Transcript Met 61

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MET 61 Introduction to Meteorology - Lecture 10
Atmospheric Dynamics
Dr. Eugene Cordero
Ahrens: Chapter 9
W&H: Chapter 7, pg 271-296
Class Outline:
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Principle forces in the atmosphere
Pressure gradient
Coriolis
Geostrophic wind
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Atmospheric forces
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 Fundamental Forces in the atmosphere
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Pressure Gradient Force
Gravity
Rotation of the Earth
Friction
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Pressure
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 Ultimately responsible
for our weather
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Horizontal Pressure Changes
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 Determines the direction and speed of winds:
– Predominate force in atmospheric flows
 Can help explain general circulation of
atmosphere.
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Pressure Gradient Force
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Pressure gradient directed from high to low pressure
 Pressure gradient:
– Dependent on spacing between isobars
– Dense or tight clustering of isobars - strong or large
pressure gradient
– Weak clustering of isobars - weak pressure gradient
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Reading a weather map
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 Orient yourself (location, date and time)
 Identify what you are looking at
 Determine the interval of the field
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•C
•A
•B
1. At what local time is this map valid?
2. What fields are we looking at?
3. Indicate the directionMET
of the
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gradient force at points A-C.
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Atmospheric Thickness
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Hypsometric Equation
 Combination of ideal gas law with
hydrostatic balance.
 Relates atmospheric thickness with
average temperature.
 Thickness of atmosphere relates to
difference between two atmospheric layers;
zt (m) = thickness between two pressure
levels
Rd
p1
z 2  z1 
T ln
g
p2
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knots
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The rotation of the Earth
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 Rockets, migrating birds, and large scale weather
systems are all deflected due to the rotation of the
Earth.
 The Earth’s rotation causes both
– Translational movement
– Rotational movement
 The Coriolis Force is the name of this rotational
force that deflects motion.
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Coriolis Force
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Affects direction, not speed of object
Maximum at the poles
Zero at the equator (only translational
movement)
Fc=2W v sinj
Calculate
Coriolis force for
wind moving at
10m/s
W - omega Earth’s rotational rate
W =360 degrees/24 hours or
2 radians/86400 seconds=7.27x10-5 s-1
v - wind speed 2(7.27x10-5 s-1)(10m/s)(sin37)=8.8e-4 m/s2
j - latitude
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Coriolis Force
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 Take home message:
– N. Hem - deflects air to the
right
– S. Hem - deflects air to the
left
– Relatively small
acceleration, thus requires
long periods of time to
influence motion.
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Geostrophic balance
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 Geostrophic balance is balance between:
Pressure gradient force
and
Coriolis force
 Result: flow of air is parallel to isobars
 friction is assumed to be zero
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Geostrophic Wind example
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Northern Hemisphere
L
Pressure Gradient Force
1000 mb
1004 mb
Geostrophic Wind
1008 mb
Coriolis Force
H
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•A
•B
•C
1.
2.
3.
Indicate with arrows the pressure gradient and Coriolis force at A, B and C.
Indicate the direction of the wind at each point.
Which point do you think the wind will be stronger?
Geostrophic Wind
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Assume friction is zero
Flow is parallel to isobars
Balance between pressure gradient and
Coriolis force
1 p
Vg 
f d
 - density,
f - Coriolis parameter (=2 W sin j)
Vg - geostrophic wind speed
d – distance between isobars
 p – pressure difference
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http://www.met.sjsu.edu/weather/avn.html
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Estimate the geostrophic wind speed for this situation
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http://www.met.sjsu.edu/weather/avn.html
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Geostrophic Wind with Friction
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Northern Hemisphere
L
Friction decreases speed of wind, thus
Coriolis force is weaker.
Pressure Gradient Force
1000 mb
1004 mb
Friction
1008 mb
Geostrophic Wind
Coriolis Force
H
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•A
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•A
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Terminology
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 Cyclone: refers to closed low pressure system
 Anticyclone: refers to a closed high pressure system
 At the surface, pressure cells are often closed.
However, at higher altitudes, pressure cells are often
elongated, forming ridges and troughs.
– Low pressure systems Troughs
– High pressure systems Ridges
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Upper atmosphere pressure gradients
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 Meteorologist often examine the upper level pressure
gradients to determine the prevailing weather
conditions.
 However, it is not convenient to simply calculate the
pressure gradient because of it’s dependence on
density.
 Rather, meteorologist calculate the height of a
particular pressure surface. The slope of these heights
determines the pressure gradient force.
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Quiz 3: Part A
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1. Write down the component form of the Geostrophic
wind.

1
Vg  kˆ 
P
f
2. Explain the difference between the total derivative and
the local derivative, and show how these are different
mathematically.
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Quiz 3: Part B
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1. Write down the component form of the momentum
equations. Be sure to show all your work (how you got
each term).
2. For each term in your above equations, provide a
physical description (explanation) for what it means.
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3. Indicate the temperature advection at points A and B.
Justify your answer.
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• A
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Activity 9: Due April 11th
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1.Use links found on the department web page to
explore wind speed and direction from maps of model
output such as shown in class. From these maps,
calculate geostrophic wind using either pressure or
height information (if you use height , then use
equations given on pg 188-189 of Stull). Compare
your answer with model wind information (isotachs).
Show calculations and maps from at least two
locations.
2. Compute by how much a soccer ball will be
deflected during a 12m penalty kick due to the coriolis
force.
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