The Greenhouse Effect & Global WarmingThe earth’s energy balance & radiation

Objectives

• Understand and apply the blackbody radiation law; • Understand the meaning of the term

emissivity;

Use the Phet applet to answer the following questions & lab activity.

https://phet.colorado.edu/en/simulation/blackbody-spectrum

• Describe what happens to the blackbody spectrum as you increase the temperature. What happens to the shape of the curve and the peak of this curve?

• What happens to the blackbody spectrum as you decrease the temperature?

• Set the temperature to that of a light bulb (around 3000 K). Based on this information, do light bulbs seem efficient? Why do light bulbs get hot?

• Imagine that you see 2 hot, glowing objects--one is glowing orange and the other is glowing blue. Which one is hotter?

The Black Body Law

• Stefan-Boltzmann Law – all bodies with temperature radiate EM waves• The amount of energy per second (i.e. the power)

radiated by a body depends on its surface area A, absolute temperature T, and the properties of the surface:

• e = emissivity ()• σ = Stefan-Boltzmann constant =

The Black Body

• Emissivity = 1• A ‘perfect’ emitter• Good real approximation:

charcoal, soda can opening• Black, dull surface• e closer to 1

• Light shiny surface• e closer to 0

Surface EmissivityBlack body 1Ocean water 0.8Ice 0.1Dry land 0.7Land with vegetation

0.6

The Black Body• A body of emissivity e that is kept at some

temperature T1 will radiate power according to the black body law, but will also absorb power at a rate if its surroundings are kept at a temperature T2. Hence the net power lost by the body is

• At equilibrium, Pnet = 0, body’s temperature remains constant and equals that of surroundings

The Black Body• Surfaces that are black and dull are also good

absorbers of radiation (wear dark colors when cold). Light colored surfaces are good reflectors of radiation (wear light colors when hot).

Black Body Radiation• The energy radiated by a body is

distributed over an infinite range of wavelengths, however, most of the energy is radiated at a specific wavelength determined by the temperature of the body – the higher the temperature the shorter the wavelength. • Room temp (20°C, 293 K) –

infrared – hence the “heat” association.

Black Body Radiation• We see that with increasing temperature, the peak

of the curve occurs at lower wavelengths and the height of the peak increases. The relation between the temperature and the peak wavelength at which most of the energy is emitted is given by Wein’s Law: • The Earth’s surface has a (global day & night

average) temperature of 288K, so – typical infrared.• The sun (T=5800 K), so – visible light (guess which

color…)

Black Body RadiationExample: By what factor does the power emitted by a body increase when the temperature is increased from 100°C to 200°C?

Black Body RadiationExample: The emissivity of the naked human body may be estimated to be 0.90. Assuming a body temperature of 37°C and a surface area of 1.60 m2, calculate the amount of energy lost by the body when exposed to a temperature of 0.0°C for 30 mins.

Assignment

• 1-3

Objectives• Understand the meaning of the term albedo; • Work with a simple energy balance equation;

Solar Radiation

• The sun may be considered to radiate as a perfect emitter (i.e. as a black body). The sun emits a total power of P=3.9x1026 W. • The average earth-sun distance is d=1.5x1011 m. • So, at the distance of the Earth, we may

imagine that the power radiated by the sun is distributed uniformly on the surface of a sphere centered at the sun of radius d.

Solar Radiation• Intensity is the power of radiation received per

unit area of the receiver.• The Earth receives only a very small fraction of

this power equal to , where a is the area used to collect the power. Thus the power per unit area (i.e. the intensity) received by Earth is = solar constant (symbol S); intensity of solar radiation & top of atmosphere.• ; P – power, I – intensity, A - area

Albedo

• Latin for ‘white’, dimensionless number• Symbol α• Definition: the ratio of the power of

radiation reflected or scattered from the body to the total power incident on the body:

Albedo• Snow has a high albedo

(0.85) indicating that snow reflects most of the radiation incident on it, whereas charcoal has an albedo of only 0.04, meaning that it reflects very little of the light incident on it.

