Download Atmospheric Pressure - Wind - General Circulation

Isaac Newton (1642-1727)
Introduction to Climatology
GEOGRAPHY 300
Tom Giambelluca
University of Hawai‘i at Mānoa
Philosophiæ Naturalis Principia Mathematica (1687)
"Mathematical Principles of Natural Philosophy”
Atmospheric Pressure, Wind, and
The General Circulation
• 
• 
• 
• 
Newton’s Laws of Motion
Newton’s Law of Universal Gravitation
Theoretical Derivation of Kepler’s Laws of Planetary Motion
Laid the Groundwork for the Field of Calculus
Newton's Laws of Motion
Newton's Laws of Motion
1st Law: Law of Inertia: If no net force acts on a particle, the particle will
not change velocity.
Newton's Laws apply only in an inertial reference frame.
An object at rest will stay at rest, and an object in motion, will continue at
constant velocity unless acted on by external unbalanced force.
An inertial reference frame cannot be accelerating; must be at rest or
moving at a constant velocity (constant speed and direction).
2nd Law: Law of Acceleration: The rate of change of velocity
(acceleration) of a particle of constant mass is proportional to the net
external force acting on the particle.
a=
F
m
or
F = m⋅a
where a = acceleration, F = force, and m = mass.
1
Pressure
P=
F
A
Pressure = Force per Unit Area
In our environment, gravity is constantly accelerating objects downward.
Gravitational acceleration (g) is approximately constant within the earth's
atmosphere:
Pressure
The weight of an object is the force determined by gravitational
acceleration and the mass of the object:
Weight = F = m × a
Pressure = Force per Unit Area = P = F/A
Atmospheric Pressure is the force exerted by the weight of the
atmosphere above a given point.
!m$
# &
m
"s%
g = 9.8
= 9.8 2 = 9.8 m s−2
s
s
Pressure
Pressure always decreases as you go up:
Pressure
Measuring Atmospheric Pressure
The Torricelli Tube: the original barometer (invented in 1643 by
Evangelista Torricelli)
Mean sea level atmospheric pressure:
1013.2 mb = 101.32 kPa = 101,320 Pa
2
Pressure
Pressure Gradients
Equation of State (Ideal Gas Law):
A Change in Pressure over a Distance
P = ρRT
A pressure gradients is important because it exerts a force on air which
acts to move air from high pressure to low pressure:
where P = pressure (Pa), ρ = density (kg m-3), R = universal gas constant
(287 J kg-1 K-1), and T = temperature (K)
Pressure Gradient Force
Changes in temperature
or density cause changes
in pressure.
High Pressure
Pressure Gradients
Pressure Gradients
Vertical Pressure Gradient
Hydrostatic Equilibrium
Because of the relationship between elevation and pressure, a strong
vertical pressure gradient is always present.
Which direction is the resulting strong vertical pressure gradient force
acting?
What effect does vertical pressure gradient force have on air motion?
Upward vertical pressure gradient force is balanced by an equal force
oriented in the opposite direction.
The balance between vertical pressure
gradient force and gravitational acceleration
(Hydrostatic Balance) limits vertical motion in
the atmosphere.
GRAVITY
3
Pressure Gradients
Pressure Gradients
Horizontal Pressure Gradients
Horizontal Pressure Gradients
Visualize the lower atmosphere seen from a cross sectional perspective.
In the diagram below, upward in the atmosphere is toward the top. The
horizontal line represents sea level. Go up from the ground until the
pressure drops to 1000 mb. Do that from several different locations
Connecting the points forms a 2-dimensional surface of all points having
the same pressure; we call this an isobaric surface; in profile, as in the
drawing above, we see the edge of the isobaric surface; it is a line of
equal pressure, called an isobar.
Pressure Gradients
Pressure Gradients
Horizontal Pressure Gradients
Horizontal Pressure Gradients
In the pressure diagrams just shown, the isobaric surfaces were seen as
flat and horizontal.
In that situation no horizontal pressure
gradients are present.
Therefore, no wind would occur.
The air would remain still.
If we went higher in the atmosphere, we would encounter isobaric
surfaces with successively lower pressure values.
