Chapter 9 – Air Pressure, Forces and Wind
Air pressure:
Using a model that assumes a constant air density with altitude:
L
ρ1
(1)
cold
H
ρ2
(2)
hot
For the warmer city (2), higher pressure aloft will eventually lead to lower surface
pressure, because wind blows from high to low pressure in response to the pressure
gradient force.
How can air density be constant with altitude? (Only approximately true over small
heights.)
Ideal Gas Law
P=CρT
If P is in millibars (mb)
T is in Kelvins
and ρ is in kg / m3
then C ≅ 2.87
This relation is valid for a parcel of air within which P, ρ and T are constant
Example:
A parcel of air is raised from the ground to a height of 2 km,
At 0 km, P1 = 1013mb, T1 = 25°C
At 2 km, P2 = 800mb
Assume lapse rate of 8°C / km
What is ρ2 / ρ1?
ρ 2  P2  CT1   800  T1 
=

=
 
ρ1  CT2  P1   1013  T2 
T1 = 25°C + 273 = 298K
T2 = 25°C - 16°C = 9°C so T2 = 9°C + 273 = 282 K
∴
ρ 2  800  298 
=
 = 0.83

ρ1  1013  282 
ρ2 = 83% of ρ1
Note: P2 is 79% of P1 so P decreases faster.
Mercury Barometer: A column of mercury (Hg) of height h = 76 cm exerts about 1 atm. of
pressure
Forces of gravity and air pressure are balanced.
Station Pressure: pressure reading at your location corrected for temperature, instrument error
(calibration) and variations in gravity.
Altitude Corrections: allow comparisons of atmospheric pressure from one city to another
correcting for different altitudes of the cities.
Sea Level Pressure: add 10mb for every 100 meters that your station is above sea level.
Connect points of equal pressure at sea level and draw them on a map.
- See map with sea level isobars (see Fig 9.9 b)
Also very useful in predicting weather trends is a 500mb map, which shows contours of altitude
at which the pressure is 500 mb. (See Fig 9.15 b).
Note: On a surface map, winds blow counterclockwise (CCW) and inward around a
surface low and across isobars. Winds blow parallel to contours on a 500 mb map.
What determines how the wind blows?
Forces cause objects to accelerate. Acceleration is any change in speed OR direction of
motion.
Constant Speed – V
Acceleration “a” because of a change in direction.
a
V
Newton’s Second law
F = ma
F is net external force on object m
a is acceleration of object of mass m
Forces that influence wind are:
1. Pressure gradient force – causes wind to blow
2. Coriolis force – deflects moving wind
3. Centripetal force – a combination of other forces that acts perpendicular to v and
allows circular motion
4. Friction – slows wind down (near earth)
P1
P2
P(z)
PATM
P3
 1atm 
 z
P ( z ) = 1atm + 
 34 ft 
3
P(z)
(atm)
P(z) is linear (straight line)
because water is incompressible.
ρ = constant
2
1
0
34
z (ft)
68
d
P2
Patm
P3
Pressure Gradient :
∆P P2 − Patm
=
d
d
Patm
PGF is directed from high to low pressure, perpendicular to isobars and is larger for
closely spaced isobars.
Coriolis Force:
We live in a rotating reference frame! (The earth)
Example: Transparency demo
Force-free (frictionless) motion will cause object to veer to the right in the Northern
Hemisphere, as viewed in rotating frame. (veer to left in Southern Hemisphere)
Fcor = 0 at equator, large at poles
Fcor is larger for high speeds
Centripetal Force :
An object moving in a circle is accelerating even if it moves at constant speed.
Sitting in a car, you need a push to accelerate forward, brake, or move around a curve.
So, if winds move in a circle around a high or low pressure system, a force must be
acting on the air directed inward toward the center of the low or high.
Isobar
L
F
Wind
Recap: Forces that affect wind
1.
Pressure Gradient Force, PGF
PGF =
m = mass of air molecule
m ∆P
ρ d
ρ = density of air
∆P = Phigh − Plow
PGF
d
900 mb
d = distance between ∆P
904 mb
∆P = 4 mb
908 mb
PGF points from high to low pressure, perpendicular to isobars. Tends to push wind
across isobars.
2.
Coriolis Force, Fcor = 2 m V Ω sin Θ
V = wind speed
Ω = rotational speed of earth
Θ = latitude angle
Fcor operates perpendicular to velocity of wind and deflects it to the right in the NH and to
the left in the SH. It does not change the wind speed. Fcor is greater for higher wind
speeds and high latitudes.
3.
Centripetal force, Fcent = m
V2
r
r is radius of circular arc wind is moving in. Fcent points radially inward and is the name
of the net inward force - it is not a separate force itself. Fcent does not change the speed of
the wind, only the direction.
4.
Friction Force, f
f changes the speed of the wind.
Geostrophic Wind
Within ~ 1 km of the earth’s surface, friction acts to slow wind down. Above the friction
layer, winds generally blow parallel to isobars.
PGF
PGF
Fcor
When wind is just
parallel to isobars
PGF = Fcor and
wind speed stay
steady.
Process is self-correcting.
PGF
Fcor
PGF
Fcor -PGF = Fcent
PGF- Fcor = Fcent
PGF shifts forward to stay
perpendicular to isobars, this
speeds up wind which
increases CF and this deflects
wind downward.
Fcor
high
PGF
low
PGF shifts back, wind slows,
wind deflects upward.
Fcor
Geostrophic wind speed is proportional to the pressure gradient.
Surface Winds
Add frictional drag to above discussion
Friction slows
wind, which
decreases Fcor .
Wind deflects
more to left.
Low
PGF
PGF
f
f
Fcor
Fcor
f
PGF
Fcor
f
High
Fcor
PGF
Fcor - PGF=Fcent
Add f - Fcor
decreases because
wind slows down.
Wind deflects to
left
Note: You get westerly winds in both the NH and SH – see focus section page 239.