• The Earth as a whole has an average global albedo of about 0.3 and varies based on:• Time of year (many/few

clouds)• Latitude (how much

snow/ice)• Desert land (high

albedo 0.3-0.4)• Forests or water (low

albedo 0.1)• Etc.

Albedo• The calculation of the solar constant as S = 1400 W

m-2 is the value at a particular point in the upper atmosphere.• At any one point in time, the Earth offers a ‘target’

area of ; where R is the radius of the Earth. As the target area is only a quarter of the total surface area of the Earth (), the power of the radiation received per square meter of the Earth’s surface is . Since 30% is reflected, this means that the earth receives a net radiation intensity of

Energy Balance• The Earth has a constant average temperature

and behaves as a black body. So the energy input to the Earth must equal (balance) the energy output by the Earth.• Taking account of albedo, the power delivered

to surface area A is • The following example introduces an energy

balance equation

Example1. Assume that the Earth has a fixed

temperature T and that it radiates as a black body. The average incoming solar radiation has intensity . Take the albedo to be α=0.30. Ignore the effect of the atmosphere.

Examplea) Write down an equation expressing the fact

that the power received by the earth equals the power radiated by the earth into space (an energy balance equation)

b) Solve the equation to calculate the constant earth temperature

c) Comment on your answer.

ExampleFixed temperature T, , α=0.30. a) Write down an equation expressing the fact that the power received by the earth equals the power radiated by the earth into space (an energy balance equation)

ExampleFixed temperature T, , α=0.30.b) Solve the equation to calculate the constant earth temperature.

c) Comment on your answer.

Energy Balance• Another drawback of the simple model

presented above is that the model is essentially a zero-dimensional model. The earth is treated as a point without interactions between the surface and the atmosphere. (Latent heat flows, thermal energy flow in oceans through currents, thermal energy transfer between the surface and the atmosphere are all ignored) Realistic models must take all these factors and many others into account, and so are very complex.

Assignment

• 4, 5, 6, 8

Objectives

Engage: Watch this videoExplore: Complete this activity• Understand the meaning of the term greenhouse

effect; • Name the main greenhouse gases and their

natural & anthropogenic sources & sinks;• Understand the molecular mechanism for

infrared radiation absorption;• Understand the definition of surface heat

capacity and apply it in simple situations;

The greenhouse effect• This effect applies to any planet with an

atmosphere. Earth assumed here.•Most solar radiation in visible region (w/ small

amounts in UV and IR). About 30 % reflected back into space, rest warms surface & atmosphere.• Earths avg surface temperature = 288 K (Earth

radiates in IR)• IR radiation is strongly absorbed by various

gases in the atmosphere – greenhouse gases

The greenhouse effect

• Greenhouse gases re-radiate the absorbed IR radiation in all directions -> some reabsorbed by earth’s surface (additional warming), would otherwise be lost in space•Without this greenhouse effect, the earth’s

temperature would be 32K lower.• No atmosphere – no greenhouse effect

The greenhouse effect

The greenhouse effect• The greenhouse effect may be described as the

warming of the earth caused by infrared radiation emitted by the earth’s surface, which is then absorbed by various gases in the earth’s atmosphere and then partly re-radiated back toward the surface. The gases primarily responsible for this absorption (the greenhouse gases) are water vapor, carbon dioxide, methane, and nitrous oxide.

The greenhouse effect

The greenhouse effectMechanism Intensity IN (arbitrary units)Radiation from sun 100Total for entire earth 100

Mechanism Intensity OUT (arbitrary units)Reflected from surface 5Reflected from atmosphere 25Radiation from clouds and atmosphere

65

Radiation from surface with no atmospheric absorption (the IR ‘window’)

5

Total for entire earth 100

The greenhouse effectMechanism Intensity IN (arbitrary units)Transmitted to surface from sun 30Absorbed IR radiation re-radiated back to Earth (greenhouse effect)

96

Total for earth’s surface 146

Mechanism Intensity OUT (arbitrary units)Reflected from surface 5Convection & evaporation 30IR radiation from surface 106Radiation from surface with no atmospheric absorption (the IR ‘window’)

5

Total for earth’s surface 146

The greenhouse effect• For the Earth as a whole: total reflected

radiation = 5+25 = 30, consistent with an albedo of 0.3• Total outgoing radiation is 100, consistent with

energy conservation.• For the surface, amount of radiation emitted is

106+5=111, compared to incoming 100. This represents 111% of the average incoming intensity , so is

The greenhouse effect• This must be consistent with the earth’s surface

temperature of 288 K. Indeed the radiation per unit area from a surface at this temperature is • The greenhouse effect is a natural consequence

of the presence of the atmosphere.• Enhanced greenhouse effect – additional

warming due to increased quantities of the greenhouse gases in the atmosphere due to human activity.

