Light, Heat and Temperatures on Earth
Temperatures on Earth or any planet are primarily determined by
1: The irradiance of sunlight (Presented in Previous Powerpoint).
2: The rate at which planets emit radiation back to space.
Irradiance is the rate energy is transmitted divided by the area it crosses, given in Watts
per square meter, Wm-2. When Earth is at its average distance from the Sun, direct
sunlight on top of the atmosphere is about 1366 Wm-2 (called the solar constant). This
means that if sunlight shines directly into a window 1 m wide and 1 m high and no light
was lost when it passed through the atmosphere then the room will be about as bright as
if it were lit by thirteen 100 Watt bulbs and one 60 Watt bulb. Electric room heaters put
out about 1500 Watts, so 1 m2 of sunlight shining in a window can warm a room.
All objects emit radiation, and the hotter they are the faster they radiate. On each planet
temperature reaches a level where heat is radiated back to space as fast as it is
absorbed from the Sun. This balance leads to the Fundamental Equation of Climate.
Secondary factors that affect temperature are caused by the nature and composition of
the atmosphere, clouds, oceans and ground including snow and vegetation. These
factors include
1: Reflection of sunlight
2: Retention of heat by the atmosphere
3: Heat transport by air and water
4: Penetration of heat below the surface
5: Evaporation and Condensation
Understanding Natural Processes and Phenomena
Using Systems and Cycles
Input
Rate
SYSTEM
The Fundamental
Equation of Systems
Change = Input – Output
(Rate) (Rate) (Rate)
Output Rate
Often, Input for one System or Reservoir is Output for another.
Cycles may occur when there are both Inputs and Outputs
Components of Systems and Cycles
S
S = Reservoir Storage: Total Amount of Material or Quantity
t
F
F: = Flux: Flow Rate of Material or Quantity into or out of the Reservoirs
t = Residence Time: Average Time Spent in Reservoir (time to fill or empty reservoir)
Feedback: Change of flow rates as reservoirs shrink or expand
Human Cardiovascular System
Reservoirs: Body Blood Supply, SBODY = 5120 cm3.
Heart Blood Supply, SHEART = 120 cm3.
Flux (Normal Cardiac Output), F = 80 cm3 s-1.
Residence Time RBODY = 64 s
RHEART = 1.5 s
Feedback: During exercise the Heart pumps faster,
arteries open and F increase by a factor of 5 or 6.
SBODY = 5120
FH→B = 80
t HEART 
S 120

 1.5 SHEART = 120
F 80
FB→H = 80
t BODY 
S BODY
5120

 64
F
80
Feedback: Impact of Dieting
12
160
140
10
8
100
6
80
4
2
Rate of Weight Loss
WEIGHT
120
Diet Begins
INPUT AND OUTPUT
Feedbacks are common in
economic,
biological,
geological, atmospheric,
and oceanic systems.
They occur when input
and/or output rates are
affected by changes in
storage. The feedbacks
greatly complicate the
behavior of and changes
in these systems.
60
40
INTAKE
OUTPUT
20
WEIGHT
0
0
0
5
10
15
20
25
30
# WEEKS
When you first go on a diet it is pretty easy to lose weight. The first weight loss is mostly
water and your metabolism is fast. But as time goes on the body fights the weight loss
by slowing the metabolic rate. Your body also tells you that you are being starved and
makes you feel ravenous. Both of these are negative feedbacks that oppose and slow
weight loss. A positive feedback would be that you eat even less and lose weight more
rapidly as you see the results of dieting on your beautiful body.
Heat, Temperature, and Changes of Phase
When heat is added to the Atmosphere, Earth and Ocean it can do 3 things
1. Raise Temperature, T
2. Change Phase: Evaporate Water or Melt Ice
3. Do Work: Expand Air
Consider the daily (annual) temperature cycle. T rises when heat enters a system more
rapidly than it leaves (excess). All night (winter) T decreases because heat escapes to
space faster than it enters since there no (little) sunshine (deficit). T begins to rise soon
after dawn (in Spring) because its heating exceeds the rate of heat lost to space. Even
though the Sun reaches its highest point in the sky and is strongest at Noon (Summer
Solstice), T continues rising for another two to four hours (one to two months) because
the Sun’s heating rate is still larger than the outgoing radiation rate. This time difference
is called the lag (of the seasons). But by late afternoon (late Summer) the Sun gets so
low in the sky and its rays are so weak that T begins to fall.
The temperature range and length of the lag depend on how much material must be
heated and cooled. The larger the mass, the longer it takes to change T and the less
that T changes. Thus, over the oceans, where sunlight penetrates to great depths and
so, must heat a great mass, the range of T is small and the lag of the seasons is large.
Inland, the Sun hardly penetrates the ground, which grows extremely hot very quickly
but cools quickly at night or during winter.
