Air Pressure
and the Wind
Up
until this chapter, we have talked about the thermodynamic structure of the
atmosphere, by talking about temperature, temperature differences etc...
Now
we’ll talk a bit about atmospheric pressure. When we examine pressure fields,
we can talk about wind fields, and thus the kinematic and dynamic structure of
the atmosphere.
Pressure
is another variable by which we can describe the state of the atmosphere, but
unlike temperature and moisture, we cannot sense these changes as readily.
Air
pressure, is a result of the force the air exerts on an object. This force is
due to the cumulative affect of molecular collisions with a surface. The force
per unit area is a standard way to measure air pressure.
Recall: Force = mass x
gravity
Pressure
= Force / Area
(About
1.0 kg per sq. centimeter, or 14.7 lbs per sq. inch)
Why
doesn’t the weight of air pressure crush things on the surface, since there is
as much as 1000 lbs of air sitting on our heads?
The
amount of pressure produced by gas molecules of the air depends on:
1) the mass of the molecules
2) the pull of gravity
3) the kinetic molecular
activity
Barometer
--> Invented in 1643 by Evangelista Torricelli.
He
invented the Mercury (Hg) barometer, by filling a tube with Hg and inverting it
in an open vat of Hg. The Hg then settles down until the weight of the mercury
in the column equals the weight of the atmosphere on the vat of Hg.
The
average air pressure supports a column of Hg 29.92” tall (760 mm).
Less
precise, but more portable.
It’s
made using a partially evacuated chamber, which is connected to a pointer. As
the chambers expand or contract, the needle moves.
Barograph,
is a similar instrument, except the pressure trace is recorded on a rotating
drum.
Aneroid
barometers can be calibrated to measure altitude, since pressure drops off
logrithmically with height.
The
change in air pressure is called the ‘pressure tendency’. The pressure tendency
can tell us something about the approaching weather.
Pressure
falls are associated with worsening weather, and pressure rises tend to be
associated with improving weather.
You
will usually hear about air pressure readings in inches. Typically Pressure is
plotted in Millibars.
Recall:
Pressure = Force / Area (kg m -1s -2 à “Pascal”)
Average
surface pressure 1013.25 mb, or 101,325 Pascals (1013.25 hectopascals (hPa)).
Thus, 1 mb = 1 hPa.
Pressure
falls off rapidly with height in the lower troposphere, and slowly higher up.
This
is due to gravity’s “tug” on the atmosphere. However, a balance is maintained
between gravity, and the tendency for air to move down gradient in the
vertical.
Recall
earlier, we showed typical heights for various pressure levels.
e.g.
(typical pressure levels used to plot atmospheric data)
850
hPa à 1.5 km
700
hPa à 3.0 km
500
hPa à 5.5 km
300
hPa à 9.0 km
200
hPa à 12.0 km
100
hPa à 16.0 km
The
amount of atmospheric mass in terms of a percentage can be calculated by using
a layer thickness.
e.g. (850 hPa - 700 hPa
layer)
850
- 700 = 150 hPa / Avg sfc pressure (1000 hPa)
means
15% of the atmospheric mass lies between 1.5 and 3.0 km.
Or:
20% of the atmospheric mass lies between 500-300 hPa, and 300 - 100 hPa. The
first layer is 3.5 km thick, the second is roughly 7.0 km thick.
Finally,
99% of the atmosphere lies below 32 km (10 hPa).
On
a weather map, station pressure is reduced to sea-level. Since pressure falls
with height are larger than horizontal pressure variations, reduction to sea -
level
provides
us a way to examine pressure gradients.
Pressure
may fall off 1 hPa as we go up 10 m, but may change 1 hPa every 100 km in the
horizontal.
Horizontal
Pressure gradients give rise to air motions (winds), as air moves from high
pressure to low pressure and is influenced by coriolis force. The stronger the
pressure gradients, the faster the winds blow.
Wind
blows clockwise (counter clockwise) around high pressure (low pressure) in the
Northern Hemisphere. It is the opposite in the Southern Hemisphere.
Examples:
Where
air moves toward one point (convergence -- associated with low pressure), where
air “spreads out” (divergence -- associated with high pressures)
Pressure is
related to density and temperature through the “ideal gas law”
Pressure = density * Const. *
Temperature (K)
Air
is less (more) dense when it is warmer (colder) and moister (drier).
Pressure
is inversely related to volume, (Boyle’s Law 1600).
