GLOBAL ENERGY BUDGET
The Greenhouse Effect
Earth’ Surface Temperature
• Amount of incident sunlight
• Reflectivity of planet
• Greenhouse Effect
– Absorb outgoing radiation, reradiate back to surface
• Clouds
• Feedback loops
– Atmospheric water vapor
– Extent of snow and ice cover
The “Goldilocks Problem”
• Venus – 460 C (860 F) - TOO HOT
• Earth – 15 C (59 F)
- JUST RIGHT
• Mars – -55 C (-67 F)
- TOO COLD
The “Goldilocks Problem”
• Temperature depends on
– Distance from the Sun
• AND
– Greenhouse effect of its atmosphere
• Without Greenhouse effect
– Earth’ surface temperature 0 C (32 F)
Global Energy Balance - Overview
• How the Greenhouse Effect works
• Nature of EMR
– Why does the Sun emit visible light?
– Why does Earth emit infrared light?
• Energy Balance – incoming & outgoing
– Calculate magnitude of greenhouse effect
• Effect of atmospheric gases & clouds on
energy
• Why are greenhouse gases greenhouse gases?
Global Energy Balance - Overview
• Understand real climate feedback mechanisms
– estimate the climate changes that occur
• Current
• Future
ELECTROMAGNETIC RADIATION
• 50% of Sun’s energy in the form of visible light
EMR
• Self-propagating electric and magnetic wave
– similar to a wave that moves on the surface of a
pond
• Moves at a fixed speed
– 3.00 x 108 m/s
ELECTROMAGNETIC WAVE
• 3 characteristics
– speed
– wavelength
– frequency
 = c
or
=c/
The longer the wavelength, the lower the frequency
The shorter the wavelength, the higher the frequency
PHOTONS
• EMR behaves as both a wave and a particle
– General characteristic of matter
• Photon – a single particle or pulse of EMR
– Smallest amount of energy able to be transported
by an electromagnetic wave of a given frequency
– Energy (E) of a photon is proportional to frequency
E = h = hc / 
where h is Plank’s constant and
h =6.626 x 10-34 J-s (joule-seconds)
PLANK’S CONSTANT
E = h = hc / 
• High-frequency (short-wavelength) photons
have high energy
– Break molecules apart, cause chemical reactions
• Low-frequency (long-wavelength) photons
have low energy
– Cause molecules to rotate or vibrate more
ELECTROMAGNETIC SPECTRUM
ELECTROMAGNETIC SPECTRUM
• Infrared (IR) Radiation
– 40% of Sun’s energy
– 0.7-1000 m (1 m = 1 x 10-6 m)
• Visible Radiation / Visible Light / Visible Spectrum
– 50% of Sun’s energy
– 400-700 nm (1nm = 1 x 10-9 m)
• red longest, violet shortest
• Ultraviolet (UV) Radiation
– 10% of Sun’s energy
– 400-10 nm
• X-Rays & Gamma Rays – affect upper atmosphere
chemistry
EMR & CLIMATE
• Visible & Infrared most important
– Why?
• Sun?
• Earth?
• Ultraviolet
– Drives atmospheric chemistry
– Lethal to most life forms
FLUX
• Flux (F) – the
amount of energy
(or number of
photons) in an
electromagnetic
wave that passes 
through a unit
surface are per unit
time
Flux & Earth’s Climate
The Inverse-Square Law
• If we double the distance from the source to
the observer, the intensity of the radiation
decreases by a factor of (½)2 or ¼
The Inverse-Square Law
S = S0 (r0 / r)2
where S = solar flux
r = distance from source
S0 = flux at some reference
distance r0
Solar Flux
• The solar flux at Earth’s orbit = 1366 W/m2
• 1AU = 149,600,000 km (average distance from
Earth to Sun)
• Venus and Mars orbit the Sun at average
distances of 0.72 and 1.52 AU, respectively.
What is the solar flux at each planet?