Daily Cycle of Temperature and Heat Flux
Min and Max T occur when Incoming
and Outgoing Heat Fluxes are Equal
Heat Flux
T
DAILY T
Incoming
Solar
Radiation
Outgoing
Terrestrial
Radiation
Heat
Deficit
Heat
Deficit
Heat
Excess
Midnight
Sunrise
Noon
Hour
Sunset
Midnight
Transporting Heat
(see next two slides for illustrations)
1. Radiation – Energy is transported through “empty” space by
Electromagnetic waves that travel at the speed of light
2. Conduction – Sensible heat is transported from hotter regions to colder
regions of a motionless volume of material by movements of individual
electrons, atoms and molecules.
3. Convection – Sensible heat is transported by winds or currents of fluids
from warmer to colder regions and Latent Heat is transported by winds
from more humid to less humid regions of the atmosphere.
RADIATION
Convection
Conduction
COLD
Boiling
Melting
HOT
Black Body Radiation – Planck’s Law, Wien’s Law and the
Stefan-Boltzmann Law
Every object with T > 0 K emits radiant energy. (Put your hands near your face
to feel the heat!) Joseph Stefan and Ludwig Boltzmann proved that the
irradiance, I, of a perfectly efficient radiator (called a Black Body because it
absorbs all the light that shines on it) is proportional to the 4th power of the
absolute temperature, T. Thus, if an object’s T doubles it will radiate 16 times
as fast. No wonder we feel so hot in front of a fire. The Stefan-Boltzmann Law
can be rearranged to solve for the equilibrium T of a planet if we know the
radiation it receives from the Sun. We call this the Fundamental Equation of
Climate.
Black bodies emit radiation over a wide range of wavelengths. Wilhelm Wien
found that the wavelength of the most intense radiation is inversely
proportional to T. Thus the hotter the object, the shorter the waves it emits
efficiently, so that as objects heat up they first glow red hot then white hot and
finally blue. (This helps us estimate the temperature of star from their color.
Max Planck found exactly how much radiation a black body would emit at
every wavelength. Planck’s Law represents the Birth of Modern Physics. We
will show that it gives rise to the Atmospheric Greenhouse Effect.
Planck Radiation
Perfect Radiators
(Black Bodies)
Stefan Boltzmann Law:
Irradiance, I is
proportional to T4
I  T
4
  5.67(10) 8
Wien’s Law: Most
Intense Irradiance
occurs at
2900
max ( m) 
T
This determines
the color of a
glowing object
T=5800 K
UV
VISIBLE
IR
Earth’s Equilibrium Temperature and the Radiation Balance
Earth attains Equilibrium Temperature when incoming Solar Radiation equals outgoing
Terrestrial Radiation. Solar Radiation consists of much shorter waves than Terrestrial
Radiation because the Sun is much hotter than Earth. This separation of wavelengths makes
the Greenhouse Effect possible by blocking outgoing long waves more efficiently than
incoming short waves
Solar Radiation
reaching Earth
Incoming
Radiation
Blocked by
Atmosphere
Terrestrial Radiation
leaving Earth
Outgoing
Radiation
Blocked by
Atmosphere
Greenhouse
5800 K
Ultraviolet
278 K
Infrared
Terrestrial Radiation and Earth’s Temperature
We can estimate the equilibrium temperature of any planet by rearranging the
Stefan-Boltzmann Law, and setting outgoing terrestrial radiation equal to
incoming solar radiation. This produces
The Fundamental Equation of Climate: Simple Version
1/ 4
I avg



TEQUIL  
8 
 5.67(10) 
Since Iavg = 342 W m-2
TEQUIL = 278 K = 5oC
Complicating
Factor #1: Albedo
Albedo is the % of light
that an object reflects.
Reflected light does not
contribute to heating.
Therefore white objects
such as cloud tops and
snow reinforce cold.
 (1  A) I avg 

T  
8 
 5.67(10) 
1/ 4
Since A = 30%
Tequil = 255K = -18oC
30 Nov 2006 Midwest Ice Storm
Albedo and Temperature
The higher the Albedo
the Colder the Planet
ISun
Space
ISun
Refected sunlight,
AISun is wasted
Atmosphere
Cloud
On a black
planet with no
atmosphere,
all sunlight is
absorbed at
the surface
Earth
On Earth, a fraction, A,
of sunlight is reflected
by air, aerosols, clouds,
snow, water, soil, rocks,
and vegetation.
Snow
Ice
The ground then radiates (1-A)ISun
Earth
absorbed
Long Infrared waves up to
The ground then radiates Long Infrared waves
space at the maximum rate,
back up to space at the reduced rate,
ISun = TBB4
(1-A)ISun = TP4
Earth’s Albedo: The more sunlight is reflected, the cooler the climate. But ice and snow
reflect much sunlight and spread when the climate cools.
