The Processes That Produce the Wind

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The Processes That Produce the Wind
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Wind

• Wind is the general term for the movement of
  air.
• Air moves in three dimensions, but meteorologists
  often separate the motion into the horizontal
  wind and the vertical motion.
• Our understanding of the movement of air is based
  on Newtons Laws of Motion.

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First Law of Motion

• Newtons First Law of Motion states that an
  object at rest will remain at rest and an object
  in motion will remain in motion and travel in a
  straight line at a constant speed unless a force
  is exerted on the object.

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Newtons First Law of Motion (Cont.)
remains at rest
Force
change of direction
travels in a straight line at a constant speed
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Newtons Second Law of Motion

• Newtons Second Law of Motion states that the
  rate of change of momentum of an object with time
  is equal to the sum of the forces acting on the
  object.
• Newton defined momentum as the mass multiplied
  times the velocity.

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Newtons Second Law of Motion (Cont.)

• The equation for Newtons Second Law of Motion is
  
• d(mV)/dt Force 1 Force 2 Force 3
• where
• m is the mass of the object
• V is the velocity of the object
• dt is the change of time

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Newtons Second Law of Motion (Cont.)

• If we assume our object is an air parcel and that
  the mass of the air parcel remains constant, then
  we can pull m out of the derivative and write
• m(dV/dt) Force 1 Force 2 Force 3
• or if we divide both sides by m we get

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Newtons Second Law of Motion (Cont.)

• dV/dt Force 1/m Force 2/m Force 3/m

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Vertical Motion

• As we discussed earlier in the course, vertical
  motion is the result of differences between the
  upward directed pressure gradient force and the
  downward directed gravitational force.
• When the two forces are equal we have the
  hydrostatic balance.

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Horizontal Motion

• In the lowest 100 km of the Earths atmosphere,
  horizontal motion is the result of three factors
• the pressure gradient force
• the Coriolis effect and
• the frictional force

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The Pressure Gradient Force

• The pressure gradient is defined as the change in
  pressure between two points divided by the
  distance between the two points.
• Since pressure is force divided by area, the
  difference in pressure is directly related to a
  difference in force.

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Pressure Gradient
p 1.03x105 Pa (1030 mb)
p 1.00x105 Pa (1000 mb)
106 m
pressure gradient (1.03x105 Pa 1.00x105
Pa)/106 m pressure gradient 0.003 Pa/m
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Pressure Gradient
More force
less force
p 1.03x105 Pa (1030 mb)
p 1.00x105 Pa (1000 mb)
106 m
The imbalance of forces accelerates the air
parcel from the higher toward the lower pressure.
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Pressure Gradient Force

• Suppose we look at the pressure gradient force in
  the x-direction.

y
dx
p dp
p
x
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Pressure Gradient Force (Cont.)

• The pressure pushing the parcel in the positive
  x-direction is p.
• The pressure pushing the parcel in the negative
  x-direction is pdp.
• The distance between the two sides of the parcel
  is dx.
• Lets assume our air parcel is a cube and the
  area of each face is A.

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Pressure Gradient Force (Cont.)

• In this case the pressure gradient force pushing
  the parcel in the positive x-direction is pA and
  the pressure gradient force pushing the parcel in
  the negative x-direction is (pdp)A.

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Pressure Gradient Force (Cont.)

• The net pressure gradient force on the parcel in
  the x-direction is the difference between these
  two forces
• pA (pdp)A
• or
• pA pA dpA -dp A

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Pressure Gradient Force (Cont.)

• The volume of the air parcel would be
• V Adx
• So,
• A V/dx

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Pressure Gradient Force (Cont.)

• If we substitute into our earlier expression we
  get
• - dp A - V (dp/dx)
• This would give us the next pressure gradient
  force in the x-direction.

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Pressure Gradient Force (Cont.)

• In our form of Newtons Second Law of Motion, we
  divided the forces by the mass.
• So, if we divide the pressure gradient force by
  the mass we get
• (-V/m)(dp/dx)

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Pressure Gradient Force (Cont.)

• Now,
• volume/mass 1/density specific volume
• V/m 1/? a
• So,
• - (V/m)(dp/dx) - (1/?)(dp/dx)
• or - a(dp/dx)
• which gives the acceleration caused by the
  pressure gradient force acting in the x-direction.

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Pressure Gradient Force (Cont.)

• The strength of the pressure gradient force is
  determined by the pressure difference.
• A large pressure difference creates a large force
  and usually produces higher wind speeds.
• A smaller pressure difference creates a smaller
  force and usually produces lighter winds.

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Isobar Analysis

• Meteorologist evaluate the pressure gradient
  force and locate centers of higher and lower
  pressure on surface weather maps by drawing
  isobars.
• An isobar is a curve connecting points that have
  the same pressure.

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Isobar Analysis of the Surface Map

• Perhaps the most fundamental synoptic analysis is
  the drawing of isobars on a surface weather map.
• An isobar is a curve connecting places that have
  the same pressure. On the surface synoptic map
  isobars connect places that have the same sea
  level pressure,

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Isobar Analysis (cont.)

• On a surface weather map the standard practice is
  to draw isobars at an interval of 4 hPa (4 mb)
  beginning with 1000 hPa (1000 mb) or the closest
  appropriate isobar.
• In cases where the pressure gradients are weak
  supplemental isobars are drawn every 2 hPa (2 mb).

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Getting Started

• First, locate all of the places on the map where
  the sea level pressure is 1000 hPa (mb) and draw
  an X at those locations.

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X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
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The 1000 hPa (mb) Isobar

• Now draw a curve connecting all of the Xs. You
  have just drawn the 1000 hPa (mb). isobar.
• Repeat the process by going up and down at a 4
  hPa interval until you have drawn all of the
  isobars.

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Local Wind Systems

• Several local wind systems are the direct result
  of the pressure gradient force.
• sea/land (lake/shore) breezes
• anabatic/katabatic winds

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Sea (lake) Breeze

• Recall that water has a higher specific heat than
  the land surface.
• Thus, water surfaces warm and cool more slowly
  than land.
• On a sunny day the water will typically be cooler
  than the land surface.

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Sea (lake) Breeze (Cont.)
Sunny Day
The pressure gradient force pushes a cooler sea
(lake) breeze toward land.
Lower pressure
Higher pressure
Water surface is cooler
Land surface is warmer
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Land (shore) Breeze
Night
The pressure gradient force pushes a cooler land
(shore) breeze toward land.
Higher pressure
Lower pressure
Water surface is warmer
Land surface is cooler
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Mountain and Valley Winds

• Differential heating and cooling can also produce
  local winds in mountainous regions.

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Anabatic Winds

• During the daytime the higher parts of mountains
  warm more quickly than the valleys because they
  receive more solar radiation.
• The warming of the higher elevations produces
  flows up the slopes called anabatic winds.

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Anabatic Winds (Cont.)
Warmer, lower pressure
Warmer, lower pressure
Anabatic winds up the slopes
Cooler, higher pressure
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Katabatic Winds

• At night the tops of the mountains cool off much
  more quickly because they emit more terrestrial
  radiation down to space.
• The cooler denser air is affected more by the
  gravitational force and flows down the slope
  creating katabatic winds.

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Anabatic Winds (Cont.)
Cooler, denser air
Cooler, denser air
Katabatic winds drain down the slopes at night.