lecture 13 the winds

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The Winds
What Wind Is
Wind is the movement of air relative to the Earth. It is named by the direction it
comes from. Thus, a northwest wind blows from the northwest and moves
toward the southeast. Blue Northers are the cold winds that sweep down the
Great Plains and invade Texas from the north. Easterlies are winds that blow
from the east and a Nor’Easter is a violent extratropical cyclone named for the
direction of the wind in the sector of the storm where blizzard conditions are
most likely.
Wind speed is the distance the air moves divided by the time interval. Thus, for
example, if air moves a distance of 100 meters in 50 seconds, the wind speed
is 2 m/s (4 mph). Meteorologists use several different units for speed. The SI
measure is m/s. The most common measure is miles per hour (mph) in the
United States and kilometers per hour outside the USA. The wind barbs on
weather maps use the mariner’s favorite measure, knots or nautical miles per
hour. Nautical miles are measured by the Earth – 60 nautical miles = 1 of
latitude (69 miles or 111 km). A wind speed of 60 knots means that the air
would move 60 nautical miles or a distance equal to 1 of latitude in an hour.
When wind speed exceeds about 20 knots the wind can pick up dust
and produce dust storms. Dust storms raged across the Great Plains
during the droughts of the Dust Bowl in the early to mid 1930’s.
Dust Storm Approaching Stratford, Texas in 1935
A dramatic dust storm (sometimes called a
haboob) engulfing Phoenix, AZ on 05 July 2011
Power from the
Winds
Power from windmills is
proportional to v3. Its
theoretical maximum value
is given by Betz’s Law
Pmax
 16  1
3
   Av
 27  2
For a windmill at sea level
with blades 50 m long (A =
pr2  7900 m2) in a wind
speed of 10 ms-1 (20 mph)
the maximum possible power
is about 3 Megawatts.
Wind Systems and the Scales of Motions
The world’s winds can be classified according to their size or scale.
1. Planetary scale motions such as the Jet Stream, the Trade Winds and
monsoons are about 10,000 km - roughly the Earth’s radius.
2. Synoptic scale phenomena are roughly 1000 km. They include moving high
pressure areas, tropical and extratropical cyclones - the grand storm systems.
3. Mesoscale winds such as thunderstorms and sea breezes are between 4
and 400 km.
4. Microscale motions such as tornadoes are less than 4 km across.
Earth’s rotation plays a major role in the character of planetary and synoptic
scale motions, which have lifetimes of days. For smaller scale motions with a
lifetime much shorter than a day, the impact of Earth’s rotation is small, so that
it has almost no direct effect on microscale motions.
Some wind systems defy easy classification. Both fronts and streaks in the jet
stream are long, narrow zones that are synoptic scale in length but mesoscale
in width.
Driving the Winds: Sea Breeze by Day, Land Breeze by Night
Temperature differences produce density and pressure differences that drive the winds.
One classic example is the sea breeze and land breeze system. During the day, the land
quickly gets hotter than the sea and air rises over the land. Cooler air over the sea then
blows in from the sea near the surface while after rising 500 or so meters the wind aloft
blows from land to sea and sinks over the ocean to complete a circulation cell. At night
the land gets colder than the sea so the direction of circulation reverses, but is generally
weaker. The sea breeze typically penetrates 10 km or more inland.
Sea Breeze: Yucatan Peninsula 15 June 2005 1625 UTC
00 UTC 18 July 1998
Valley Breeze by Day, Mountain Breeze by Night
During the day the sun heats the mountainsides. This heats the air right over
the slopes more than the air at the same level over the valley. The warm, light
air then slides up the slopes and up the valley. If it rises enough it will produce
cumulus or even cumulonimbus clouds over the summits while over the valley
the cooler air sinks, making the sky clear.
At night the mountainsides radiate heat to space and cool. This chills the air
above the slopes, which then slides down the slopes and down the valley, often
in spurts. The sky clears over the summits and stratus or fog may form in the
chilled air of the valleys.
Cu
Stratus, Fog
Fog fills the Imperial Valley of
California 13 Jan 2004
This fog sometimes gets so
thick that it does not burn off
during the day but can persist
for days on end. Lines in the
fog are flow lines (click to
highlight them) showing
(humid) air blowing into the
valley from the Pacific Ocean
through the Golden Gate, just
north of San Francisco (SFO).
At the same time, snow covers
the Sierra Nevada Mountains,
which enclose the Valley on its
Eastern side. Sinuous breaks
in the snow identify narrow
river valleys.