4
Pressure Gradients
Pressure Gradients
Horizontal Pressure Gradients
How Do We Get Horizontal Pressure Gradients?
In the previous diagram note that the distance between the 1000 and 900
mb surfaces is less than the distance between the 900 and 800 mb
surfaces. Why is that?
We know that air density is affected by air temperature. Warm air is less
dense than cold air. The isobaric surfaces will have to be farther apart for
warm air than for cold air.
Answer: As you go up, the density of air decreases, therefore the distance
necessary to reduce the pressure by 100 mb is greater as you go higher.
Another way to think about this is that the mass of air between any 2 isobaric
surfaces 100 mb apart is the same, i.e. you can equate the pressure difference
with a given mass of air. But at higher elevations, the air is less dense, so you
have to go farther to reduce the mass of air above you by the amount
necessary to lower the pressure by 100 mb.
Pressure Gradients
Pressure Gradients
Horizontal Pressure Gradients
Horizontal Pressure Gradients
Suppose you have one area with warm air and another area with cold air:
Now we see horizontal differences in pressure. Along the ground, the
cold air has higher pressure:
5
Pressure Gradients
Pressure Gradients
Horizontal Pressure Gradients
Horizontal Pressure Gradients
Higher up, we see the pressure gradient is reversed:
SEA BREEZE
The resulting circulation, if no other forces were acting, would be a cell
such as:
Pressure Gradients
Pressure Gradients
Sea Breeze and Land Breeze
Sea Breeze and Land Breeze
LAND BREEZE
6
Pressure Gradients
Pressure Gradients
Horizontal Pressure Gradients
Horizontal Pressure Gradients
The horizontal pressure gradient can also be represented by the slope of
an isobaric surface. Regarding the height of a pressure surface, areas
where it is higher correspond to high pressure areas and vice versa. The
steeper the slope of the isobaric surface, the stronger the horizontal
pressure gradient.
The spacing of the isobars indicates the strength of the gradient and,
therefore, the speed of the wind.
Pressure Gradients
CORIOLIS EFFECT
Horizontal Pressure Gradients
Horizontal pressure patterns in the upper atmosphere are shown using
pressure surface height maps.
The rotation of the earth on its axis means that the
surface of the earth is constantly accelerating. In
our non-inertial reference frame, large-scale
motion such as atmospheric winds and ocean
currents appear to be deflected away from the
direction of the forces acting.
7
CORIOLIS EFFECT
Let's try to understand Coriolis effect by looking at the
Earth from above the North Pole:
At the start (t1), a force causes an object to start moving south.
The object continues in the same direction, but the Earth is
rotating. As a result, an hour later (t2), the path of the object
appears to have veered off to the right, as viewed from the
ground.
CORIOLIS EFFECT
CORIOLIS EFFECT
How about in the Southern Hemisphere? Let's look at the
Earth from above the South Pole:
Now the object appears to have veered to the left of its
original direction.
Geostrophic Wind
Up in the atmosphere, away from the frictional influence of
the earth's surface, the two important forces controlling
wind speed and direction are horizontal pressure gradient
force and coriolis. The balance between these two forces is
called Geostrophic Balance. The wind resulting from this
balance is called the Geostrophic Wind.
8
Geostrophic Wind
Take a situation where the isobars are running east-west with low
pressure towards the north and high pressure towards the south. In that
case, the pressure gradient force acting on air is directed from south to
north:
Geostrophic Wind
The Geostrophic Wind always flows parallel to the isobars:
Geostrophic Wind
In the absence of other forces, the wind would therefore
blow from south to north. But, due to the earth's rotation,
coriolis acts on the moving air, always directed at 90° to the
right of the direction of motion in the Northern Hemisphere.
That changes the direction of the wind. The pressure
gradient force and Coriolis force come into balance when
they are oriented in opposite directions. That balance
occurs when wind is directed at 90° to the right of the
pressure gradient force in the Northern Hemisphere (and
90° to the left of the pressure gradient force in the Southern
Hemisphere).
Geostrophic Wind
Some other examples:
9
Geostrophic Wind
Southern Hemisphere examples:
Pressure Cells
For a low pressure cell, pressure gradient force is directed
inward toward the center of the cell:
Pressure Cells
Often the pressure distribution produces cells of low or high
pressure. In that case, the isobars are more or less circular,
and wind would flow around the cells parallel to the isobars.
