Lectures 16-18. Sci A-30 8. 10 & 15 April 2008 The Planck function gives the energy emission rate for an object, which is a function of it's temperature. The earth exchanges energy with it's environment primarily through electromagnetic radiation. Solar radiation in the visible and near-infrared regions of the spectrum. Wavelengths between 0.4 and 0.8 µm (micrometers, or "microns") are visible, the near infrared goes from 0.8 to about 3 µm. Planetary radiation is in the "long-wave infrared" ( 5 50 µm ), not visible to the human eye. Solar and planetary radiation have most of their energy in disjoint parts of the electromagnetic spectrum. Thus atmospheric and surface properties affect them differently. The total energy emitted (J m -2 s -1 ) for a black body is a function of temperature alone, given by the Stefan-Boltzmann forumula, σ T 4, where σ = 5.67 10-8 W m -2 K -4. The energy balance of the earth is determined by the balance between incoming solar radiation (minus the portion reflected) and outgoing terrestrial radiation. Analysis of the energy balance leads to definition of the effective temperature of the earth, T eff, the average temperature for black-body emission that balances solar input (F s solar flux at Earth's orbit, A = earth's albedo (fraction of solar radiation reflected): T eff = [F s (1 - A)/(4σ)] ¼ = 252.6 K.
The "Greenhouse Effect" The Stefan-Boltzmann equation describes the flux of energy emitted by 1 square meter of surface (units: Watts m -2 ) Flux = σt 4, σ = 5.67 10-8 W m -2 K -4. The Earth must, on average, radiate to out to space the same amount of energy received by the sun. The energy balance equation for Earth shows this balance, 4πR e2 σt eff4 = F s πr e2 (1 - A), where T eff is the "effective temperature" required to achieve energy balance. It is the temperature of an equivalent black body that radiates just the amount of energy received from the sun. (A is Earth's average albedo (~0.30), F s is the solar energy flux at Earth's orbit, 1379 W m -2 ). T eff = [F s (1 - A)/(4σ)] ¼ = 252.6 K. The Earth's surface is warmer than T eff because certain gases in the atmosphere (H 2 O, CO 2, CH 4 ) absorb terrestrial infrared radiation, and they reradiate in both the upward and downward directions. The downward-going radiation warms the Earth's surface. This phenomenon is known as the "Greenhouse Effect" ; it is a potent, natural process. The earth would be too cold for life to exist if the surface temperature were not elevated over T eff by the Greenhouse Effect.
Course structure: an update Atmospheric physics: air motions, regional and global circulation; the "first basics" of climate Lectures 1-10 (completed) Atmospheric composition: the controls on absorption and emission of radiation and on heating and cooling of the atmosphere 11-12 13-14 Atmospheric radiation: shortwave (solar) and longwave (terrestrial) radiation, planetary energy balance, the "greenhouse effect"; the "second basics" of climate. 15 Climate change: effects of "greenhouse gases" on the planetary energy balance; observations of the climate; the "third basics" of climate. 16-17 Topics in current climate science: hurricanes, floating ice, glaciers.
Road map to Science A-30 (Lectures 15-18): Atmosphere Heat, Energy, Radiation Black Bodies, Planck Function, Stefan Boltzmann Law Effective T, greenhouse effect Feedback! Solid bodies emit thermal radiation at rates that depend on temperature. Hot bodies (sun) emit more radiation at shorter wavelengths than cold bodies (earth). Emission rate=σt 4 Planets radiate on average at the Effective Temperature, to maintain energy balance with sun and space, Absorption of ir in the atmosphere traps energy, radiating back to the surface and causing it to warm up. Teff = [Fs(1 - A)/(4σ)]¼ = 252.6 K Tg = [n + 1] 1/4 Teff. Lecture 15 Lectures 16, 17 Lecture 18
The energy balance of planet earth The temperature of the earth s surface has been remarkably constant over geologic time. Even the dramatic cooling during the ice age represented a change of only 3 C in the global average surface temperature, occurring over thousands of years. Seasonal changes in temperature, although large in a particular place, correspond to very tiny changes in global mean temperature. How is this remarkably steady condition maintained? To maintain the long-term stability of earth s temperature, the planet must radiate to space a flux of energy sufficient to just balance the input from the sun, i.e. the earth is, to good approximation, in radiative energy balance.
