1. GLOBAL ENERGY BUDGET
The Greenhouse Effect

2. 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

3. The “Goldilocks Problem”
Venus – 460 C (860 F) - TOO HOT
Earth – 15 C (59 F) - JUST RIGHT
Mars – -55 C (-67 F) - TOO COLD

4. 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)

5. 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?

6. Global Energy Balance - Overview
Understand real climate feedback mechanisms
estimate the climate changes that occur
Current
Future

7. ELECTROMAGNETIC RADIATION
50% of Sun’s energy in the form of visible light

8. EMR Self-propagating electric and magnetic wave Moves at a fixed speed
similar to a wave that moves on the surface of a pond
Moves at a fixed speed
3.00 x 108 m/s

9. ELECTROMAGNETIC WAVE 3 characteristics speed wavelength frequencyor
 = c / 
The longer the wavelength, the lower the frequency
The shorter the wavelength, the higher the frequency

10. 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 J-s (joule-seconds)

11. 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

12. ELECTROMAGNETIC SPECTRUM

13. ELECTROMAGNETIC SPECTRUM
Infrared (IR) Radiation
40% of Sun’s energy
m (1 m = 1 x 10-6 m)
Visible Radiation / Visible Light / Visible Spectrum
50% of Sun’s energy
nm (1nm = 1 x 10-9 m)
red longest, violet shortest
Ultraviolet (UV) Radiation
10% of Sun’s energy nm
X-Rays & Gamma Rays – affect upper atmosphere chemistry

14. EMR & CLIMATE Visible & Infrared most important Ultraviolet Why?
Sun?
Earth?
Ultraviolet
Drives atmospheric chemistry
Lethal to most life forms

15. 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

16. Flux & Earth’s Climate

17. 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

18. The Inverse-Square Law
S = S0 (r0 / r)2
where S = solar flux
r = distance from source
S0 = flux at some reference distance r0

19. 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?

20. The Inverse-Square Law
Small changes in earth’s orbital shape + inverse-square law + solar flux CAN CAUSE LARGE CHANGES IN EARTH’S CLIMATE

21. 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

22. TEMPERATURE SCALES Celsius - °C Fahrenheit - °F Kelvin (absolute) – K
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

23. TEMPERATURE SCALES

24. TEMPERATURE CONVERSIONS
T (°C) = [T(°F) – 32] / 1.8 T(°F) = [T (°C) x 1.8] + 32.

25. TEMPERATURE CONVERSIONS
Convert the following:
98.6 °F to °C
20 °C to °F
90 °C to °F
100 °F to °C

26. ABSOLUTE TEMPERATURE T(K) = T (°C) + 273.15
0 K (absolute zero) = °C
Convert the following:
98.6 °F to K
20 °C to K
90 °C to K
100 °F to K

27. BLACKBODY RADIATION
Blackbody – something that emits/absorbs EMR with 100% efficiency at all wavelengths

28. 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

29. BLACKBODY RADIATION CURVE

30. Blackbody Simulation
Blackbody Simulation

31. 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 ≈ , where T is temperature in kelvins
T λ max is the max radiation flux in μm

32. WIEN’S LAW

33. 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

34. WEIN’S LAW

35. ELECTROMAGNETIC SPECTRUM

36. 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

37. THE STEFAN-BOLTZMANN LAW

38. 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

39. 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

40. 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

41. EARTH’S SURFACE TEMPERATURE
Depends on:
The solar flux (S) available at the distance of Earth’s orbit (30% of incident energy reflected)
Earth’s reflectivity or albedo (A) – the fraction of the total incident sunlight that is reflected from the planet as a whole
The amount of warming provided by the atmosphere (magnitude of the greenhouse effect)

43. PLANETARY ENERGY BALANCE
energy emitted by Earth = energy absorbed by Earth

44. 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

45. 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

46. ENERGY ABSORBED energy absorbed =  R2 S -  R2 S x A =  R2 S (1 – A)
energy absorbed = energy intercepted – energy reflected
energy absorbed =  R2 S -  R2 S x A
=  R2 S (1 – A)

47. 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

48. 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

49. 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

50. 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

51. 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

52. ATMOSPHERIC COMPOSITON

53. ABUNDANT NON-GREENHOUSE GASES
Nitrogen
Inert
As N important role in biological cycles
Oxygen
Reactive
Respiration
Argon
Byproduct of potassium decay

56. 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

57. 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

58. ATMOSPHERIC TEMPERATURE
THERMOSPHERE MESOSPHERE STRATOSPHERE TROPOSPHERE

59. TROPOSPHERE Lowest layer Temperature decreases rapidly with altitude
0 - ±15 km
Important in climatic studies
Where weather occurs
Well mixed by convection

60. 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

61. 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

62. LATENT HEAT
Heat energy absorbed or released by the transition form one phase to another – solid, liquid, gas

63. 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

64. MESOSPHERE
50 – 90 km
Temperature decreases

65. THERMOSPHERE
90+ km
Temperature increases

66. EXOSPHERE Outermost fringe of the atmosphere
Infrequent molecular collisions

67. ATMOSPHERIC TEMPERATURE
THERMOSPHERE MESOSPHERE STRATOSPHERE TROPOSPHERE

68. 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

69. WHY DO SAME GASES CONTRIBUTE TO THE GREENHOUSE EFFECT & OTHERS DO NOT?
Gas molecules absorb/emit radiation in two ways
Changing the rate at which the molecule rotates
Changing the amplitude with which a molecule vibrates

70. 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

72. 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

73. H2O ROTATION BAND

74. 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

75. CHANGE IN AMPLITUDE OF VIBRATION
Absorption of Infrared Radiation by Carbon Dioxide

76. 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

77. 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

78. O2 & N2 Poor absorbers of IR radiation Perfectly symmetrical molecules
Electromagnetic fields unable to interact with symmetrical molecules

79. EFFFECT OF CLOUD ON RADIATION BUDGET
Quantification of effect difficult
Many types of clouds
Cumulus – water
Cumulonimbus – water
Stratus – water
Cirrus – ice

80. CLOUD TYPES

81. 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

82. CLOUD EFFECTS Stratus – low, thick Cirrus – high, thin Increase albedo
Reflect incoming solar radiation
Radiate at higher temperature, and according to Stefan-Boltzmann 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 Stefan-Boltzmann law radiate less energy to space

83. COM TRAILS FROM JETS?

84. EARTH’S GLOBAL ENERGY BUDGET

85. 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

86. 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

87. 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

88. 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

89. 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)

90. 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 

91. THE WATER VAPOR FEEDBACK

92. 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

93. 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

94. The Feedback Factor
The ratio of the equilibrium response to forcing (the response with feedback) to the response without feedback
 = temperature change with feedback = C  2
temperature change w/out feedback C
Negative feedback loop if 0 <  < 1
Positive feedback loop if 1 < 
STRONGLY POSITIVE

95. 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

96. SNOW & ICE ALBEDO FEEDBACK

97. 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

98. THE IR FLUX/TEMPERATURE FEEDBACK

99. 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)