SFO
Newton’s Laws of Motion
govern the motions of all objects including air.
Newton’s First Law of Motion
If no force is exerted on an object, its velocity will not change.
Newton’s Second Law of Motion:
F = ma
The force on an object equals its mass times its acceleration.
The first law represents a fundamental change from the mistaken notion that
the natural state of things is be still. Any object resists attempts to change its
speed or its direction of motion. This resistance to change is called inertia.
Speed is the distance traversed divided by the time interval. Velocity is
speed in a particular direction. If the direction of a moving object changes, its
velocity also changes, even if the speed remains constant. Acceleration is
the change of velocity divided by the time interval. Objects accelerate when
their speed or direction of motion changes.
Run Program
FREEFALL
Forces and their Accelerations
Newton’s Second Law (F = ma) enables us to predict changes in motion (i. e.,
acceleration, a) provided we know the forces acting on air. The four primary
forces on air (and water) and their resulting accelerations are,
1. Weight (Gravity), produces a downward acceleration, g = 10 m s-2 at the
surface of the Earth.
2. The Pressure Gradient Force produces an acceleration, apg from a point of
high pressure to a point of low pressure that is proportional to the pressure
difference between the two points divided by the distance between the points
3. Friction (viscosity for fluids) produces an acceleration, af in the direction
opposite the motion and is proportional to the speed of the wind or current.
Friction acts to reduce all relative motions (e. g., shear).
4. The Coriolis Force (a consequence of Earth’s Rotation) produces an
acceleration, acor to the right of the motion in the North Hemisphere, that is
proportional to the speed of the wind or current (and to the sine of the latitude).
Buoyancy is a residual force that results when density differences cause an
imbalance of weight and pressure in air or any fluid.
Pressure differences accelerate air directly from high to low pressure. The
motive force is called the pressure gradient force because it is proportional
to the pressure gradient, the pressure difference between two points divided
by the distance between the points.
Earth’s Rotation and the Coriolis Force
Coriolis force accelerates moving objects to their right in the NH and to their left in the
SH because the sense of Earth’s rotation is opposite in the two hemispheres.
Earth as a Coriosel:
The cannon ball
moves in a straight
line, but curves
relative to a viewer
on the coriosel, who
is turning to his left
(counterclockwise)
Run Program
CORIOLIS
Combinations of the Forces
Most air motions result from combinations of several forces. Some classical
situations result from the balance of two or more forces. They include
Hydrostatic balance
Cyclostrophic wind
Geostrophic wind
Ekman Spiral
Gradient wind
1. Hydrostatic Balance and Buoyancy
The sky does not fall because the downward force of gravity almost exactly
cancels the upward pressure gradient force. The hydrostatic equation
expresses the balance and is more than 99% accurate in the atmosphere
except for extreme cases such as tornadoes.
When the atmosphere is not perfectly hydrostatic, the difference between the
upward pressure gradient force and the force of gravity is the buoyancy force. A
parcel or balloon x% less (more) dense than the surroundings will have an
upward (downward) acceleration due to buoyancy x% that of gravity. Thus, a
parcel 10% denser than the surroundings will accelerate downward at 1 m/s2 or
10% of g.
Archimedes' Principle: Any object, wholly
or partly immersed in a fluid, is buoyed
up by a force equal to the weight of the
fluid displaced by the object.
envVg
env
parVg
Hot air balloons were invented in China. Zhuge Liang (250 AD) used Kongming
lanterns for military signaling. The first documented balloon flight in Europe was made
on August 8, 1709, in the Portuguese Court in Lisbon using a small paper burning
balloon built by Bartolomeu de Gusmão, a priest. The first recorded balloon flight with
humans took place on October 19, 1783 in Annonay, France in a balloon built by the
brothers Joseph-Michel and Jacques-Etienne Montgolfier, paper manufacturers.
2. The Geostrophic Wind
Normally, water flows downhill--directly to low pressure. But water spinning in
a pail, flows around the pail even though the water slopes down toward the
center. Similarly, large-scale winds do not blow directly towards low pressure,
but instead blow with low pressure to their left in the Northern Hemisphere and
to their right in the Southern Hemisphere. Thus, If you stand with your back
to the wind, then low pressure is on your left (in the Northern
Hemisphere). This strange behavior of the large scale winds is called Buy’s
Ballot’s Law after the Dutch meteorologist, Christopher Buys-Ballot.