A
“sample” of air with the temperature being held constant:
Raise
the pressure:
Lower
the pressure:
Air
volume is directly related to temperature (Charles’ Law 1787)
Take
a sample of air at constant Volume:
Warm
the air:
Cool
the air:
Ideal
Gas Law (Equation of State) is a combination of Boyle’s and Charles Law
The
“Constant” is the dry air gas constant (R), which is unique for each gas, or
mixture of gasses based on their molecular weight. Thus, the value for dry air
is based on a mixture of Nitrogen, Oxygen, Argon, etc.
Q:
Why is moist air less dense than dry air?
A: Density = Pressure / (R * Temperature)
The
molecular weight of water is: 18
A
mixture of dry air and water has a smaller molecular weight than dry air, which
results is a larger value for R.
Using
a larger “R” in the ideal gas law results in a smaller
density.
The
wind à Is the motion of air relative to the planet.
The
atmosphere is coupled with the Earth and rotates with it. Thus, the speed of
the wind is:
Thus,
a west wind is moving faster in the absolute sense (from an observers point of
view in space). An east wind is moving slower.
Wind
can be defined as a speed (scalar property), or wind velocity (vector quantity).
Wind
conventions:
Wind
direction is defined by what direction the wind is coming from, thus a west
wind is coming from the west!
Wind
direction uses the cardinal (Compass) directions North, South, East, and West.
Cartesian
(math) Compass
(meteorology)
Example:
Thus,
a NW wind is coming from the northwest (defined as 315 degrees).
In
meteorology, we distinguish between horizontal winds, and vertical motions
(each represents a slightly different force balance to bring them about).
Vertical
motions on the large-scale are ignored because they are typically less than 10%
the value of horizontal motions.
The
horizontal wind has a west - east component (u) and a north - south (v)
component.
Convention
(u and v),
u
component positive for west wind (+)
negative for an east wind (-)
v
component positive for south wind (+) negative for an north wind (-).
What
forces influence the wind or bring it about?
Force:
is defined as an agent that causes a resting (non-accelerating) object to move,
or alters it’s movement. The action of a force is called acceleration.
Since
wind is a vector, a force can be defined as changing the speed or direction of
the wind.
Examples:
A
Northeast wind at 10 mph can accelerate to a Northeast wind at 20 mph if acted
upon by a force.
Or,
a Northeast wind at 10 mph can change direction to an east wind at 10 mph. This
is still acceleration.
Thus,
acceleration is a force per unit mass of air. This is a statement of
The
resultant acceleration of an air parcel (wind) is the sum of all the forces.
What
forces accelerate the wind?
1) Pressure gradient force (PGF)
2) coriolis force (Co)
3) centripetal force (Ce)
4) frictional forces (F)
5) gravity (g)
Expressed
as a relationship:
Pressure
Gradient Force:
Air
moves down the pressure gradient from regions of mass surplus (high pressure)
to mass deficit (low pressure).
Again,
nature does not like order (as represented by gradients), thus, pressure
gradient force acts to destroy these gradients in order to restore equilibrium.
Lines
of equal pressure on a weather map: isobars!
Thus,
pressure gradient force moves air perpendicular to these lines. The stronger the gradient (more isobars per
unit distance) the stronger this force is.
Weak Strong
Centripetal
force:
This
force is a “center seeking” force. If we tie a rock to a string and twirl it in
a circular path over our head:
The
rock is kept in a circular path (balance) as a result of centripetal force
being equal to the force that would throw the rock in a straight path if we
release the string.
In
the atmosphere Centripetal force arises from the imbalance of other atmospheric
forces.
Coriolis
Force (Coriolis effect):
Arises
from the fact that we are located on a rotating sphere (Earth).
If
there were no rotation, storms would move in a straight line over the surface
(as appear to do so from space).
On
earth, the storm appears to move along a curved path.
An
observer in space is on a fixed coordinate system, the earthbound observer is
on a rotating coordinate system.
The
difference between the motions as they appear to each observer is the Coriolis
effect!
The
Coriolis effect then is a relative motion, it does NOT exist in the absolute
coordinate system!
Coriolis
effect influences motions by deflecting a moving object to the right (left) in
the Northern (Southern Hemisphere).
This
force is only influential on sufficiently long time and space scales.
Example: Coriolis effect?
Walking NO
A
storm’s path Yes
A
missle’s path (ICBM) Yes
A
long plane flight Yes
Your
toilet bowl NO
A
Roger Clemens fastball NO
Friction
is the resistance that objects encounter when it moves into contact with
another body.
Friction
also affects the atmosphere as it contacts the earth’s surface.
A
rougher surface (e.g. cities, mountainous terrain) will generate more
frictional forcing than a smoother surface (the oceans).
