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

= cor

= c / The longer the wavelength, the lower the frequencyThe 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 andh =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 LawS = 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) + 273.150 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 EMR2898 / 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 SunFsun = 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 = -18C or 0F

MAGNITUDE OF THE GREENHOUSE EFFECT

• Actual surface temperature or Earth = 15C • Difference between effective and actual caused by

greenhouse effect∆ Tg = Ts – Te

For Earth ∆ Tg = 15C –(–18C) = 33C

• 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 ways1. Changing the rate at which the molecule rotates2. 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 17C

• 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 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

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 (33C)– Allow prediction of temperature increase due to GHG• Doubling CO2 from 300ppm to 600ppm would produce a

1.2C 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

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Mathematically Speaking . . .

• Comparing equilibrium temperature with and without water vapor feedback (from Ch 2)

∆Teq = ∆T0 + ∆Tf

∆Teq = 1.2C+ 1.2C 2.4C

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The Feedback Factor• The ratio of the equilibrium response to forcing

(the response with feedback) to the response without feedback

= temperature change with feedback = 2.4 C 2 temperature change w/out feedback 1.2 C

Negative feedback loop if 0 < < 1Positive feedback loop if 1 < STRONGLY POSITIVE

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)