The Greenhouse effect

• The radiation incident on the earth is mainly visible light. Photons of visible light, unlike photons of IR radiation are not absorbed by the gases of the atmosphere• The incident radiation passes through the

atmosphere and arrives at earth’s surface (having had about 25% of the radiation reflected back into space from the upper atmosphere).

The greenhouse effect – sources & sinks

• Sources: • Carbon dioxide

(CO2)

• methane (CH4)

• water vapor (H2O)

• nitrous oxide (N2O)• chlorofluorocarbons

(cfcs)

• Sinks: • CO2 absorbed by plants

during photosynthesis• methane destroyed in

lower atmosphere by chemical rxns involving free hydroxyl radicals (-OH)• nitrous oxide destroyed

in atmosphere by photochemical rxns

Natural & anthropogenic (man-made) origins

The greenhouse effectGreenhouse Gas

Natural Sources Anthropogenic Sources

H2O Evaporation of water from oceans, rivers, & lakes

CO2 Forest fires, volcanic eruptions, evaporation of water from oceans

Burning fossil fuels in power plants and cars, burning forests

CH4 Wetlands, oceans, lakes & rivers

Flooded rice fields, farm animals, termites, processing of coal, natural gas, and oil, and burning biomass

N20 Forests, oceans, soil & grasslands

Burning fossil fuels, manufacture of cement, fertilizers, deforestation (reduction of nitrogen fixation in plants)

Mechanism of photon absorption• Consider a molecule of carbon dioxide.

Remember energy is quantized in electrons in atoms. The same principle of quantized energy states applies to molecules due to their vibrational & rotational motion.

Mechanism of photon absorption• The big difference between

the two kinds over energy level (vibrational/rotational vs atomic) is that the difference in energy levels is approximately the same as the energies of infrared photons (less than atomic).

Mechanism of photon absorption• This means IR photons

travelling through these gases will be absorbed (exciting the molecules to a higher energy level), then re-emitted as the molecule transitions back to a lower energy level.• Re-emission back to earth

or to space.

Mechanism of photon absorption• Precise mechanism requires quantum

mechanics & won’t be discussed here. • Analogy using SHM: consider 2 atoms forming a

diatomic molecule. Force between atoms loosely modeled as mass-spring system. • Frequency of oscillation: ; where m is related to

the masses of the 2 atoms, m1 & m2 by

Mechanism of photon absorption• For carbon monoxide (CO), the ‘spring’ constant

has a value k=1900 N/m and m=1.14x10-26 kg• = natural frequency of the molecule• If photons travelling through the gas have the same

frequency, they will resonate• A typical IR photon has energy 0.25 eV, so

Transmittance curves• As IR radiation passes through

the atmosphere, some of it is absorbed so that by the time it hits the surface, it’s intensity will be less than the incident intensity.We may then make a transmittance curve that shows the variation with wavelength of the percentage of radiation that actually gets through the gas.

Transmittance curves• This figure shows the

theoretical blackbody spectrum of the sun and the actual spectrum due to absorption by gases in the atmosphere.

• This figure shows a realistic transmittance curve for earth’s atmosphere at sea level for IR radiation.

Surface heat capacity

• Cs

• The energy required to increase the temperature of 1 m2 of the surface by 1 K.• Units: J m-2 K-1

Surface heat capacity - ExampleShow that the surface heat capacity is related to the ordinary specific heat capacity c, through Cs = ρhc, where ρ is the density of the material and h is the depth of the surface.

