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GEU 0047: Meteorology
Lecture 8
Air Pressure and Winds
How can you know this wind direction?
Pressure
• The steady drumbeat of countless numbers of atoms
and molecules, exchanging momentum with the
walls of a container and providing the “Pressure”.
Gas Law
• The pressure is related to the density and
temperature of the gas through its internal energy.
– Kinetic Energy = 1/2 m v2
– Exchange of Momentum, the drumbeat of atoms and
molecules.
• Equation of State
– PV = NkT
N = number
k = Boltzman's constant = 1.38 x 10-23 J/K
– PV = nRT
n = grams per mole / molar mass
R = Gas constant = 8.31 Joules/mole/K
Partial Pressures
Pressure = PN2 + PO2 + + PAr + PH20 + PCO2 + ...
Pressure = Force / Area
(Snow shoes on thin ice, high heels on asphalt)
Force = Weight of overlying air
= mass x gravity
Weight
Pressure = Force / Area
Force = Weight of overlying column of air = mass x gravity
Pressure Units
Units of Pressure
• Force / Area = Newton/m2 = Pascal
Weather Related
Pascals
Millibars
Atmospheres
Inches of Mercury
PSI
Sea Level
101,325
1013.25
1.0
30.0
14.7
5,000 feet
10,000 feet
500
0.5
15.0
7.4
250
0.2
7.5
3.0
Pressure Records
Fluid Pressure at Height (or Depth)
Since pressure (P) = Force / Area and the force
is the weight (W = mg) of the overlying column...
P = mg/A
Multiply the top and bottom by the volume (V)
P = Vmg/VA
m/V is the density and V/A is just the height for a
Therefore,
P=rgh
Pressure and Columns
At what depth do we encounter a pressure = 1 atm.
In a) water, b) gasoline, c) mercury?
Pressure and Columns
At what depth do we encounter a pressure = 1 atm.
In a) water, b) gasoline, c) mercury?
1 atm = 101325 Pascals
P = rgh
ha = P/rag
hb = P/rbg
hc = P/rcg
Pressure and Columns
At what depth do we encounter a pressure = 1 atm.
In a) water, b) gasoline, c) mercury?
1 atm = 101325 Pascals
P = rgh
ha = P/rag = 101325/1000*9.8
hb = P/rbg = 101325/680*9.8
hc = P/rcg = 101325/13600*9.8
Inches of Mercury
At what depth do we encounter a pressure = 1 atm.
In a) water, b) gasoline, c) mercury?
1 atm = 101325 Pascals
P = rgh
ha = P/rag = 10.3 meters
hb = P/rbg = 15.2 meters
hc = P/rcg = 0.76 meters
1 atm ~ 30 inches mercury (0.76 meters)
Pressure and Altitude
• There is a large difference in pressure with altitude.
Pressure Changes
Horizontal: Changes ~ 1 mb over 10,000s of meters
Vertical: 1 mb over 10s of meters
Barometric Pressure must be corrected for Altitude
(and Temperature).
Vertical atmospheric motions are more important
than horizontal ones because of temperature and
pressure changes in this direction are much larger
than similar distances in the horizontal direction.
Pressure and Altitude
Station pressure:
Local Reading
Local Values
must be corrected
for elevation and
reduced to
sea level for
comparison.
Pressure Lapse Rate
In an average standard atmosphere with a lapse rate
of ~ 6.5 oC/1000 m, atmospheric pressure decreases are
approximated by ~ 100 mb/1000 m.
Station pressure at its elevation is then corrected to sea level
with this standard gradient.
Example:
Station Pressure 894 mb, Elevation +1100 m
Equivalent Sea Level Pressure = 894 + 1100*(100/1000)
= 1004 mb
Pressure Gradients
DP/Dd = Pressure Gradient (Change in Pressure/Distance)
Example:
DP/Dz = - rg
DP = change in pressure
Dz = change in altitude
r = density (air)
g = gravity (9.8 m/s2)
Pressure Gradient Force (PGF): Force due to pressure
differences, and the cause of air movement (winds).
Pressure Gradient Force
F = m a,
acceleration
a = F/m = Dv/Dt
P = F/A
r = m/V
pressure
density
acceleration
a = F/m = -(1/r)*DP/Dd
Wind is accelerated perpendicular to isobars from High to
Low pressure.
Wind velocity ~ (1/r)*DP/Dd
Isobars
Contours of Constant Pressure
Topographical Analogy: Just as close topographic lines
indicate steep terrain, close isobars mean steep pressure
gradient, large pressure force and therefore strong winds.
SURFACE MAP
Pressure Gradient Force (PGF)
Air moves from High
pressure to Low
pressure.
The force provided by
the pressure difference
is the pressure gradient
force. Force is directed
perpendicular to the
isobars from Highs to
Lows.
Isobar Levels
Standard isobaric levels
Each isobaric level picks
out a general altitude to
study. These are constant
altitude charts, similar to
the surface map.