Millenial NH temperature trend [IPCC, 2001]
If we could take a snapshot of a light wave as it traveled for 1 s, it would be 3 10 8 m long, and would look like the sine wave shown in the figure. The distance between two successive crests on the wave is called the wavelength (denoted λ). The frequency (denoted ν) is the number of wave cycles (wavelengths) that pass a reference point per unit time, and since our snapshot shows exactly the number of peaks that passed in one second, ν is also the number of peaks in the picture, i.e. ν =c/λ. Alternatively, 1/ν is the time it takes the wave to travel one wavelength at speed c.
Electromagnetic radiation, although wave-like in nature, is composed of packets of energy called photons. Thus light is both a wave and a particle. For a given electromagnetic wave of wavelength λ the energy associated with each photon is given by E = hc/λ = hν where h is Planck's constant (h=6.626x10-34 J sec). This was one of Planck's great discoveries; it implies that photons with shorter wavelengths are more energetic than photons with longer wavelengths and light comes in defined packets with a particular amount of energy in each one (given by hν). Light and matter in fact are always dual: waves and particles.
Matter emits radiation if its temperature is above 0 K (absolute zero). An object that absorbs radiation at all wavelengths incident on it necessarily emits radiation at all wavelengths. This ideal material is called a black body; solid objects, such as the the earth, or liquid water, behave almost as black bodies. Planck showed that the intensity of light that is emitted from a black body as a function of wavelength (λ) or frequency (ν), is given by the following function (now called the Planck function): FLUX (λ) = [2π hc 2 / λ 5 ] [exp( hc/(λ kt) ) 1 ], <= Planck function (units: Watts m -2 m -1 ; 1 W 1 J s -1 ) is the amount of energy in light with λ between λ and λ+ λ passing through surface with area 1 m 2 each second. Planck s Law indicates that the temperature of an object determines the intensity of radiation emitted by the object at any wavelength, provided that the object can absorb radiation at that wavelength.
The Planck function gives the energy flux from an object divided up according to wavelength (or frequency), for a given temperature. Long before Planck, however, scientists had determined by direct experiment that the total energy flux from an object, at all wavelengths, depended only on temperature, and they derived an empirical equation called the Stefan-Boltzmann law to describe this relationship: TOTAL ENERGY FLUX = σ T 4. (sum of Planck fcn) Here the total energy flux (units: W m -2 ) is shown to vary as the 4th power of the absolute temperature, T (K), with a constant of proportionality σ = 5.67 10-8 W m -2 K -4, the Stefan-Boltzmann constant. The Stefan-Boltzmann law was obtained in the 19th century by observing the rate at which real objects lost energy via radiation, with many decades passing before Planck showed that it could be derived from his radiation law. λ max = b/t (Wien's displacement law: peak of Planck function)
visible "color temperature"
SOLAR RADIATION SPECTRUM: blackbody at 5800 K
O sun r=1.5 x 10 11 m o earth Diagram of the sun and earth, and an imaginary sphere with radius 1.5x10 11 m with the sun at the center. The surface area of this sphere is 4πr 2. We can compute, using the Stefan-Boltzmann Law, the total amount of energy (L) radiated by the sun each second, L = σt s4 4πR s2 = 3.9 x 10 26 watts, where 4πR s2 is the surface area of the sun (Rs=6.6 10 8 m), σt s4 is the Stefan-Boltzmann law giving the energy flux per unit area, and T s is the temperature of the sun s surface, 5800 K.
The same total amount of energy L must also cross the sphere of radius r each second. The solar flux (Watts m -2 ) at earth's orbit, F s, is defined as the energy crossing a square meter of the sphere at earths orbit each second. It is given by F s = L/(4πr 2 ) = σt s4 (R s2 /r 2 ) = 3.9x10 26 /( 4π(1.5x10 11 ) 2 ) = 1379 W m -2 The solar flux F s (also called the solar constant) is the radiant energy from the sun that falls per second a 1 m 2 surface oriented perpendicular to the sun s rays, at the top of the earth's atmosphere.