Strictly speaking, geostrophic wind only applies to straight
wind flow. But for curved flow such as wind moving around
low or high pressure cells, we can use the geostrophic wind
as an approximation.
Pressure Cells
But, Coriolis will deflect the wind to the right of the pressure gradient in
the Northern Hemisphere:
10
Pressure Cells
That produces a counterclockwise wind pattern around low
pressure centers in the Northern Hemisphere:
Pressure Cells
For a high pressure cell, the pressure gradient force is
oriented outwards from the center of the cell:
Pressure Cells
The direction of flow is opposite (clockwise) for low
pressure cells in the Southern Hemisphere:
Pressure Cells
Coriolis causes wind to be directed to the right of the
pressure gradient force in the Northern Hemisphere:
11
Pressure Cells
And that produces clockwise circulation of air around high
pressure cells in the Northern Hemisphere:
Pressure Cells
In the Southern Hemisphere, air flows counterclockwise
around high pressure cells:
In either hemisphere, we call high pressure cells anticyclones
and low pressure cells cyclones. The flow direction around
an anticyclone is always refered to as anticyclonic, and
around a cyclone the flow is always called cyclonic.
Pressure Cells
In either hemisphere, we call high pressure cells
anticyclones and low pressure cells cyclones. The flow
direction around an anticyclone is always referred to
as anticyclonic, and around a cyclone the flow is always
called cyclonic.
Gradient Wind
In reality, geostrophic balance is only possible with straight
flow. Curved flow, such as that around a high or low
pressure cell, requires that pressure gradient force and
Coriolis be out of balance. For flow around an anticyclone
(high pressure), Coriolis has to be stronger than pressure
gradient force. Therefore the wind speed has to be greater
than it would be for straight flow. Conversely, for flow
around a cyclone, Coriolis has to be weaker than pressure
gradient force, requiring wind speed to be lower than for
straight flow.
12
Gradient Wind
Surface Wind
Near the earth's surface, frictional force comes into play.
Friction acts to slow the wind, and therefore can be thought
of as always acting in the direction opposite of the wind
direction. When the friction vector is added into the picture,
the force vectors are no longer balanced:
Surface Wind
Balance is achieved when the wind direction changes so that wind is
directed across the isobars at an angle instead of flowing parallel to the
isobars. The direction of Coriolis and friction depend on the wind
direction. So when the wind shifts, they shift. With the wind crossing the
isobars at an angle toward low pressure, the forces come into balance:
Surface Wind
And for the Southern Hemisphere:
13
Surface Wind
Near surface winds when isobars are straight and parallel:
Northern Hemisphere:
Surface Wind
For curved flow around high or low pressure cells:
Northern Hemisphere:
Surface Wind
Near surface winds when isobars are straight and parallel:
Sothern Hemisphere:
Surface Wind
For curved flow around high or low pressure cells:
Southern Hemisphere:
14
Surface Wind
Surface Pressure Patterns and Wind
Surface Pressure Patterns and Wind
Upper Level Pressure Patterns and Wind
15
The General Circulation of the Atmosphere
Hadley: 1-cell model of atmospheric circulation
The General Circulation of the Atmosphere
3-cell model of atmospheric circulation
•  Hadley cell
•  Ferrel Cell
•  Polar Cell
George Hadley
(1682-1744)
William Ferrel
(1817-1891)
The General Circulation of the Atmosphere
3-cell model of atmospheric circulation
•  Hadley cell
•  Ferrel Cell
•  Polar Cell
The General Circulation of the Atmosphere
See animation of idealized atmospheric circulation:
http://kingfish.coastal.edu/marine/Animations/Hadley/hadley.html
William Ferrel
(1817-1891)
16
The General Circulation of the Atmosphere
Belts of Pressure and Zonal Winds
Pressure Belts
The General Circulation of the Atmosphere
Mean Pressure Patterns
January
•  Intertropical Convergence Zone (ITCZ, Low Pressure)
•  Sub-Tropical High Pressure Belt
•  Polar Front (Low Pressure)
