8/31/2010
Lecture 3: Seasons and the
Earth’s Atmosphere
Last Lecture: The Seasons
• Seasonality
• Reasons for seasons
• Annual march of the seasons
August 31, 2010
Dr. Holly Barnard
Seasonality
Revolution and Rotation
• Seasonal changes
– Sun’s altitude – angle
above horizon
– Declination – location of
the subsolar point
– Daylength
Figure 2.13
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Axial Tilt and Parallelism
Reasons for Seasons
• Tilt of Earth’s axis
– Axis is tilted 23.5° from plane of ecliptic
• Axial parallelism
– Axis maintains alignment during orbit around the
Sun
• Sphericity
Figure 2.14
Annual March of the Seasons
Sphericity and Lambert’s Cosine Law
• Winter solstice – December 21 or 22
•The way energy changes with
angle is described by Lambert’s
Cosine Law:
– Subsolar point Tropic of Capricorn
θ
• Spring equinox – March 20 or 21
E = Eo * cosθ
– Subsolar point Equator
•Increasing angle increases area
illuminated at the surface and
therefore per unit area decreases.
•When θ is zero (sun overhead),
cos(θ) is 1, the point receives
maximum radiation, when it 90
deg. (sunrise and sunset), cos(θ) is
zero and the point receives no
radiation.
• Summer solstice – June 20 or 21
– Subsolar point Tropic of Cancer
• Fall equinox – September 22 or 23
θ
– Subsolar point Equator
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Annual March of the Seasons
June (Summer Solstice)
66.5 N (Arctic circle)
23.5 N (tropic of Cancer)
0 (equator)
23.5 S (tropic of Capricorn)
66.5 S (Antarctic circle)
Figure 2.15
December (Winter Solstice)
Sun is directly over head at 23.5º N (tropic of Cancer)
-Also called subsolar point or declination
- note subsolar point latitude of 23.5º N = tilt angle of 23.5º
23.5º
Arctic circle has 24 hours of daylight
- Note latitude of Arctic circle is 66.5º N which is 90º (latitude of north pole) – tilt angle of 23.5º
11:30 P.M. in the Antarctic
66.5 N (Arctic circle)
23.5 N (tropic of Cancer)
0 (equator)
23.5 S (tropic of Capricorn)
Sun is directly over head at 23.5º S
(tropic of Capricorn)
66.5 S (Antarctic circle)
- note that subsolar point latitude 23.5º
of 23.5º S = tilt angle of 23.5º
Arctic circle has 24 hours of darkness and Antarctic circle has 24 hours of daylight.
- Note latitude of Antarctic circle is 66.5º S which is 90º (latitude of south pole) – tilt angle of
23.5º
Figure 2.16
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Energy basics: Stefan-Boltzmann Law
• the warmer the object, the greater the
energy emitted by that object
Stefan-Boltzmann Law
• We estimate the total emission from a black body
using Stefan-Boltzmann’s Law:
• A black body is a theoretical object that absorbs
100% of the radiation that hits it. Therefore it
reflects no radiation and appears perfectly black.
L = σT4
L = Energy emitted
 Stefan-Boltzmann constant 5.6710–8Wm–2K–4
T = temperature in Kelvin
(Kelvin is degrees Celsius + 273.15 (thus 0 *C = 273.15 K)
Stefan-Boltzmann Law
• In reality objects are not perfect black bodies.
Meaning they are not perfect emitters. Thus
we introduce the term emissivity (ε).
• Emissivity is the relative ability of its surface to
emit energy by radiation (ranges 0-1).
L = εσT4
In class exercise:
1) Calculate the average energy emitted by
earth when temperature (T) = 15˚C and
emissivity = 0.97
• Name, ID number, and lab section on top of
your paper.
 Stefan-Boltzmann constant 5.6710–8Wm–2K–4
T = temperature in Kelvin
(Kelvin is degrees Celsius + 273.15 (thus 0 *C = 273.15 K)
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Wavelength and Frequency
The Electromagnetic Spectrum
• Sun radiates shortwave energy
• Shorter wavelengths have higher energy
• Earth radiates longwave energy
Figure 2.5
Electromagnetic Spectrum
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Wien’s Law
In class exercise:
2) Calculate the wavelength for the sun (To =
6000K) and the Earth (To=288K)
• The warmer the object, the shorter the
wavelength emitted by that object
λmax = 2897μmK
To
• Name, ID number, and lab section on top of
your paper.
λ = wavelength of peak energy emission
To = temperature in Kelvin
Summary
Earth’s Energy Budget
• Earth’s orbit is an ellipse
• Because of earth curvature energy is more
concentrated at equator (Lamberts Cosine Law)
• Tilt of Earth’s axis controls seasonality.
• Energy expressed as wavelength or frequency
• Energy and wavelength of maximum energy are
dictated by temperature (sun is hotter than earth
so energy is at shorter wavelength)
– Stefan-Boltzmann law
– Wien’s law
Figure 2.8
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Chapter 3: Atmospheric Profile
• Three criteria to examine atmosphere
– Composition
– Temperature
– Function
Profile of
Atmosphere
• Atmosphere extends to
32,000 km (20,000mi)
from earth surface
• Thermosphere is at 480
km (300 mi)
• top of the principle
atmosphere
• Outer boundary of
the Earth’s energy
system
Figure 3.2
Atmosphere
• Three criteria to examine atmosphere
Gravity’s role on air
↑Altitude ↓ gravity
 ↓density
– Composition
– Temperature
– Function
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8/31/2010
Profile of
Atmosphere
90% of Atmosphere
mass lies below 11Km
height
Figure 3.2
Atmospheric pressure = Atmospheric weight
• Air molecules create P through
– Motion
– Size
– Number
• How do we handle such huge pressure on top
of our body?
– Body pressure (= Atm pressure), which
avoids us to be “crushed” by the mass of air
around us.
August 16, 1960
• Col. Kittinger jumps from a
the altitude of 102,800
feet.
• Reached a speed of 614
mph (speed of sound ±768
mph)
• At 50,000 feet, his speed
slowed to 250 mph
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Atmospheric Composition
• Heterosphere – outer atmosphere
– 80 km (50 mi) outwards, to thermosphere
– Layers of gases sorted by gravity
• Homosphere – inner atmosphere
– Surface to 80 km (50 mi)
– Gases evenly blended
Atmospheric Temperature
Atmospheric Temperature
• Thermosphere
– Roughly same as heterosphere
– 80 km (50 mi) outwards
• Mesosphere
– 50 to 80 km (30 to 50 mi)
• Stratosphere
– 18 to 50 km (11 to 31 mi)
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Atmospheric Temperature
Temperature
Profile
• Troposphere
– Surface to 18 km (11 mi)
– 90% mass of atmosphere
– Normal lapse rate – average cooling at rate of 6.4
C °/km (3.5 F°/1000 ft)
– Environmental lapse rate – actual local lapse rate
Figure 3.5
Atmospheric Function
Atmospheric Function
• Ionosphere
– Absorbs cosmic rays, gamma rays, X-rays, some UV
rays
• Ozonosphere
– Part of stratosphere
– Ozone (O3) absorbs UV energy and converts it to
heat energy (or long wavelength EM or infrared
radiation)
Protective Atmosphere
• Mostly to remove harmful
wavelength of insolation
and particles from the Sun &
beyond
Figure 3.6
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Solar and
Terrestrial
Energy
6000 K
Summary
• Earth atmosphere can be characterized based on
composition, temperature, or function.
• Pressure decreases with altitude due to
gravitational pull on gasses.
• Temperature decreases with altitude (lapse rate)
Figure 2.7
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