Surface heat capacity• The example showed that in order to

calculate the surface heat capacity, one must make estimates of relevant depth, h, that will go into the expression.• Additionally, one has to take an average over

various surface heat capacities corresponding to different materials on the surface (water, ice, dry land, etc.)• For 100 m deep water: ; CS for dry land is

smaller by about a factor of 10.

ExampleRadiation of intensity 340 W m-2 is incident on the surface of a lake of surface heat capacity Cs = 4.2 x 108 J m-2 K-1. Calculate the time t requires to increase the temperature by 2.0 K. Comment on your answer.

(unrealistic) assumption: the lake receives the radiation for the whole day.

Surface heat capacityWe can use the idea of surface heat capacity to make a simple model of energy balance for the planet with the following assumptions:• Planet’s surface heat

capacity, Cs

• Receives solar intensity, Iin

• Loses energy, Iout

• Net power = Iin-Iout

• Over time t, energy received by area A is (Iin-Iout)At = A Cs ΔT• The increase in the

planet’s surface temp after a time t: • If Iin > Iout

Assignment• 9 & 11

Objectives

• State the evidence linking global warming to the increased concentrations of greenhouse gases in the atmosphere; • Discuss the expected trends on climate caused

by changes in various factors and appreciate that these are interrelated; • State possible solutions to the enhanced

greenhouse effect and international efforts to counter global warming.

Global Warming• The greenhouse effect keeps Earth’s temperature

at 288K, making life as we know it on earth possible. Human activity has caused the concentration of greenhouse gases in the atmosphere to increase, leading to additional warming.

The variation of the deviations of the Earth’s

average temperature from the expected long-term average since 1880.

The deviations are positive and increasing.

Global Warming• Variation with

time of the concentrations of the main greenhouse gases over geological, recent, and present time periods. All increasing.• CO2 almost

double pre-industrial.

Global Warming• The previous 2 figures on global temperature

and greenhouse gas concentrations are strong evidence of a connection.• Criticism: not long enough time span• Counter: ice cores in Antarctica & Greenland –

analyze very old ice core samples gives info about gas concentrations & atmospheric temp & time of freezing.• Results – very close link between global

warming & greenhouse gases.

Global Warming: Antarctic Ice Cores

Global Warming: Antarctic Ice Cores

• Extracted from 3600 m deep over (frozen) lake Vostok in East Antarctica in 1998 have been thoroughly analyzed to reveal a connection btwn temp changes & changes in concentrations of CO2 & CH4. • Can give detailed accounts of global

climate over 42,000 years!

Global WarmingVariation with time of temperature & CO2 concentration over the last 400,000 yrs.

Global Warming: ? That need !• Best estimate for temperature

increase over a given time period?• Effects of a higher temperature on

the amount of rainfall?• How much ice will melt?• What will be the rise in sea level?• Will there be areas of extra dryness

and drought and, if so, where will they be?

• Will the temperature of the oceans be affected and, if so, by how much?

• Will there be periods of extreme climate variability?

• Will the frequency & intensity of tropical storms increase?

• What is the effect of sulfate aerosols in the atmosphere? Do they offset global warming?

• What are the feedback mechanisms affecting global climate?

• Can the observed temperature increase be blamed on greenhouse gases exclusively?

• Can the process of global warming be reversed even if present emissions are drastically reduced?

• Ecological implications of the expected changes in the habitat?

• Effects on agriculture?• More diseases?• Social & economic effects?

Global Warming: Other theories• Increased solar activity?• General consensus: GW patterns not consistent

w/ changes in solar activity.• Increased concentrations of greenhouse gases

due to volcanic activity& changes in Earth’s orbit around the sun.• Changes in eccentricity (how oval/circular) & tilt

causing variations in received energy• Occur over huge timescales (20,000 – 100,000 yrs)• Probably not relevant for the climate changes of

the last 200 yrs.

Global Warming: Sea level• Sea level always varies• Atmospheric pressure• Plate tectonics• Wind• Tides• Flow of large rivers• Changes in salinity

• Temp determines how much ice melts/water freezes• Ice age (18,000 ya) – 100

m lower than present

• Changes in sea level affect the amount of water that can evaporate and the amount of thermal energy that can be exchanged with the atmosphere. • Affect ocean currents –

transfer thermal energy from warm tropics to colder regions.

