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NATS 101
Lecture 11
Air Pressure
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http://en.wikipedia.org/wiki/Atmospheric_pressure
Plastic bottle sealed at 14,000’; crushed at 1,000’.
What is Air Pressure?
Recoil
Force
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
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
Air Pressure
Recoil
Force
At any point, pressure
is the same in all
directions
But pressure can vary
from one point to
another point
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 between
faster moving molecules
Ideal Gas Law
• Relation between pressure, temperature and
density is quantified by the Ideal Gas Law
P(mb)=Const(mb m3/kg/K)  d(kg/m3)  T(K)
• Where P is pressure in millibars (mb)
• Where d is density in kilograms/meter3 (kg/m3)
• Where T is temperature in Kelvin (K)
• Where Const=2.87 is a constant (mb m3/kg/K)
(Parenthetical expressions are units)
Ideal Gas Law
• Ideal Gas Law is complex
P(mb) = Const  d(kg/m3)  T(K)
P(mb) = 2.87 mb m3/kg/K  d(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
Ideal Gas Law
P = constant  d  T (constant)
With T constant, Ideal Gas Law reduces to
 P varies with d 
Boyle's Law
Denser air has a higher pressure than less
dense air at the same temperature
Why? You give the physical reason at home.
Ideal Gas Law
P = constant  d (constant)  T
With d constant, Ideal Gas Law reduces to
 P varies with T 
Guy Lussac’s Law
Warmer air has a higher pressure than
colder air at the same density
Why? You answer the underlying physics.
Ideal Gas Law
P (constant) = constant  d  T
With P constant, Ideal Gas Law reduces to
 T varies with 1/d 
Charles Law
Colder air is more dense (d big, 1/d small)
than warmer air at the same pressure
Why? Again, you reason the mechanism.
Summary
• Ideal Gas Law Relates
Temperature-Density-Pressure
Fundamental Relationship that governs
the state of air in our atmosphere
Pressure-Temperature-Density
300 mb
500 mb
9.0 km
9.0 km
400 mb
600 mb
700 mb
800 mb
900 mb
Minneapolis
Houston
Pressure
Decreases with height
at same rate in air of
same temperature
Constant Pressure
(Isobaric) Surfaces
Slopes are horizontal
Pressure-Temperature-Density
WARM
8.5 km
9.5 km
COLD
Minneapolis
Houston
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
Pressure-Temperature-Density
WARM
L
H
8.5 km
PGF
H
PGF
Minneapolis
SFC pressure rises
9.5 km
COLD
L
Houston
SFC pressure falls
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
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!
NATS 101
Lecture 11
Surface Weather Maps
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N. Pacific Pressure Analysis
(isobars every 4 mb)
2000 km
Pressure varies by 1 mb per 100 km horizontally
or 0.0001 mb per 10 m
Review: Pressure-Height
Consequently……….
Vertical pressure changes from
differences in station elevation
dominate horizontal changes
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
0m
1013 mb
1 mb per 10 m height
Station Pressure
Ahrens, Fig. 6.7
Pressure is recorded at stations with different altitudes
Station pressure differences mostly reflect height differences
Wind is forced by horizontal pressure differences
Since true horizontal pressure changes are 1 mb per 100 km
We adjust station pressures to one standard horizontal level:
Mean Sea Level
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
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
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
Local Example to Try at Home
The station pressure at PHX is ~977 mb.
The station pressure at TUS is ~932 mb.
Which station has the higher SLP?
Sea Level Pressure Values
882 mb (26.04 in.)
(October, 2005)
Wilma
Ahrens, Fig. 6.3
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
PGF
Ahrens, Fig. 6.7
Key Points
• 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 Mean-Sea-Level to Mitigate the
Dominate Impact of Altitude on Pressure Change
Surface Maps
• Pressure reduced to Mean Sea Level is
plotted and analyzed for surface maps.
Estimated from station pressures
• Actual surface observations for other
weather elements (e.g. temperatures,
dew points, winds, etc.) are plotted on
surface maps.
NCEP/HPC Daily Weather Map
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Next Lecture Assignment
Newton’s Laws, Upper-Air Maps
• Reading - Ahrens
3rd: 146-155
4th: 148-157
5th: 148-156
• Problems - D2L (Due Wednesday Mar 3)
3rd-Pg 162: 6.09, 10, 12, 13, 17, 19, 22
4th-Pg 164: 6.09, 10, 12, 13, 17, 19, 22
5th-Pg 165: 6.10, 11, 13, 14, 18, 20, 23