The Inverse-Square Law
• Small changes in earth’s orbital shape +
inverse-square law + solar flux CAN CAUSE
LARGE CHANGES IN EARTH’S CLIMATE
TEMPERATURE SCALES
• Temperature – a measure of the internal heat
energy of a substance
– Determined by the average rate of motion of
individual molecules in that substance
– The faster the molecules move, the higher the
temperature
TEMPERATURE SCALES
• Celsius - °C
– boiling and freezing points of water
• Fahrenheit - °F
– mixture of snow & salt and human body
• Kelvin (absolute) – K
– The heat energy of a substance relative to the
energy it would have at absolute zero
• Absolute zero – molecules at lowest possible energy
state
TEMPERATURE SCALES
TEMPERATURE CONVERSIONS
T (°C) = [T(°F) – 32] / 1.8
T(°F) = [T (°C) x 1.8] + 32.
TEMPERATURE CONVERSIONS
• Convert the following:
 98.6 °F to °C
 20 °C to °F
 90 °C to °F
 100 °F to °C
ABSOLUTE TEMPERATURE
T(K) = T (°C) + 273.15
0 K (absolute zero) = -273.15 °C
Convert the following:
98.6 °F to K
 20 °C to K
 90 °C to K
 100 °F to K
BLACKBODY RADIATION
• Blackbody – something that emits/absorbs
EMR with 100% efficiency at all wavelengths
BLACKBODY RADIATION
• Radiation emitted by a blackbody
• Characteristic wavelength distribution that
depends on the absolute temperature of the
body
• Plank Function – relates the intensity of the
radiation from a blackbody to its wavelength
or frequency
BLACKBODY RADIATION CURVE
Blackbody Simulation
• Blackbody Simulation
WIEN’S LAW
• The flux of radiation emitted by a blackbody
reaches its peak value at wavelength λ max,
which depends on the body’s absolute
temperature
– Hotter bodies emit radiation at shorter
wavelengths
λ max ≈ 2898 , where T is temperature in kelvins
T
λ max is the max radiation flux in μm
WIEN’S LAW
WEIN’S LAW
• Sun’s radiation peaks in the visible part of EMR
2898 / 5780 K ≈ 0.5 μm
• Earth’s radiation peaks in the infrared range
2898 / 288 K ≈ 10 μm
WEIN’S LAW
ELECTROMAGNETIC SPECTRUM
THE STEFAN-BOLTZMANN LAW
• The energy flux emitted by a black body is
related to the fourth power of a body’s
absolute temperature
F = σ T4 ,
where T is the temperature in kelvins and
σ is a constant equal to 5.67 x 10-8 W/m2/K4
• The total energy flux per unit are is
proportional to the area under the blackbody
radiation curve
THE STEFAN-BOLTZMANN LAW
THE STEFAN-BOLTZMANN LAW
• Example a hypothetical star with a surface
temperature 3x that of the Sun
Fsun = σ T4 = (5.67 x 10-8 W/m2/K4) (5780 K)4
= 6.3 x 107 W/m2
Fstar = σ T4 = (5.67 x 10-8 W/m2/K4) (3x5780 K)4
= 34 x σ (5780 K)4
= 81 Fsun
THE NATURE OF EMITTED RADIATION
• Wien’s Law – hotter bodies emit radiation at
shorter wavelengths
• Stefan-Boltzmann – energy flux emitted by a
blackbody is proportional the fourth power of
the body’s absolute temperature
• SO – the color of a star (wavelength) indicates
temperature, temperature indicates energy
flux
EARTH’S ENERGY BALANCE
• The amount of energy emitted by Earth must
equal to amount of energy absorbed
– The average surface temperature is getting
warmer
– Imbalance caused by increase in CO2 and other
greenhouse gases OR
– Imbalance caused by natural fluctuations in the
climate system
EARTH’S SURFACE TEMPERATURE
• Depends on:
1. The solar flux (S) available at the distance of
Earth’s orbit (30% of incident energy reflected)
2. Earth’s reflectivity or albedo (A) – the fraction of
the total incident sunlight that is reflected from
the planet as a whole