The total solar energy striking by the earth per second can be calculated by multiplying Fs by the shadow area (not the total surface area!) of the earth, i.e. the area of solar beam intersected the earth. SUN The amount of energy striking the earth is given by the [shadow area (black circle) the solar flux] =πr e2 F s. (R e is the radius of the earth). The total energy flux striking the surface of the earth is therefore F s πr e2.
Energy INPUT to the earth from the sun Not all solar radiation intercepted by the earth is absorbed. The fraction of incident solar radiation reflected is defined as the albedo, A, and the fraction absorbed is therefore (1-A). The total energy input to earth (Joules per second) is thus E abs = F s πr e2 (1 - A). INPUT Energy OUTPUT from earth by thermal radiation The total energy emitted per unit area is given by σt 4, and the emitting area is the surface area of the earth, 4πR e2. The total energy emitted by the planet per second is therefore E emit = 4πR e2 σt 4. OUTPUT
Energy balance requires that input=output, when averaged over a longenough period of time, i.e. on average E emit = E abs. Thus 4πR e2 σt 4 = F s πr e2 (1 - A). (This is the Energy Balance Equation). This equation can be solved for the average temperature at which the earth must emit radiation to bring the energy budget into balance, called the effective temperature Teff of the planet: T eff = [F s (1 - A)/(4σ)] ¼ = 252.6 K.
Effective Temperatures of the Planets planet solar flux orbit radius albedo T e T g Ground pressure (W m -2 ) (10 11 m) (K) (K) (bar) Mercury 9200 0.6 0.058 442 442 ~0 Venus 2600 1.1 0.77 227 750 90 Earth 1400 1.5 0.33 253 288 1 Mars 600 2.3 0.15 216 240 0.007 Jupiter 49 7.8 0.58 98 (no surface) (no surface) After Goody and Walker, "Atmospheres"
Atmospheric absorption of infrared radiation The most abundant gases in the atmosphere, N 2, O 2, and Ar, neither absorb nor emit terrestrial radiation. (They also neither absorb or emit most wavelengths of solar radiation, except for ultraviolet light). The relatively rare molecules that can absorb long-wave (terrestrial) infrared radiation are called greenhouse gases. They can trap infrared radiation emitted by the Earth much as the glass in a greenhouse traps heat. The most important greenhouse gases in the atmosphere are H 2 O and CO 2, and gases such as methane (CH 4 ) and chlorofluorocarbons are also significant.
Greenhouse gases: Water, CO 2, CH 4 O = C = O Water interacts with electromagnetic waves with both a permanent dipole moment (left) and dynamic ("transition") dipole moment due to the changes in the +δ and δ as the molecule vibrates. -δ -δ O O C = +2δ = CO 2 with electromagnetic waves with only dynamic ("transition") dipole moment due to the changes in the +δ and δ as the molecule vibrates (bending or "asymmetric stretch"). molecules radiate frequencies they can absorb: Kirchhoff's Law
Due to the presence of gases that can absorb infrared radiation, the atmosphere acts as a blanket, allowing solar energy to reach the surface but preventing the heat from escaping directly back to space. The atmosphere is warmed by the absorbed terrestrial radiation. Molecules that can absorb radiation of a particular wavelength can also emit that radiation according to Kirchhoff's radiation law. The Greenhouse gases in the atmosphere will therefore radiate, both to space and back towards the earth's surface. This backradiation warms the earth's surface.
Course structure: 2 nd half Atmospheric physics: air motions, regional and global circulation; the "first basics" of climate Lectures 1-10 (completed) Atmospheric composition: the controls on absorption and emission of radiation and on heating and cooling of the atmosphere 11-12 13-14 Atmospheric radiation: shortwave (solar) and longwave (terrestrial) radiation, planetary energy balance, the "greenhouse effect"; the "second basics" of climate. 15 Climate change: effects of "greenhouse gases" on the planetary energy balance; observations of the climate; the "third basics" of climate. 16-17 Topics in current climate science: arctic climate, especially with respect to sea ice (floating ice). 18-20 21-22 Are humans causing dangerous climate change? Has climate really changed?