•  Polar High
Zonal Winds
•  Trade Winds: Tropical Easterlies
•  Mid-Latitude Westerlies
•  Polar Easterlies
The General Circulation of the Atmosphere
Mean Pressure Patterns
July
The General Circulation of the Atmosphere
Components of the Hadley-Cell Circulation
•  ITCZ
–  vigorously lifted air in the equatorial region
–  produces huge thunderstorms
–  visible in satellite images as a line of clouds
–  shifts seasonally
–  shifts more over land areas
–  remains in the Northern Hemisphere over the central
and eastern Pacific Ocean
17
The General Circulation of the Atmosphere
The General Circulation of the Atmosphere
Components of the Hadley-Cell Circulation
•  Poleward flowing air aloft
–  gradually cools by radiation
–  starts to sink due to cooling, and convergence
•  Subtropical high pressure belt
–  zone of subsiding (sinking) air and high pressure
around 30 degrees north and south
–  subsiding air causes this region to have very little
precipitation
–  the great subtropical deserts, such as the Sahara
and Kalahari Deserts are located in this zone
–  subsiding air also produces the trade wind inversion
Components of the Hadley-Cell Circulation
•  Trade winds
–  return flow of air from decending limb of Hadley cell
back to the equator
–  flow has strong easterly component in both
hemispheres due to Coriolis
The General Circulation of the Atmosphere
Movement of the ITCZ
•  Seasonal shifts
–  Moves north during northern
hemisphere summer and vice
versa
–  Over land, the seasonal shift is
greater
–  Accounts for seasonal rainfall
in some equatorial/tropical land
areas, such as the Amazon
basin and the Sahel
The General Circulation of the Atmosphere
Upper-Level Westerly Winds
•  Thickness Patterns
–  The pressure gradient force, and hence the wind velocity, is
determined by the slope of the isobaric surfaces.
–  In the presence of a horizontal temperature gradient, the
thickness of each pressure layer changes horizontally. As a result
the isobaric surfaces tilt more and more toward the colder air.
–  Lines of constant thickness are parallel to lines of constant
temperature, i.e. the thickness pattern and the temperature
pattern are the same. This is because the temperature pattern
creates the thickness pattern.
18
The General Circulation of the Atmosphere
The General Circulation of the Atmosphere
Upper-Level Westerly Winds
Upper-Level Westerly Winds
•  The Thermal Wind
–  The Thermal Wind can be thought of as a vector added to wind at
one level to give the wind at a higher level. The size and direction
of the Thermal Wind vector are determined by the thickness
pattern (temperature pattern) of the air layer in between.
–  The Thermal Wind is always pointed so that warm air is on its
right side (in the Northern Hemisphere).
•  The Thermal Wind
–  As a consequence of the Thermal Wind, air flow in the midlatitudes becomes more and more westerly as you go up in
altitude.
The General Circulation of the Atmosphere
The General Circulation of the Atmosphere
Upper-Level Westerly Winds
Upper-Level Westerly Winds
•  The Polar Front Jet Stream
–  The north-south temperature gradient is strongest along the Polar
Front.
–  As a result, the Thermal Wind is strongest there, and the upperlevel westerlies become extremely strong.
–  The Polar Front Jet is a narrow stream of very fast moving air in
the upper atmosphere.
•  Meanders in the upper level westerly winds
–  Mid-latitude isotherms do not always run exactly east-west, for
example,because of ocean-continent temperature contrasts.
–  Wave-patterns are common in the westerly wind flow.
19
The General Circulation of the Atmosphere
Upper-Level Westerly Winds
•  Rossby Waves
–  Large waves in the westerly flow are known as Rossby waves.
–  Rossby waves constantly change in position and amplitude with
major consequences for mid-latitude weather.
The General Circulation of the Atmosphere
The General Circulation of the Atmosphere
Rossby Waves
•  Vorticity, Upper-Level Divergence and Convergence
–  Vorticity is a measure of the rotation of a parcel of air.
–  Vorticity can be positive (cyclonic) or negative (anticyclonic).