3. The amount of warming provided by the
atmosphere (magnitude of the greenhouse
effect)
PLANETARY ENERGY BALANCE
energy emitted by Earth = energy absorbed by Earth
Effective Radiating Temperature (Te)
• The temperature that a true blackbody would
need to radiate the same amount of energy
that Earth radiates
• Use Stefan-Boltzmann law to calculate energy
emitted by Earth
Energy emitted = σ Te4 x 4  R2
Energy Absorbed by Earth
energy absorbed = energy intercepted – energy reflected
• Energy Intercepted (Incident Energy)- the product
of Earth’s projected area and the solar flux
=  R2 S
• Energy Reflected - the product of Earth’s incident
energy and albedo
=  R2 S x A
ENERGY ABSORBED
energy absorbed = energy intercepted – energy reflected
energy absorbed =  R2 S -  R2 S x A
=  R2 S (1 – A)
PLANETARY ENERGY BALANCE
energy emitted by Earth = energy absorbed by Earth
σ Te4 x 4  R2 =  R2 S (1 – A)
σ Te4 = (S/4) (1 – A)
where σ is 5.67 x 10-8 W/m2/K4 , T is temperature in kelvin, S is
solar flux, and A is albedo
The planetary energy balance between outgoing
infrared energy and incoming solar energy
MAGNITUDE OF THE GREENHOUSE
EFFECT
• Effective Radiating Temperature
– Atmospheric temperature at which most outgoing
infrared radiation derives
– Average temperature that Earth’s surface would
reach with no atmosphere
– Using planetary energy balance equation • Earth’ s effective radiating temperature = -18C or 0F
MAGNITUDE OF THE GREENHOUSE
EFFECT
• Actual surface temperature or Earth = 15C
• Difference between effective and actual caused
by greenhouse effect
∆ Tg = Ts – Te
For Earth ∆ Tg = 15C –(–18C) = 33C
• By absorbing part of the infrared radiation
radiated upward from the surface and reemitting
it in both upward and downward directions, the
atmosphere allows the surface to be warmer that
it would be if no atmosphere were present
THE GOLDLOCKS PROBLEM
• A planet’s greenhouse effect is at least as
important in determining a planet’s surface
temperature as is its distance from the Sun
• For homework – Critical Thinking #2
FAINT YOUNG SUN PARADOX
• Solar luminosity, and flux (S), is estimated to
be 30% lower early in Earth’s history
– Earth’s average surface temperature would have
been below freezing (if albedo & greenhouse
effect unchanged)
– The early Earth had liquid water and life
• HOMEWORK – Critical Thinking #5
ATMOSPHERIC COMPOSITON
ABUNDANT NON-GREENHOUSE GASES
• Nitrogen
– Inert
– As N important role in biological cycles
• Oxygen
– Reactive
– Respiration
• Argon
– Inert
– Byproduct of potassium decay
ATMOSPHERIC PRESSURE
• Influences climate & radiation budget
• Force per unit area
• Pressure at Sea Level
– 1 atmosphere (1 atm)
– 14.7 lbs/in2
– 1.013 bar
– 1013 millibars
ATMOSPHERIC PRESSURE
• Barometric Law – the pressure decreases
exponentially with altitude
– a factor of 10 for every 16 km increase in altitude
• Pressure decreases faster with increasing
altitude when the air is colder
ATMOSPHERIC TEMPERATURE
THERMOSPHERE
MESOSPHERE
STRATOSPHERE
TROPOSPHERE
TROPOSPHERE
•
•
•
•
•
•
Lowest layer
Temperature decreases rapidly with altitude
0 - ±15 km
Important in climatic studies
Where weather occurs
Well mixed by convection
METHODS OF HEAT TRANSFER
• Convection – transfer of heat energy by
moving fluids
– Generated when fluid heated from below
• Conduction – transfer of heat energy by direct
contact between molecules
• Radiation – transfer of heat energy by
electromagnetic waves emitted from a body