Road map to Science A-30 (Lectures 15-17): Atmosphere Heat, Energy, Radiation Black Bodies, Planck Function, Stefan Boltzmann Law Effective T, greenhouse effect Feedback: clouds, albedo! Solid bodies emit thermal radiation at rates that depend on temperature. Hot bodies (sun) emit more radiation at shorter wavelengths than cold bodies (earth). Emission rate=σt 4 Planets radiate on average at the Effective Temperature, to maintain energy balance with sun and space, Absorption of ir in the atmosphere traps energy, radiating back to the surface and causing it to warm up. Teff = [Fs(1 - A)/(4σ)]¼ = 252.6 K Tg = [n + 1] 1/4 Teff. Lecture 15 Lectures 16, 17 Factors other than gases: aerosols, land use change Lecture 18
The Greenhouse Effect: influence of atmospheric absorption and emission of planetary (infrared) radiation incoming solar radiation (F s ) (visible, near infrared) σt e 4 σt e 4 far infrared radiation from the atmosphere z=h reflected solar (A) σt g 4 terrestrial (far infrared) radiation from the surface
The atmosphere and the ground radiate energy according to the Stefan-Boltzmann law. Examine the energy balance of the layer at H (intended to be a scale height, or ~ 7km, on earth) in this hypothetical planet. The total amount of energy radiated per square meter per second is 2σT 14, (OUT) because the layer radiates equally both up and down. But the amount received by the layer is σt g4, (IN) (heated only from below!). If the layer has a balanced energy budget, these two fluxes must be equal (IN = OUT), σt g4 = 2σT 14. { T 1 =>> T eff } Thus the ground is warmer than the atmosphere by T g = 2 1/4 T eff. This happens because the atmosphere is warmed only by absorbing radiation from the earth's surface, i.e. from one side (below), but it radiates both up and down. The atmosphere must have a lower temperature than the ground in order to satisfy its energy balance. This result for 1 layer in the atmosphere can be generalized to any number (n) of layers, σt g4 = [n + 1] σt 1 4 T g = [n + 1] 1/4 Teff. The atmosphere therefore gets colder as we go up due to the effects of absorption and emission of radiation (terrestrial infrared radiation).
TERRESTRIAL RADIATION SPECTRUM FROM SPACE: composite of blackbody radiation spectra for different T Scene over Niger valley, N Africa cf. clouds, aerosols
ATMOSPHERIC CO 2 INCREASE OVER PAST 1000 YEARS
FEEDBACKS Consider how these factors may change, what may cause these changes, and how the various changes may interact with each other. This brings us to the concept of feedback: property A increases property B changes causes property A to increase further + positive feedback (amplification) property A increases property B changes causes property A to decrease + negative feedback (damping) Positive feedback makes the climate system more sensitive to a change in property A; negative feedback makes it less sensitive. The concept of feedback depends on a formulation of direct vs. secondary effects, based on separation in time or some other criterion.
Feedback is taking place in the climate system because the number of absorbing "layers", n (also called the "optical thickness") can depend on the temperature of the atmosphere, or on other climatic parameters such as precipitation. The effective temperature Te depends on the albedo might also which might also depend on the climate itself. Thus we allow for n and A to be functions of Tg : Tg = { [n(tg) + 1][1 - A(Tg) ] Fs/(4σ) } 1/4 Tg depends on itself! This self-interaction is called feedback, and it may involve complexity, and it may manifest itself over long or short time scales. Example: Snow albedo or ice-albedo feedback Example: Water vapor temperature feedback
FEEDBACKS INVOLVING ABSORPTION OF IR (HEAT) Examine some of the most important feedbacks in the Earth s atmosphere. water vapor feedback. Temperature increases atmosphere H 2 O increases (Clapeyron equation) atmospheric absorption increases (n) Temperature increases + This is the strongest feedback mechanism in the atmosphere. It is also the best understood since it is based simply on the measured increase in water vapor pressure increase with temperature (Clapeyron equation). cloud feedback terrestrial radiation Temperature increases atmosphere H 2 O increases (Clapeyron equation) cloudiness increases (n) Temperature increases + This is a very strong feedback that is not well understood because it is hard to know whether or how much cloudiness would increase as temperature does cloudiness depends on upward air motion more than on T or H 2 O directly.