There
can also be frictional forces within the gas itself due to turbulence or “eddy
motions” within the fluid. These frictional forcing results from molecular
motions themselves.
Gravitational
force as we speak of it is actually the combination of gravity and centripetal
force resulting from the earth’s rotation.
Gravitational
forces obviously act in a downward direction and normal to the earth’s surface.
Gravitational
forces thus only affect the vertical component of motion.
There
are two important force balances that act on individual air parcels on the time
and space scales we study in our class:
Again,
a “balance condition’ means no accelerations, or:
Force A = Force B
1) Hydrostatic balance
2) Geostrophic balance
The
atmosphere on the largest scales is assumed to be in hydrostatic balance, that
is:
Vertical
Pressure Gradient Force = Gravitational Force
This
implies no acceleration of air in the vertical, although the air may move up or
down with constant speed.
Accelerations
in the vertical result from imbalances between Pressure gradient force and
gravitational forces.
(e.g.
Thunderstorms)
Geostrophic balance:
Geostrophic
balance is the result of the equivalence, or near equivalence in the pressure
gradient force and the coriolis force.
In
a geostrophically balance atmosphere, the wind blows parallel to the pressure
lines (isobars).
Geostrophic
balance describes large-scale flows to within 10% accuracy.
Winds in the
boundary layer:
The
boundary layer is that layer of earth where the frictional forcing of the
atmosphere with the earth’s surface influences atmospheric motions. This layer
is 0.5 - 1.5 km thick depending n time of day and season.
Force
balance in the boundary layer:
Pressure
gradient force = Coriolis force + frictional forcing
This
balance of forces describes the motions around high and low pressure:
In
the troposphere, winds typically increase with height, and maximize near the
tropopause (jet stream level).
Wind
shear, is a sudden shift in wind speed, direction, or both, in either the
horizontal or the vertical.
Vertical
wind shear is called the “thermal wind”. This concept is important in
meteorology. This combines the geostrophic and hydrostatic balance conditions.
Also,
the vertical wind shear vector (the thermal wind) blows parallel to temperature
gradients. Temperature gradients are associated with fronts.
Air
is a continuous fluid. Continuity implies a connection between the horizontal
and vertical flows.
Within
high pressure, we have divergence at the surface, downward motion and
convergent flow aloft.
Within
low pressure, we have convergence at the surface, upward motion and divergent
flow aloft.
Continuity: Sea and land breeze circulations
We
talked about the atmosphere as a continuous fluid. We have talked about
atmospheric winds, and thus motion.
But,
as we have stated, we examine horizontal and vertical motions separately, and
we have implied that there are different scales of motion.
Scales of
atmospheric motion:
Circulation Space-scale time-scale
Planetary-Scale: > 6,000 km > 7 days
(e.g.
Bermuda High, trade winds, jet streams)
(geostrophic
and hydrostatic balance hold)
Synoptic-scale 2,000 - 6,000 km 1 - 7 days
(e.g.,
air masses, highs, lows)
(geostrophic
and hydrostatic balance hold)
Mesoscale 10 - 2,000 km 1 hour - 1 day
(e.g.,
fronts, thunderstorms, hurricanes, sea breeze circulations.)
(coriolis
force becomes less influential, hydrostatic balance begins to weaken, bouyancy
force begins to dominate)
Micro-scale < 10 km < 1 h
(e.g.,
clouds, tornadoes, dust devils, turbulence)
(neither
geostrophic nor hydrostatic balance holds)
Wind
Pressure:
Pressure
(Force / Unit Area), wind pressure is the same.
Wind
pressure is proportional to the SQUARE of the wind speed.
Wp v2
Thus,
a hurricane wind speeds exert 25 times more force on your home than a breezy
day. (15 mph vs. 75 mph)
A
category 5 hurricane (Mitch) exerts 4 times the force on your home than a
“weak” hurricane (150 mph vs. 75 mph).
Wind
vane: shows wind direction, should point TOWARD the direction the wind is
coming from.
Anemometer:
Cup anemometer, 3 or four cups catch the wind. A monitor counts the “spins” per
unit time (e.g. 15 sec) and converts this to a wind speed.
Wind
instruments should be placed 10 m (33 ft) above the ground in a flat, wide open
area (or on top of the tallest structure in a city).
Wind
speed: average over an hour.
Wind
gust: maximum wind speed sustained for 1 minute.
Wind
speed measurement by eye: The Beaufort Scale
Developed
in the 1800’s by Sir Francis Beaufort, of the British Navy.