TROPOSPHERE
• Incoming solar energy absorbed by surface
(land and water)
• Energy reradiated as IR radiation
• IR radiation absorbed by greenhouse gases
and clouds
• Energy transported by convection instead
• Where atmosphere more transparent to IR,
the energy radiated from Earth
LATENT HEAT
• Heat energy absorbed or released by the
transition form one phase to another – solid,
liquid, gas
STRATOSPHERE
•
•
•
•
•
•
±15 – 50 km
Temperature increases with altitude
Pressure much lower
Contains most of Earth’s ozone
Very dry - <5 ppm water vapor
Non-convective, less well mixed
MESOSPHERE
• 50 – 90 km
• Temperature decreases
THERMOSPHERE
• 90+ km
• Temperature increases
EXOSPHERE
• Outermost fringe of the atmosphere
• Infrequent molecular collisions
ATMOSPHERIC TEMPERATURE
THERMOSPHERE
MESOSPHERE
STRATOSPHERE
TROPOSPHERE
VERTICAL TEMPERATURE PROFILE
• Troposphere - 
– Ground absorbs sunlight, heats atmosphere above
• Stratosphere - 
– Ozone absorbs solar radiation
– Maximum heating occurs at top of layer
• Mesosphere - 
– Ozone & heating rate decline
• Thermosphere - 
– O2 absorbs shortwave UV radiation
WHY DO SAME GASES CONTRIBUTE TO
THE GREENHOUSE EFFECT & OTHERS
DO NOT?
• Gas molecules absorb/emit radiation in two
ways
1. Changing the rate at which the molecule rotates
2. Changing the amplitude with which a molecule
vibrates
CHANGE IN ROTATION
• Molecules rotate at discreet frequencies
• If the frequency of the incoming wave is just
right, the molecule absorbs the photon
• The molecule emits the photon when the
rotation slows down
• Depends on structure of molecule
H2O ROTATION BAND
• Strong absorption feature of Earth’s
atmosphere
– H2O molecule absorbs IR radiation of 12μm or
longer
– Virtually 100% of infrared radiation > 12μm
absorbed
H2O ROTATION BAND
CHANGE IN AMPLITUDE OF VIBRATION
• If the frequency at which the molecule
vibrates matches frequency of incoming wave,
molecule absorbs photon and vibrates more
• Bending mode of CO2 allows molecule to
absorb IR radiation about 15 μm λ
CHANGE IN AMPLITUDE OF VIBRATION
• Absorption of Infrared Radiation by Carbon
Dioxide
15 μm CO2 BAND
• Strong absorption feature of Earth’s
atmosphere
• Important to climate because it occurs near
peak of Earth’s outgoing radiation
– very little of Earth’s outgoing radiation can escape
because it is absorbed by CO2
OTHER GREENHOUSE GASES
• CH4, N2O, O3 and freons
– More effect on outgoing radiation than low
concentrations would suggest
– Absorb at different wavelengths than H2O & CO2
O2 & N2
• Poor absorbers of IR radiation
• Perfectly symmetrical molecules
• Electromagnetic fields unable to interact with
symmetrical molecules
EFFFECT OF CLOUD ON RADIATION
BUDGET
• Quantification of effect difficult
• Many types of clouds
– Cumulus – water
– Cumulonimbus – water
– Stratus – water
– Cirrus – ice
CLOUD TYPES
CLOUD EFFECTS
• Day – cool Earth by reflecting sunlight back to
space
– Without clouds albedo would be ~0.1
– At 0.1 Te would increase 17C
• Night – warm Earth – reemit outgoing IR
radiation
CLOUD EFFECTS
• Stratus – low, thick
– Increase albedo
– Reflect incoming solar radiation
– Radiate at higher temperature, and according to StefanBoltzmann law radiate more energy to space
• Cirrus – high, thin
– Increase greenhouse effect
– Ice crystals more transparent to incoming solar radiation
– Radiate at lower temperatures and according to StefanBoltzmann law radiate less energy to space
COM TRAILS FROM JETS?
