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=σT4

Road map to EPS 5 Lectures 3 and 4: Atmosphere Heat, Energy, Radiation

Black Bodies, Planck Function, Stefan Boltzmann Law

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]1/4Teff.

Effective T, greenhouse effect Feedback!

Atmospheric Radiation: The Earth receives energy from the sun (on average 344 W/m2) and emits the same amount to space

The energy balance of planet earthThe 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.

Scientists 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 T4

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

Many decades passing Planck showed that this relationship could be derived from his radiation law, which describes the complete spectrum of radiation from a “perfect” (black, absorbs and emits with 100% efficiency at all wavelengths) object.

If we could take a snapshot of a light wave as it traveled for 1 s, it would be 3108 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).

λmax = b/T (Wien's displacement law: peak of Planck function)

The Planck function gives the energy flux from an object divided up according to wavelength (or frequency), for a given temperature—it is pictured on the next slides.

Electromagnetic spectrum: Atmospheric Radiation

106

visible

"color temperature"

The earth’s albedo (fraction of solar radiation *reflected* to space) was first measured by observing earthshine on the moon, reflected back to earth and visible just after the new moon. It is now measured from spacecraft. About 33% of the solar energy incident on the earth is reflected back to space, A=0.33.

Most of the reflection of solar radiation from earth is due to clouds, with help from sea ice and glacial ice in Antarctica and Greenland, plus snow and deserts (albedo 0.6—0.9).

The albedo of the earth’s surface is mostly much lower than 0.33, about .07 for land with vegetation, 0.05-0.1 for the ocean.).

Thus the albedo, and the entire energy budget of earth, is sensitive to cloudiness and ice cover, factors that change on both weather and climate time scales (short and long times).

Albedo

Earth's albedo for March, 2005 (CERES satellite)

ALBEDO The term has its origins from a Latin word albus, meaning “white”. It is quantified as the fraction of incident solar radiation of all wavelengths reflected by a body or surface. 

Or=1.5 x 1011 m

o

sun earth

Diagram of the sun and earth, and an imaginary sphere with radius 1.5x1011m with the sun at the center.

The surface area of this sphere is 4πr2.

We can compute, using the Stefan-Boltzmann Law, the total amount of energy (L) radiated by the sun each second,

L = σTs4 4πRs

2 = 3.9 x 1026 watts,where 4πRs

2 is the surface area of the sun (Rs=6.6 108m), σTs4

is the Stefan-Boltzmann law giving the energy flux per unit area, and Ts 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 the earth, Fs, is defined as the energy crossing a square meter of the sphere at earth's orbit each second. It is given by

Fs = L/(4πr2) = σTs4 (Rs

2/r2) = 3.9x1026/( 4π(1.5x1011)2 ) =

1379 W m-2

The solar flux Fs (also called the solar constant) is the radiant energy from the sun that falls per second a 1 m2 surface oriented perpendicular to the sun’s rays, at the top of the earth's atmosphere.

1379 / 4 344

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.

The amount of energy striking the earth is given by the [shadow area (black circle) the solar flux] =πRe

2 Fs. (Re is the radius of the earth).

The total energy flux striking the surface of the earth is therefore Fs πRe2.

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

Eabs = FsπRe2(1 - A). INPUT

Energy INPUT to the earth from the sun

Energy OUTPUT from earth by thermal radiation

The total energy emitted per unit area is given by σT4, and the emitting area is the surface area of the earth, 4πRe

2.

The total energy emitted by the planet per second is therefore

Eemit = 4πRe2 σT4 . OUTPUT

Energy balance requires that input=output, when averaged over a long-enough period of time, i.e. on average Eemit = Eabs. Thus

4πRe2σT4 = FsπRe

2(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:

Teff = [Fs(1 - A)/(4σ)]¼ = 252.6 K.  

planet solar flux orbit radius albedo Te Tg Ground pressure

(W m-2) (1011 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)

Effective Temperatures of the Planets

After Goody and Walker, "Atmospheres"

2001

Earth's Albedo can change with time, affecting the energy budget and temperature of the planet.