Sea level: melting of ice•Melting a mass m of ice at 0°C requires thermal

energy Q = mL, where L is the specific latent heat of fusion of ice -> removes energy from surroundings (cooling)• Land ice: increases sea level when melted• Sea ice: does not change sea level (Archimedes

principle – weight of ice = weight of displaced water)

Sea level: estimating sea level changes

•Water is weird: contracts in volume when heated from 0°C to 4°C, then expands. Density highest at 4°C (important to water life)• depends on temperature for water

• Volume increase• Coefficient of volume expansion – fractional

change in volume per unit temperature change.• Initial volume• Temperature increase

Sea level: estimating sea level changes EXAMPLE

The area of the oceans of the Earth is about 3.6x108 km2 and the average depth of water is about 3.7 km. using a coefficient of volume expansion of water of 2x10-4 K-1, estimate the expected rise in sea level after a temperature increase of 2 K. Comment on your answer.

Effects of global warming on climate• Higher than average earth temp implies

rise in sea level• Changes albedo – more water, less dry

land

Effects of global warming: EXAMPLE

About 50% of the area of a certain large region of the earth’s surface was covered by water. As a result of ice melting, 60% of this region is now covered by water. Estimate the change in the albedo of the region. Take the albedo of sea water to be αs=0.20 and that of land to be αl=0.40 .

Effects of global warming on climate

• Expected changes in temp due to change in albedo b/c of more water covering land are actually small• More significant – more water + higher temp =

increased rate of evaporation = more water vapor in atmosphere.• Cools earth’s surface• More cloud cover• More precipitation (not necessarily in region of

interest)• CO2 solubility in oceans decreases – more in

atmosphere

Example

Large areas of rainforests are being destroyed by cutting down (and burning) trees. Discuss the possible effects of this on the energy balance of the region.

Deforestation

• Rainforests must be preserved to maintain the existing habitat & prevent extinction of many plant & animal species• Effect on climate uncertain b/c rainforests

do produce methane & contribute to increased concentrations of greenhouse gases• Absorb carbon dioxide but returned to

atmosphere when trees die & decompose

Measures to reduce global warming

• Using fuel-efficient cars & further developing hybrid cars• Increase efficiency of coal-burning power plants• Replacing coal-burning power plants w/natural gas fired

power plants• Consider methods of capturing & storing carbon dioxide

produced in power plants (CCS)• Increase in wind & solar power production• Consider nuclear power• Being energy conscious w/ buildings, appliances,

transportation, industrial processes & entertainment• Stopping deforestation

The Kyoto Protocol & the IPCC• 1997 in Kyoto, Japan – industrial nations agreed

to reduce their emissions of greenhouse gases by 5.2% from 1990 levels over the period 2008-2012• Allowed mechanisms for developed nations to

use projects aimed at reducing emissions in developing nations as part of their own reduction targets• Endorsed by 160 countries – legally binding at

55 – not signed by US or Australia

The Kyoto Protocol & the IPCC• Kyoto protocol – mandatory limits on greenhouse

gas emissions• 2005: Asia-Pacific Partnership on Clean

Development and Climate (APPCDC or AP6) – voluntary reductions• Signed by US, Australia, India, the People’s

Republic of China, Japan & South Korea• Agree to cooperate in reducing emissions• Criticized as worthless b/c reductions are voluntary • Defended b/sc it includes major GH gas producers

not bound by Kyoto protocol.

The Kyoto Protocol & the IPCC• Intergovernmental Panel on Climate Change (IPCC) -

Major, detailed, comprehensive, scientifically impartial analysis of global climate• Created by the World Meteorological Organization

(WMO) and the United Nations Environment Programme (UNEP) in 1988.• Conducts no research of its own, but reports on

technical, scientific, and socio-economic aspects of climate change using assessments of existing published scientific material.• Four reports (1990, 1997, 2001, 2007) – instrumental

in providing accurate analysis of the global situation.

Assignment

• 23-26 & 28-31