EARTH’S GLOBAL ENERGY BUDGET
PRINCIPLE OF PLANETARY ENERGY
BALANCE
• At the top of the atmosphere, the net
downward solar radiation flux (incoming
minus reflected), must equal the outgoing
infrared flux
CLIMATE MODELING
• Climate system complex
• Computer models based on data used to
simulate climate systems
• GCM – General Circulation Model aka global
climate model - include
– 3-d representation of atmosphere (winds,
moisture, energy)
– Weather (clouds, precipitation
– Require huge amounts of computer power
One Dimensional Climate Model
• Radiative-Convective Model (RCM)
– Climate system approximated by averaging
incoming solar and outgoing IR over Earth’s entire
surface
– Vertical dimension divided into layers
– Temperature of each layer calculated
• Energy received or emitted
• Convection
• Latent heat release
RCMs
• Allow estimation of greenhouse effect magnitude
– uses concentrations of greenhouse gases in
atmosphere
– Models accurately predict ∆Tg (33C)
– Allow prediction of temperature increase due to GHG
• Doubling CO2 from 300ppm to 600ppm would produce a
1.2C increase
• The temperature change ∆T0 in the absence of any climate
system feed back loops
CLIMATE FEEDBACKS
• Amplify or moderate radiative effect due to
GHG concentrations
– Water Vapor Feedback
– Snow and Ice Albedo Feedback
– The IR Flux/Temperature Feedback
– The Cloud Feedback (Uncertain)
THE WATER VAPOR FEEDBACK
• If Earth’s surface temperature , then water
vapor  (precipitation)
• If water vapor , then greenhouse effect ,
and surface temp 
• If Earth’s surface temperature , then water
vapor  (evaporation)
• If water vapor , then greenhouse effect ,
and surface temp 
THE WATER VAPOR FEEDBACK
THE WATER VAPOR FEEDBACK
• Incorporated into RCM by assuming fixed
relative humidity in troposphere
• RCM predicts equilibrium change in surface
temperature for CO2 doubling is 2X effect
without water vapor
Mathematically Speaking . . .
• Comparing equilibrium temperature with and
without water vapor feedback (from Ch 2)
∆Teq = ∆T0 + ∆Tf
∆Teq = 1.2C+ 1.2C  2.4C
93
The Feedback Factor
• The ratio of the equilibrium response to forcing
(the response with feedback) to the response
without feedback
 = temperature change with feedback
temperature change w/out feedback
= 2.4 C  2
1.2 C
Negative feedback loop if 0 <  < 1
Positive feedback loop if 1 < 
STRONGLY POSITIVE
94
SNOW & ICE ALBEDO FEEDBACK
• Snow & ice have higher albedo than land &
water
• Increases in snow and ice coverage should
decrease surface temperature
• Positive feedback loop
• Snow & ice restricted to middle & high
latitudes, 2- or 3-d models are required
SNOW & ICE ALBEDO FEEDBACK
THE IR FLUX/TEMPERATURE FEEDBACK
• Strong negative feedback loops
• Stabilizes Earth’s climate on short time scales
• If Earth’ surface temperature , outgoing IR
flux , if outgoing flux , surface
temperature would 
– More energy is lost from the system
• System can fail if the atmosphere contains too
much water vapor
– Venus – runaway greenhouse
THE IR FLUX/TEMPERATURE FEEDBACK
THE CLOUD FEEDBACK (UNCERTAIN)
• Adds significant uncertainty to climate models
– Clouds can warm or cool, depending on height
– Form at some locations and not others
• Most current GCMs
– Net positive feedback for doubled CO2
• Increase in cirrus clouds (warming) outweighs any
increase in stratus clouds (cooling)