NATS 101
Lecture 5
Greenhouse Effect and
Earth-Atmo Energy Balance and the Seasons

Review Items
• Heat Transfer
• Latent Heat
• Wien’s Displacement Law Ramifications
 max



 m



 2900
 mK
T
• Stefan-Boltzman Law Ramifications
E (W m )
  
8 Wm K ) T 4

New Business
• Selective Absorption and Emission
• Earth-Atmo Energy Balance

Modes of Heat Transfer
Williams, p. 19
Latent
Heat
Conduction Convection Radiation
Remember this thought experiment and the incandescent light bulb thru the prism

Williams, p 63
Latent Heat
Take 2
Takes energy from environment
Emits energy to environment

General Laws of Radiation
• All objects above 0 K emit radiant energy
• Hotter objects radiate more energy per unit area than colder objects, result of
Stefan-Boltzman Law
• The hotter the radiating body, the shorter the wavelength of maximum radiation, result of
Wien’s Displacement Law
• Objects that are good absorbers of radiation are also good emitters…today’s lecture!

Sun’s Radiation Spectrum
Planck’s Law
Ahrens, Fig. 2.7
Key concept: Radiation is spread unevenly across all wavelengths

Sun - Earth Radiation Spectra
Ahrens, Fig. 2.8
Planck’s Law
Key concepts: Wien’s Law and
Stefan-Boltzman Law

What is Radiative Temperature of
Sun if Max Emission Occurs at 0.5
 m?
• Apply Wien’s Displacement Law
 max
 2900
 mK
T
T
 2900

 max mK
T
 2900

0.5
 mK m
T

5800 K

How Much More Energy is Emitted by the Sun than the Earth?
E
• Apply Stefan-Boltzman Law
 
8
W m K -4 ) T 4
E
Sun
E
Earth
 (5.67 10 ) 5800 4
 5800 4
( 5.67


10 ) 290 4 290 4

20
4
  5
A
Sun
A
Earth
 4

4
 r 2
Sun r 2
Earth






5
3



2
  4
1.2 10 (12,000 times larger )
A E
Sun Sun
A E
Earth Earth
 billion times more )

Radiative Equilibrium
• Radiation absorbed by an object increases the energy of the object.
– Increased energy causes temperature to increase (warming) .
• Radiation emitted by an object decreases the energy of the object.
– Decreased energy causes temperature to decrease (cooling) .

Radiative Equilibrium (cont.)
• When the energy absorbed equals energy emitted, this is called
Radiative Equilibrium.
• The corresponding temperature is the Radiative Equilibrium
Temperature.

Why Selective, Discrete
Absorption/Emission?
Life as we perceive it: A continuous world!
Atomic perspective:
A quantum world!
Gedzelman 1980, p 103

Energy States for Atoms
Gedzelman 1980, p 104
Hydrogen Atom
Electrons can orbit in only permitted states
A state corresponds to specific energy level
Only quantum jumps between states
Intervals correspond to specific wavelengths

Energy States for Molecules
H
2
Gedzelman 1980, p 105
O molecule
H2O Bands
Molecules can rotate, vibrate
But only at specific energy levels or frequencies
Quantum intervals between modes correspond to specific wavelengths

Selective Absorption
H
2
O molecule
The Bottom Line
Each molecule has a unique distribution of quantum states!
Each molecule has a unique spectrum of absorption and emission frequencies of radiation!
Williams, p 63

Visible
IR
Absorption
Visible (0.4-0.7  m) is absorbed very little
O
2 an O
3 absorb UV
(shorter than 0.3  m)
Infrared (5-20  m) is selectively absorbed
H
2
O & CO
2 are strong absorbers of IR
Little absorption of IR around 10  m – atmospheric window
Ahrens, Fig. 2.9

Total Atmospheric
Absorption
Ahrens, Fig. 2.9
Visible radiation (0.4-0.7  m) is not absorbed
Infrared radiation (5-20  m) is selectively absorbed, but there is an emission window at 10  m

Global Solar Radiation Balance
(Only half of Solar Radiation SR reaches the surface)
30% SR reflects back to space
Albedo: percent of total SR reflected
~20% absorbed by atmosphere
70% SR absorbed by earth-atmosphere
Ahrens, Fig. 2.13
~50% SR absorbed by surface

Atmosphere Heated from
Below
Ahrens, Fig. 2.11 old ed.
Air above ground heats by convection and absorption of some IR from ground
Net Effect:
Atmosphere is Heated
From Below
Air contacting ground heats by conduction absorption of IR from atmosphere

Global Atmo Energy Balance
Ahrens, Fig. 2.14
Solar
Atmosphere
Ground

Summary
• Greenhouse Effect (A Misnomer)
Surface Warmer than Rad. Equil. Temp
Reason: selective absorption of air
H
2
O and CO
2 most absorbent of IR
• Energy Balance
Complex system has a delicate balance
All modes of Heat Transfer are important