The Nature of Feedbacks
Some Light Reflected
when Some Land Covered
with White Paint
Falling T does not Spread Paint
Some Light Reflected
when Some Land Covered
with White Snow
As T Falls, Snow Spreads – More
Light is Reflected so T Falls More
No Feedback
Positive Feedback
Sunlight
Ground
Temperature Falls Somewhat
when Some Light is Reflected
T
Temperature Falls Somewhat
when Some Light is Reflected
T
time
T Falls More when Snow Spreads
and More Light is Reflected
Snow, Ice Albedo Positive Feedback Mechanism
Extra Snow and Ice
Perhaps by Chance
More Light Reflected
Less Absorbed
Temperature Falls
Even More
Snow and Ice
Even More Light Reflected
Less Absorbed
Temperature Falls More
Ice Age Begins ??
Hot atmosphere levels are
those that efficiently absorb
solar radiation of some
wavelength.
Molecules
atoms, and ions in the
Thermosphere
absorb
short waves of ultraviolet
radiation (UV-C). Oxygen
(O2) and Ozone (O3) in the
Stratosphere
absorb
medium wave UV (UV-B).
The surface absorbs all
remaining
wavelengths
(mainly visible and short
wave infrared IR).
Cold atmosphere levels
are those that do not
absorb any wavelength of
radiation efficiently.
Layers of the
Atmosphere
Thermosphere
UVC heating of O
Mesosphere
UVB heating of O3
Stratosphere
Troposphere
VIS heating of Rock
Complicating Factor #2: The Greenhouse Effect
Sunlight (short wave) or solar radiation easily penetrates the atmosphere.
It is absorbed, transformed, and then re-emitted as long wave*****,
infrared terrestrial radiation, which has great difficulty escaping from the
atmosphere. Even though most of the atmosphere is N2 (78%) or O2 (21%),
infrared waves are only absorbed and reemited by the minor gases with
three or more atoms (CO2, H2O, CH4, O3). Some of the terrestrial radiation
heads back down to the ground. This extra radiation has warmed Earth by
some 35oC (63oF) and makes our planet habitable.
Now, we are rapidly increasing Greenhouse gases so the atmosphere
retains heat more efficiently. This extra heat has accumulated in the
oceans so climate has warmed.
*****Note: Reflected Radiation retains its wavelength.
Absorbed Radiation is later emitted with a different
wavelength. The analogy is that if someone squirts whip
cream in your face, the whip cream that falls off is still
whip cream, but the whip cream that you eat changes
form when you digest and emit it.
Run ABSORB_EMIT
Terrestrial Radiation Spectrum Measured by Satellite
Upwelling Terrestrial
by the atmosphere’s
Radiation from
absorbed
the Ground
(blocked).
greenhouse gases
Computer climate models have radiation modules that can simulate these wiggles,
which are caused by emissivity and absorptivity that vary with wavelength.
The Atmospheric Greenhouse Effect
Space
Only a little IR from
the ground escapes
directly to space.
Most of the IR
radiation is absorbed
by the atmosphere’s
Greenhouse gases
(H2O, CO2, O3, CH4)
Sunlight,
which
consists of
Short waves
penetrates
atmosphere
easily
The absorbed
IR heats the
atmosphere
And down to
the ground
Atmosphere (the
Greenhouse)
Earth
…The sunlight
is absorbed at
the ground,
which heats up
…which then
radiates the
IR both up to
space …
…The ground
then radiates
Long Infrared
waves upward
The ground absorbs the IR
radiation from the atmosphere,
raising ground temperature.
This is Greenhouse warming.
Within a year after starting the CO2 measurements, David Keating realized that it was
increasing. This increase has continued ever since. The wiggles represent the seasons.
Secular trend due to burning
fossil fuels and forests
The annual cycle of CO2 in the atmosphere has a range of 7 ppm. Excess of decay over
growth of vegetation in the North Hemisphere Fall and Winter adds 7 ppm and net
growth in Spring and Summer removes it. If there were only net growth and it continued
at its present rate (without feedback), it would take 378/7 = 54 years to remove the CO2.
Sunshine, Radiation and The Daily Temperature Cycle near
and in the Ground
T
During the Day, intense sunshine heats
the ground more than the air. Infrared
radiation travels up from the surface
while IR radiation from the atmosphere
travels down to the ground.
T
At night, more IR radiation travels up
from the ground than down from the
atmosphere, so the surface gets
colder than the air above. Enough
cooling in humid air can produce fog.
Underground Temperature variations are largest near
the surface and decrease with depth. The greater the
conductivity of the ground the deeper heat and cold
penetrate and the smaller the daily and annual range of
temperature at the surface.
UNDERGROUND
TEMPERATURE
VARIATIONS
Fog in the Alps