FEEDBACKS INVOLVING ALBEDO cloud feedback solar radiation Temperature increases atmosphere H 2 O increases (Clapeyron equation) cloudiness increases (n) Albedo increases Temperature decreases This is also very strong feedback that is not well understood because it is hard to know whether or how much cloudiness would increase as temperature does, and because of the trade-off (competition) between the effects of clouds on absorption of infrared radiation versus reflection of solar radiation. Low-altitude clouds affect albedo more than they affect ir radiation, and conversely for high clouds (discussed below). vegetation feedback solar radiation Temperature increases deserts expand Albedo increases - - Temperature decreases This is a very complex feedback that will take a long time to be realized. Maybe deserts won't expand, or plants will be greener because there is more CO 2?
FEEDBACKS INVOLVING ALBEDO (continued) ice-albedo feedback solar radiation Temperature increases polar ice recedes Albedo decreases + Temperature increases This is a very strong feedback when there is a lot of polar ice, for example, at the height of the last ice age. It works both ways, helping the ice sheets to advance as the earth cooled, by amplifying the cooling, and accelerating the retreat of the ice sheets as the climate started to warm. There is rather little polar ice in glaciers today, so feedback on land ice is not likely to play a major role in climate change. But sea ice coverage is significant, and uptake of heat by the underlying ocean could have effects on both temperature and rainfall. Sea ice will be discussed in detail later. snow albedo feedback (class discussion) vegetation (polar) albedo feedback (class discussion) vegetation CO 2 feedback (class discussion) snow surface-t feedback (class discussion) Desertification
reflected solar incoming solar radiation σt 1 4 σt 1 4 far infrared radiation from the atmosphere high altitude clouds incoming solar radiation σt a 4 σt c 4 σt a 4 far infrared radiation from the atmosphere σt g 4 terrestrial radiation from the surface σt c 4 far infrared radiation from high clouds warming: T c T e > T a > T g cloud above the "radiating level" T 1 of the atmosphere σt g 4 terrestrial radiation from the surface simple greenhouse model low altitude clouds add clouds cloud albedo σt a 4 σt a 4 far ir from atmosphere σt g 4 terrestrial radiation from the surface no warming: T a T e > T c T a σt c 4 T c T g σt c 4 far infrared radiation from low clouds cloud below the "radiating level" of the atmosphere Clouds close to the ground increase albedo; but they emit and receive ir radiation much like the ground does, so in the ir they are having no effect on atmospheric temperatures. High clouds reside above the level of atmospheric absorption and warm the atmosphere.
ORIGIN OF THE ATMOSPHERIC AEROSOL Aerosol: dispersed condensed matter suspended in a gas Size range: 0.001 µm (molecular cluster) to 100 µm (small raindrop) Soil dust Sea salt Environmental importance: health (respiration), visibility, radiative balance, cloud formation, heterogeneous reactions, delivery of nutrients
Atmospheric aerosols: Global cooling? Aerosols are suspended particles in the air which are small enough to resist gravitational sedimentation (i.e. they remain afloat despite the force of gravity acting on them). Aerosols can be solid, liquid, or a combination of both. They typically range in size from 0.1 to 1.0 micrometers. The main sources of aerosols are dust from the surface, sea spray (liquid droplets and solid sea-salt particles), volcanoes, forest fires, and anthropogenic combustion. Direct effect: aerosols scatter sunlight, increasing albedo, cooling the atmosphere. Black carbon effect: if aerosols have black carbon (soot ) inside, they can be heated by sunlight, warming the atmosphere. Indirect effect: aerosols affect the formation of cloud droplets. Increased aerosols may lead to smaller droplets, more cloudiness, and higher albedo, cooling the earth by lowering Teff.