NATS 101
Intro to Weather and Climate
Next subject:
The Seasons

Supplemental References for Today’s Lecture
Aguado, E. and J. E. Burt, 2001: Understanding Weather & Climate, 2 nd
Ed. 505 pp. Prentice Hall. (ISBN 0-13-027394-5)
Danielson, E. W., J. Levin and E. Abrams, 1998: Meteorology. 462 pp.
McGraw-Hill. (ISBN 0-697-21711-6)
Gedzelman, S. D., 1980: The Science and Wonders of the Atmosphere.
535 pp. John-Wiley & Sons. (ISBN 0-471-02972-6)
Lutgens, F. K. and E. J. Tarbuck, 2001: The Atmosphere, An Intro- duction to the Atmosphere, 8 th Ed. 484 pp. Prentice Hall.
(ISBN 0-13-087957-6)
Wallace, J. M. and P. V. Hobbs, 1977: Atmospheric Science, An
Introductory Survey. 467 pp. Academic Press. (ISBN 0-12-732950-1)

Reasons for Seasons
• Tilt of Earth’s Axis - Obliquity
Angle between the Equatorial Plane and the Orbital Plane
• Eccentricity of Earth’s Orbit
Elongation of Orbital Axis

Eccentricity of Orbit
Perihelion Aphelion
Ahrens (2nd Ed.), akin to Fig. 2.15
Earth is 5 million km closer to sun in January than in July.
Solar radiation is 7% more intense in January than in July.
Why is July warmer than January in Northern Hemisphere?

Ahrens, Fig. 2.17
147 million km 152 million km

Equal
Energy
Short
Path
Long
Path
Solar Zenith Angle
Depends on latitude, time of day & season
Has two effects on an incoming solar beam
Surface area covered or
Spreading of beam
Path length through atmosphere or
Attenuation of beam
Ahrens, Fig. 2.19

Ahrens, Fig. 2.16
Beam Spreading
Large
Zenith
Angle
Zero
Zenith
Angle
Large
Zenith
Angle
Small
Zenith
Angle
Low Zenith - Large Area, Much Spreading
High Zenith - Small Area, Little Spreading

Beam Spreading
Schematic Ignores
Earth’s Curvature
Zenith Angle
0 o
10 o
30 o
50 o
70 o
80 o
Horizon
Equivalent Area
1.00
1.02
1.15
1.56
2.92
5.76
Infinite

Atmospheric Path Length
Schematic Ignores
Earth’s Curvature
Cloud
Zenith Angle Equivalent Atmospheres
0 o
1.00
10 o
30 o
50 o
70 o
80 o
1.02
1.15
1.56
2.92
5.70
Horizon 45.0

Lutgens & Tarbuck, p33
Length of Day

Day Hours at Solstices - US
Arctic Circle
Sites
Summer-Winter
Tucson (32 o 13’ N)
14:15 - 10:03
Seattle (47 o 38’ N)
16:00 - 8:25
Anchorage (61 o 13’ N)
19:22 - 5:28
Fairbanks (64 o
21:47 - 3:42
49’ N)
Hilo (19 o 43’ N)
13:19 - 10:46
Gedzelman, p67

Danielson et al., p75
Path of Sun
Hours of daylight increase from winter to summer pole
Equator always has 12 hours of daylight
Summer pole has 24 hours of daylight
Winter pole has hours of darkness
24
Note different Zeniths

Noon Zenith Angle at Solstices
Aguado & Burt, p46
Summer-Winter
Tucson AZ (32
08 o o 13’ N)
43’ - 55 o 43’
Seattle WA (47 o
24 o
38’ N)
08’ - 71 o 08’
Anchorage AK (61 o
N) 37 o
13’
43’ - 84 o 43’
Fairbanks AK (64 o
N) 41 o
49’
19’ - 88 o 19’
Hilo HI (19 o
3 o
43’ N)
47’ (north) - 43 o 13’

Is Longest Day the Hottest
Day?
Consider Average Daily Temperature for Chicago IL:
USA Today WWW Site

Annual Energy Balance
Radiative
Warming
Radiative
Cooling
Radiative
Cooling
NH
Ahrens, Fig. 2.21
SH
Heat transfer done by winds and ocean currents
Differential heating drives winds and currents
We will examine later in course

Summary
• Tilt (23.5
o
) is primary reason for seasons
Tilt changes two important factors
1. Angle at which solar rays strike the earth
2. Number of hours of daylight each day
• Warmest and Coldest Days of Year Occur after solstices, typically around a month
• Requirement for Heat Transport
Done by Atmosphere-Ocean System

Assignments for Next
Lectures
• Ahrens (next lecture)
Pages 55-64
Problems:
3.1, 3.2, 3.5, 3.6, 3.14