The General Circulation of the Atmosphere
Rossby Waves
Rossby Waves
•  Vorticity, Upper-Level Divergence and Convergence
–  Earth Vorticity:
•  Vorticity, Upper-Level Divergence and Convergence
–  Relative Vorticity:
• 
• 
• 
• 
• 
is the rotation imparted by the earth’s rotation.
is related to Coriolis.
is maximum at the poles and zero at the equator
Is cyclonic (counterclockwise in the Northern Hemisphere)
Is anticyclonic in the Southern Hemisphere
•  is the additional rotation due to the spin of the air, curved flow of air,
or shear in the air flow
20
The General Circulation of the Atmosphere
The General Circulation of the Atmosphere
Rossby Waves
Rossby Waves
•  Vorticity, Upper-Level Divergence and Convergence
–  Absolute Vorticity:
•  Vorticity, Upper-Level Divergence and Convergence
–  The Law of Conservation of Angular Momentum:
•  is the sum of Earth Vorticity and Relative Vorticity
–  The Law of Conservation of Angular Momentum:
•  a familiar example of conservation of angular momentum is the
increase in spin rate of an ice skater when the arms and leg are
pulled in closer to the axis of rotation:
•  when applied to air, can be simply stated as: The absolute vorticity of
an air column divided by the height of the air column must remain
constant. Or another way of stating it is: The absolute vorticity of an
air column multiplied by the area of the air column must remain
constant.
–  Level of Non-Divergence:
•  Generally, air is either divergent or convergent aloft (in the upper
atmosphere) and the opposite in the lower atmosphere. There is a
gradual change from divergence to convergence, or vise versa as
you go from the surface upward. Somewhere in between the surface
and the upper atmosphere is a level where the air is neither
convergent nor divergent: The Level of Non-Divergence.
The General Circulation of the Atmosphere
The General Circulation of the Atmosphere
Rossby Waves
Rossby Waves
•  Vorticity, Upper-Level Divergence and Convergence
–  The Law of Conservation of Angular Momentum:
•  Vorticity, Upper-Level Divergence and Convergence
•  Conservation of Angular Momentum requires that air crossing a
mountain barrier must compensate for the decreased height of the air
column by curving in an anticyclonic direction (clockwise in the N.
Hemisphere).
•  For example, westerly flow encountering the Rocky Mountains of
western North America, will turn to the right as it passes the
mountains, becoming northwesterly. As a result, the air is flowing
toward lower latitudes, and its Earth Vorticity is decreasing as a
result. At the level of non-divergence, the air must turn in a cyclonic
direction (counterclockwise in the northern hemisphere) to conserve
angular momentum. This causes the flow to change direction,
becoming southwesterly. Succeeding changes in latitude will cause
alternating anticyclonic and cyclonic changes in direction, setting up a
series of waves downstream of the mountain barrier. The
equatorward dips in the flow are called "troughs" and the poleward
meanders are called "ridges".
–  These waves in the westerly flow are known as Rossby waves.
–  Rossby waves can also be triggered by SST anomalies.
–  Cyclogenesis: Above the level of non-divergence, angular momentum
conservation can be maintained by convergence or divergence of the air, i.e. by
increasing or decreasing the air column height, or in other words, by decreasing
(converging) or increasing (diverging) the horizontal area of the air column. Air
moving downstream of a Rossby wave trough is moving from high positive relative
vorticity (cyclonic curvature) to zero relative vorticity (straight flow). The resulting
decrease in absolute vorticity is compensated for (above the level of nondivergence) by a decrease in the air column height, i.e. an increase in the area or
diameter of the column. In other words the air aloft diverges. This causes air below
to rise, setting in motion the process of developing a low pressure center at the
surface. As air rises, surface air will converge: lower level convergence. But as
long as the upper level divergence is greater than the lower level convergence, the
low pressure center (cyclone, storm) will continue to strengthen.
21
The General Circulation of the Atmosphere
Rossby Waves
•  Vorticity, Upper-Level Divergence and Convergence
–  As a result of this relationship between the voriticy changes in upper level
flow and surface pressure, Rossby waves exert strong control on the
formation and movement of midlatitude storms. These storms tend to
form beneath the area of upper-level divergence downstream of a Rossby
wave trough, and subsequently move in a path that tracks the upper-level
wind. In the northern hemisphere, midlatitude cyclones tend to move from
southwest to northeast as they go from intitial disturbance to maturity and
occlusion.
22