To

p o

f Atm

osp

he

re F

lux

An

om

aly

W m

-2

Atmospheric absorption of infrared radiation

•The most abundant gases in the atmosphere, N2, O2,

and Ar, neither absorb nor emit terrestrial radiation. (They also neither absorb nor 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 H2O and CO2, and gases such as

methane (CH4) and chlorofluorocarbons are also

significant.

Greenhouse gases: Water, CO2, CH4

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.

O = C = O

O OC ==

+2δ

-δ-δ

CO2 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 back-radiation warms the earth's surface.

The Greenhouse Effect: influence of atmospheric absorption and emission of planetary (infrared) radiation

reflectedsolar (A)

incoming solar radiation (Fs)(visible, near infrared)

σTg4

terrestrial (far infrared)radiation from the surface

σTe4

σTe4

far infrared radiationfrom the atmosphere

z=H

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 2σT1

4, (OUT) because the layer radiates equally both up and down.

But the amount received by the layer is σTg4, (IN) (heated only from below!). If the layer

has a balanced energy budget, these two fluxes must be equal (IN = OUT),

σTg4 = 2σT1

4 . { T1 =>> Teff}

Thus the ground is warmer than the atmosphere by Tg = 21/4Teff. 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,

σTg4 = [n + 1] σT1

4

Tg = [n + 1]1/4Teff.

The atmosphere therefore gets colder as we go up due to the effects of absorption and emission of radiation (terrestrial infrared radiation).

SOLAR RADIATION SPECTRUM:blackbody at 5800 K

TERRESTRIAL RADIATION SPECTRUM FROM SPACE:composite of blackbody radiation spectra for different T

Scene overNiger valley,N Africa

cf. clouds, aerosols

Climate forcing due to changes in concentrations of greenhouse gases, atmospheric aerosols, and clouds, since 1850 (Hansen, 2001).

Class discussionWhat about engineering the climate:

•add aerosols to the atmosphere?•add iron to stimulate the ocean ?

•plant trees to take up CO2 and cool the surface?

ATMOSPHERIC CO2 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

property A increases →

property B changes →

causes property A to decrease

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.

+ positive feedback(amplification)

+ negative feedback(damping)

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.

+

FEEDBACKS INVOLVING ALBEDO (continued)

+

+

FEEDBACKS INVOLVING ABSORPTION OF IR (HEAT)Examine some of the most important feedbacks in the Earth’s atmosphere.

water vapor feedback.

Temperature increases → atmosphere H2O 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 H2O 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 H2O directly.

cloud feedback – solar radiation

Temperature increases → atmosphere H2O 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 CO2 ?

-

FEEDBACKS INVOLVING ALBEDO

-

Longwave radiation as viewed from the satellite sensor "ERBS" on

NOAA-9, April, 1985

Low OLR in the tropics is due to: 1. Obscuring the surface by clouds; 2. Cold T at cloud tops 3. Smoke from fires 4. Both 1 and 2 are correct.

No Data 100 150 200 250 300 350 Watts m-2

FUTURE TEMPERATURE PROJECTIONS FROM CLIMATE MODELS (IPCC, 2001)

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.

Aerosol Optical Depth after the eruption of Mt. Pinatubo

(SAGE-II Satellite data)

Mt. Pinatubo eruption

1991 1992 1993 1994

-0.6

-0

.4

-0.

2

0

+0

.2

Te

mp

era

ture

Ch

ang

e (

oC

)

Global Temperature

Climate Model

Effect of a major volcanic eruption on climate ( after Hansen et al., 1993). Note: many feedbacks have not come into play.

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.

http://www.atoptics.co.uk/atoptics/sunvolc.htm

AEROSOL OBSERVATIONS FROM SPACE

                                                                                                                     

    

Biomass fire haze in central America (4/30/03)

Fire locationsin red

Modis.gsfc.nasa.gov

BLACK CARBON EMISSIONSDIESEL

DOMESTICCOAL BURNING

BIOMASSBURNING

“…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)

EPA REGIONAL HAZE RULE: FEDERAL CLASS I AREAS TO RETURN TO “NATURAL” VISIBILITY LEVELS BY 2064

Acadia National Park

clean day moderately polluted day

http://www.hazecam.net/