolving drum

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Isobaric Maps
Ahrens, Fig. 2, p141
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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!

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Isobaric Maps
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
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Contour Maps

• Display undulations of 3D surface on 2D map
• A familiar example is a USGS Topographic Map
• Its a useful way to display atmospheric
  quantities such as temperatures, dew points,
  pressures, wind speeds, etc.

Gedlezman, p15
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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.

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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.

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570 dam contour
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576 dam contour
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570 and 576 dam contours
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All contours at 6 dam spacing
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All contours at 6 dam spacing
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-20 C and 15 C Temp contours
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-20 C, 15 C, -10 C Temp contours
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All contours at 5o C spacing
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Height contours Temp shading
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(No Transcript)
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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

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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 marbles direction

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Assignment

• Reading - Ahrens pg 148-149
• include Focus on Special Topic Isobaric Maps
• Problems - 6.9, 6.10

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Assignment

• Topic Newtons Laws
• Reading - Ahrens pg 150-157
• Problems - 6.12, 6.13, 6.17, 6.19, 6.22

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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/m3) ? T(K)
• ?(kg/m3) P(mb) / 2.87 ? T(K)
• ?(kg/m3) (1013 mb) / (2.87 ? 288 K)
• ?(kg/m3) 1.23 kg/m3 ? 2.00 lbs/yard3

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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

100 mb
200 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

100 mb
200 mb
300 mb
400 mb
500 mb
H
L
PGF
9.5 km WARM
600 mb
700 mb
8.5 km COLD
800 mb
900 mb
1000 mb
L
H
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Measuring Air Pressure
Ahrens, Fig. 6.4

• 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

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Recording Aneroid Barometer
Ahrens, Fig. 6.6

• Aneroid cell is partially evacuated
• Contracts as pressure rises
• Expands as pressure falls
• Changes recorded by revolving drum

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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?