Fig. 8-12, p. 199
Isobar Levels
Bernoulli’s Equation
Recall that WORK = change in both Potential Energy
and Kinetic Energy.
W = Force * Distance
=PAx
=PV
Finally, P2, v2, x2, h2, A2
h2
Initially, P1, v1, x1, h1, A1
Bernoulli’s Equation
D KE = 1/2 m (v2-v1)2
D PE = mg (h2-h1)
Finally, P2, v2, x2, h2, A2
h2
Initially, P1, v1, x1, h1, A1
Bernoulli’s Equation
D KE = 1/2 m (v2-v1)2
D PE = mg (h2-h1)
DW = DKE + DPE
Leads to the equation of continuity...
P + 1/2 r v2 + r g h = constant
The sum of pressure, kinetic energy per volume and
potential energy per volume have the same value
along all points in a streamline.
Bernoulli’s Principle
Pressure is lower for faster steady flow than for slower
Higher v, Lower P
Airplane Wings
Lower v, Higher P
Wind Speed Vectors
Vectors are arrows representing wind direction and
speed.
Bernoulli Winds
Ridge and Trough
Wavelike patterns of constant pressure surfaces reflect
pressure changes due to air temperature differences.
Constant Pressure Surfaces
At what height do you experience a Pressure of 500 mb?
Density and Pressure
• The warmer air column is less dense.
• At the same height, the pressure is higher in the
warmer air column.
Latitude Pressure Gradient
• At the same altitude, the pressure is higher on average in the
warmer (i.e. lower) latitudes.
Temperature PGF versus Altitude
Air Forces
Force = Pressure Gradient Force + Coriolis + Friction
• For any fixed height, the pressure decreases toward cooler
latitudes.
• Isobars for a fixed altitude show this decrease to the North
(South) in the Northern (Southern) Hemisphere.
• In the absence of rotation, air (in the upper level) would
tend to flow from the equator toward the poles.
Global Circulation
• In the absence of rotation, air would tend to flow
from the equator toward the poles.
Hot, less dense air
rising at the equator,
becomes denser as
it cools and descends
at the poles, traveling
back to tropical areas
to heat up again.
Coriolis
Outsider’s view
Insider’s view
Outsider’s view
Insider’s view
From http://www.windpower.dk/tour/wres/coriolis.htm
Coriolis FORCE
A. Force: due to a rotating frame of reference.
B. Objects moving in a straight line with respect to the stars,
will experience an apparent deflection to the RIGHT in
the N.Hemisphere and an apparent deflection to the LEFT
in the S. Hemisphere.
C. The Coriolis force is strongest at the poles and zero at the
equator.
D. The Coriolis force is proportional to the speed.
E. The "force" affects the direction NOT the speed.
But since velocity is a vector, with both direction and
speed, the velocity change is the same as acceleration and
the Coriolis force is the culprit.
Coriolis Force Equation
Relative to a carousel, someone walking on a carousel
moves in a straight line with respect to the fixtures.
Relative to others and equipment on the ground,
the person moves in an arc as if affected by a force.
The (horizontal) Coriolis Force
Fc = 2W v sin f
v = wind speed
W = angular velocity (earth rotation, 360 degrees/24 hours)
f = latitude
(sin 0 = 0.0 equator, sin 90 = 1.0 poles)
Coriolis Deflection
Fc = 2W v sin f
Increase of the
Coriolis Force with
wind speed.
Pressure Gradient Force
• Air flows from high pressure to low pressure, so on average,
from the equators to the poles.
Geostrophic flow
• Remember that the coriolis force depends upon
velocity.
As air is accelerated by
the PGF its speed
increases and the
coriolis deflection
grows. Equilibrium is reached when the PGF and
coriolis effect are equal.
PGF = Coriolis
1/r*DP/Dd = 2 W v sin f
The wind velocity
v = DP/Dd * (1/r 2 W sin f)
Utilizing the coriolis parameter fc = 2 W sin f
The wind velocity v = (1/rfc)*DP/Dd = vg
This is known as the geostrophic wind equation.
Geostrophic flow
• With the inclusion of the Coriolis Force, air flows
parallel to isobars of constant pressure.
Westerlies
• At mid latitudes, air moving from S. to N. in the
northern hemisphere flows from west to east.
Friction Effect
Friction retards
wind speed near
the surface due
to topography,
lowering the
coriolis force.
Therefore, wind
direction is
altered from
parallel to isobars.
Cyclonic Flow
Low Pressure Cyclonic Winds
High Pressure Cyclonic Winds
Isobar Surface Map
Cyclone Anticyclone Circulations
Summary
• Pressure = Force / Area
• Forces on Air
– Pressure Gradient Force
– Coriolis Force
– Friction
• Isobar Charts
• Global Circulation Pattern (3 cell model)
• Cyclone and Anticyclone Circulations