Above the atmospheric boundary layer (more than about 1 km above ground
level) there is almost no friction, so low pressure is almost exactly 90 to the left
of the wind. If, the wind also flows in a straight line at a steady pace there is no
net acceleration and it is called the geostrophic wind. The geostrophic wind
blows parallel to the isobars with low pressure exactly 90° to its left (right) in
the North (South) Hemisphere.
Only two forces act on the geostrophic wind. The pressure gradient force pulls
wind toward low pressure. It is exactly cancelled by the Coriolis force, which
pulls the wind to its right. The geostrophic wind represents a perfect balance
between the pressure gradient force and the Coriolis force. The geostrophic
wind speed is inversely proportional to the distance between isobars
Buys Ballot’s Law and the Geostrophic Wind
The Forces: Pressure Gradient Force points towards Low Pressure; Coriolis
Force points to the right of the wind (North Hemisphere). When there is no
friction (at least 1 km above the ground) and the wind is steady, the two forces
are equal and opposite so they cancel. The result: The Geostrophic Wind
Buys Ballot’s Law: Stand with your back to the wind in the North Hemisphere
and Low Pressure is on your left.
Forecasting Application: If high level clouds such as cirrus move from left to
right when your back is to the wind then low pressure is approaching.
The Geostrophic Wind and Constant Pressure Charts
Weather above the ground is depicted using charts at constant pressure. Standard
(mandatory) levels for constant pressure charts are 850, 700, 500, 300, 250, and 200
hPa (1 hPa = 100 Pascals). Constant pressure charts have hills and valleys that
correspond to high and low pressure areas. All contain contour lines of height. Other
contour lines include T (850), vertical velocity and RH (700), vorticity (500) and wind
speed (300, 250, and 200). They are used because,
1. High and Low pressure areas are displayed as hills and valleys.
2. Wind speed is inversely proportional to the distance between contours.
3. Temperature patterns are free of compression effects.
The next slide shows why highs appear as hills on constant pressure surfaces and
relates the pressure surfaces to the geostrophic wind and to geostrophic currents.
If sea level pressure is 1020 hPa at the center of a high pressure area, the 1000 hPa
surface lies directly above the high center because p decreases with height. Lower
pressure at sea level surrounds the high. If the pressure at sea level at some distance
from the high pressure center is 1000 hPa, we can find the 3-dimensional 1000 hPa
surface by connecting all points where pressure is 1000 hPa. This produces a domelike surface that arches over the high and intersects sea level at the 1000 hPa isobar.
To see how geostrophic winds and currents develop, release a ball on a constant p
surface. As the ball slides down, the Coriolis force will deflect it to its right until it finally
moves so that the surface’s downslope side is on its left. This explains why the Gulf
Stream, doesn’t flood NYC even though sea level is more than 1 m higher at Bermuda!
Forecasting Temperature by Advection (Wind)
Temperature changes over time when the air upwind is colder or warmer. This
is seen on constant pressure charts when Isotherms (typically solid lines) cross
Contours (typically dashed lines).
Directions for making a 12 hour Temperature Forecast
1. Estimate average wind speed and direction upwind from forecast city.
3. Calculate distance air travels (each 5 knots = 1° latitude per 12 hours).
4. Pinpoint upwind source of air arriving at forecast city.
5. Future T at forecast city is current T at upwind source.
Assumptions: No heating or cooling, no vertical motions, no change of wind.
Problems: 1: When the atmosphere is stable, rising air causes cooling. 2: Weather
systems also tend to move from west to east and change shape so that wind changes
both speed and direction.
In the drawing to the right, cold
air in the Northwest (NW)
moves to the SE while warm air
in the SE moves toward the N.
The next slide shows how T
changed as the snowstorm of
26-27 Dec 2010 moved up the
East Coast of the USA.
WARM
The Strange Tilt of Weather Systems
Outside the tropics, it is often observed that highs and lows and troughs and
ridges are not vertically aligned but tilt upward to the West. In fact,
1: Lows and troughs always tilt upward toward the coldest air.
2: Highs and ridges always tilt upward toward the warmest air.
3. Systems with symmetrical Temperature patterns do not tilt with height.
L
C
O
L
D
W
A
R
M
L
L
C
O
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D
C
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D
W
A
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Note how the trough (red dashed lines on next slide) slopes up to the West
(where air is much colder) for the major snowstorm of 26-27 December 2010.
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