Effect of a major volcanic eruption on climate ( after Hansen et al., 1993). Note: many feedbacks have not come into play. Temperature Change ( o C) -0.6-0.4-0.2 0 +0.2 Global Temperature Climate Model 1991 1992 1993 1994 Mt. Pinatubo eruption
http://www.atoptics.co.uk/atoptics/sunvolc.htm Volcanic eruptions can inject millions of tonnes of dust and gaseous sulfur dioxide into the stratosphere. The finer dust particles remain aloft for years and spread around the world while the sulphur dioxide evolves to an aerosol of sulfur acids that add to the particulates. The dust and aerosol produce vivid sunset and twilight effects like the intense yellow-red horizon and purple-pink glows of the photograph. The purple glow is probably a combination of red-orange light transmitted through the lower atmosphere and scattered blue light from still sunlit stratospheric dust.
AEROSOL OBSERVATIONS FROM SPACE Biomass fire haze in central America (4/30/03) Fire locations in red Modis.gsfc.nasa.gov
BLACK CARBON EMISSIONS DIESEL DOMESTIC COAL BURNING BIOMASS BURNING Kyoto also failed to address two major pollutants that have an impact on warming: black soot and tropospheric ozone. Both are proven health hazards. Reducing both would not only address climate change, but also dramatically improve people's health. (George W. Bush, June 11 2001 Rose Garden speech)
Aerosols have health effects, too! ANNUAL MEAN PARTICULATE MATTER (PM) CONCENTRATIONS AT U.S. SITES, 1995-2000 NARSTO PM Assessment, 2003 PM10 (particles > 10 µm) PM2.5 (particles > 2.5 µm) Red circles indicate violations of national air quality standard: 50 µg m -3 for PM10 15 µg m -3 for PM2.5
EPA REGIONAL HAZE RULE: FEDERAL CLASS I AREAS TO RETURN TO NATURAL VISIBILITY LEVELS BY 2064 clean day Acadia National Park moderately polluted day http://www.hazecam.net/
ASIAN DUST INFLUENCE IN UNITED STATES Dust observations from U.S. IMPROVE April 16, 2001 Asian dust in western U.S. network April 22, 2001 Asian dust in southeastern U.S. 0 2 4 6 8 µg m -3 Glen Canyon, AZ Clear day April 16, 2001: Asian dust!
Climate forcing due to changes in concentrations of greenhouse gases, atmospheric aerosols, and clouds, since 1850 (Hansen, 2001). Class discussion What about engineering the climate: add aerosols to the atmosphere? add iron to stimulate the ocean? plant trees to take up CO 2 and cool the surface?
PROJECTIONS OF FUTURE CO 2 CONCENTRATIONS [IPCC, 2001]
FUTURE TEMPERATURE PROJECTIONS FROM CLIMATE MODELS (IPCC, 2001)
Mean temperature change (K) predicted by large ensemble of climate models for 2071-2100 vs. 1961-1990, for a pessimistic CO 2 scenario (A2) and an optimistic one (B2) Warming of 2C represents a ~12% increase in water vapor pressure. What does this imply about aridity in Africa? A2 B2
Course structure: 2 nd half Atmospheric physics: air motions, regional and global circulation; the "first basics" of climate Lectures 1-10 (completed) Atmospheric composition: the controls on absorption and emission of radiation and on heating and cooling of the atmosphere 11-12 13-14 Atmospheric radiation: shortwave (solar) and longwave (terrestrial) radiation, planetary energy balance, the "greenhouse effect"; the "second basics" of climate. 15 Climate change: effects of "greenhouse gases" on the planetary energy balance; observations of the climate; the "third basics" of climate. 16-17 Topics in current climate science: arctic climate, especially with respect to sea ice (floating ice). 18-20 21-22: interactive! Are humans causing dangerous climate change? Has climate really changed?