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MET 61 Introduction to Meteorology - Lecture 2
“The atmosphere (II)”
Dr. Eugene Cordero
San Jose State University
W&H Chapter 1
Class Outline:
Thermodynamics
Hydrostatic balance
Hypsometric equation
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Functions of the Atmosphere
What is the structure of the atmosphere?
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Discussion Questions
• What is the weight of the atmosphere?
• What is the altitude where 99% of the
atmosphere exists below?
• What is the approximate temperature of the
atmosphere at 5 km above the surface?
• How is the atmosphere different on the top
of Mt. Everest compared to San Jose in
terms of
– Composition
– Density
– Pressure
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Principal Atmospheric Gases
GAS
MASS
Nitrogen
3870 (78%)
Oxygen
1185 (21%)
Argon
67
(1%)
Water Vapor
17
(0.3%)
CO2
3
(0.06%)
TOTAL
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Permanent
gases
Variable
gases
Unit: 1018 g
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Thermodynamics
• Definition: The study of heat and its
transformation into mechanical energy.
• Definition: The study of the processes that
involve the transformation of heat into
mechanical work, of mechanical work into
heat, or the flow of heat from a hotter body
to a colder body.
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Thermodynamics
• The thermodynamic state of the atmosphere
can be described by three variables:
Pressure
– ________________
Density
– ________________
Temperature
– ________________
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Lapse Rate
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• Environmental lapse rate, .
– From radiosonde (sounding)
• Dry adiabatic lapse rate, d
– Constant (9.8°/1000m)
• Moist adiabatic lapse rate, s
– Varies with temperature/moisture
– 1°/1000m - 9°/1000m; typical =
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Pressure
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 Measured in
 millibars (mb) or
 hPa (hecto pascals)
 inches of mercury
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Air Pressure
• The weight of the air about us.
• Pressure equals
– a force over a given area (P = F/A)
• Weight is the force exerted by gravity (g) on
a unit mass
•
•
•
•
The average pressure at sea level is about ~
~ 14.70 pounds force per sq inch
1013 mb; 101.3 kPa or 1013 hPa
~ 29.9 in Hg
Pa – N/m2 (N-Newton is Kg m/s2)
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 Pressure measured
via a:
Barometer
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Pressure (I)
• What does pressure represent physically?
• How does atmospheric pressure change
with height?
p  p0e
z H p
– p0 is average sea level pressure
– Hp is the pressure scale height (~ 7km)
– Assumption is that temperature is
constant within that layer.
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Scale Height
• The scale height is proportional to the
average temperature in a layer:
RT
H
g0
• R- gas constant for dry air (287 J K-1kg-1)
• g – gravitational acceleration (9.8 m s-2)
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Question 1
Question:
• What is the pressure at 10km?
• At what altitude is the pressure 50%
of the surface value?
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Atmospheric Pressure and Density
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• Density and Pressure related…
• Density refers to number of air molecules per
volume
– Units are given in Kg/m3
• Pressure refers to the ‘weight’ of the
atmosphere above.
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Density
• What does density represent physically?
• How does atmospheric density change with
height?
ρ  ρ0e
 z Hρ
– 0 is average sea level pressure
– H is the density scale height (~8km)
– Assuming temperature constant
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Temperature
• What does temperature represent
physically?
• How does atmospheric temperature change
with height?
T  amw v
2
– a is a constant
– mw is the molecular weight
– v is the average molecular speed
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Equation of State
• Ideal Gas Law; relates the thermodynamic
states of a gas
p-Pressure (Pa)
P  ρRT
 - density (kg m-3)
R - Gas Constant for dry air
(287 J K-1 kg-1)
T - Temperature (K)
 For moist air one can use the virtual
temperature; Tv=T(1+0.61r)
r- water vapor mixing ratio
Virtual temperatures allows for the use of R
for dry air in ideal gas law.
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Hydrostatic Balance (I)
• Pressure gradient: the change in
pressure with distance.
• Horizontal variations in air pressure
are much less than the vertical ones.
• However, horizontal pressure
differences drive our weather, while
vertical pressure changes don’t exert
as much influence
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Hydrostatic Balance (I)
• Pressure decrease produces a vertical
pressure gradient force.
• Vertical pressure gradient force is directed
__________.
• Vertical pressure gradient force is balanced
by gravity.
p
z
dp
dz
 ρg
p+p
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Hydrostatic Balance (II)
• Hydro – fluids
• Static – balance
• Atmosphere is nearly always in hydrostatic
balance.
• Exceptions are in severe weather
conditions - “non-hydrostatic”
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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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Question 2
• What is the thickness between
500hPa and 200hPa if the average
temperature of the layer is 10F?
• Compare the average thickness at
latitudes between 60N-70N with the
thickness between 20N-30N.
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Principle forces
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Q: What drives the weather in the atmosphere?
Q: What causes the weather to change?
We will develop a foundation for answering these
questions through understanding the predominant
forces in the atmosphere, namely:
•
•
•
•
pressure and pressure gradients,
gravity
rotation of the earth
friction
Today
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Pressure Changes
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• Caused by
– Temperature or density changes
• Determines the direction and speed of winds
• Can help explain general circulation of atmosphere.
• General guidelines:
– High pressure: clear skies/fine weather
– Low pressure: cloudy skies/changeable weather
Why is this?
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Pressure (II)
• Pressure can be used as a vertical
coordinate. Convenient as many
instruments have pressure sensors
• Example questions:
Compare the pressures at 5 km above
sea level for average layer temperatures
of 25C and 35C.
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