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The Radiation Environment and the Greenhouse Effect

The sun's energy makes life possible.

An understanding of these effects requires an understanding of what is called the ‘radiation environment’.

The atmospheric ozone layer provides a filter removing harmful Ultra-Violet radiation that can kill living cells.

The CO2 and H2O in the atmosphere create a

natural greenhouse effect. This increases keeps the Earth’s surface by about 33K.

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The Sun’s spectrum

Hot dense objects emit electro-magnetic radiation with a continuous spectrum.

This approximates to a universal form called the ‘black-body’ spectrum which depends only on the object's temperature.

A black body is an idealised absorber that absorbs all the radiation falling upon it.

The sun has a ‘black-body’ spectrum.

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The Black Body Spectrum

The peak position, obtained from setting dI/d = 0, is giving by

which agrees with the long experimentally established Wien’s Law. By integration we obtain the Stefan-Boltzmann Law for the total intensity.

where σ = 5.667 10-8 W m-2 K-4 is Stefan’s constant.

Wm

1-kT

hchc2

= )I( 2-

5

2

exp

Wm

1-kT

hc

h2 = )I( 2-

2

3

exp

The emitted intensity is

c -speed of light. Alternatively

mT10 2.898 = -1-3max

Wm T = )dI( = I -24o

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Measured Solar Spectrum

The Suns' spectrum, measured in space, is reasonably close to that of a black body with a temperature of 5777K.

It is not a coincidence that this peak coincides with the visible spectrum: eyes sensitive to other parts of the electro-magnetic spectrum would be of little use.

The peak in the spectrum is close to 0.5μm, which is the blue/green boundary in the visible.

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The Solar constant

It is defined as the solar power per square meter incident on a surface normal to the Suns' rays at the Earth-Sun distance in the absence of an atmosphere.

The total intensity of the solar radiation at the distance of the earth is termed the Solar constant, S, or Solar irradiance.

The solar constant can be measured by satellite. The average measured value is 1,367 Wm-2.

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Measurements of The Solar Constant

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Calculating the Solar Constant

We can calculate S for a Black-Body Sun of temperature Ts as

follows. The total power emitted from the sun in Watts is

Wm T d

R = S 2-4s

S-E

s

2

Rs = 6.960 108m and dE-S = 1.496 1011m so for Ts = 5.777K we

obtain

To find the power per unit area at the Earth-Sun distance, dE-S, we

must then divide this by 4dE-S2, which is the area of the sphere

over which this energy is distributed. Thus

(power emitted per m2)(surface area of the sun) σTs44Rs

2  

where Rs is the Suns' radius.

S = 1, 367 Wm-2.

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Solar intensity at the Earth’s SurfaceThe area presented to the sun by the earth is RE

2, where RE is its

radius.

The total surface area of the Earth is 4RE2.

The Earth plus its' atmosphere has an average reflection coefficient (also called the Albedo). The current value is r = 0.30.

So the average Solar energy absorbed per unit area of the earth’s' surface is

Wm239 4

0.3)-S(1 2-

So the average solar energy per unit area of the earth’s surface in the absence of an atmosphere would be a quarter of the solar constant.

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Radiation BalanceThe equilibrium temperature without an atmosphere

The Earth and its' atmosphere absorb an average solar power of 239W per m2 of the Earth’s surface. At equilibrium the Earth’s surface and atmosphere must radiate the same power back into space.

Treating the Earth as a black body: σTE4 239 Wm-2

This gives an equilibrium temperature TE 255K or -18oC.

Without an atmosphere the surface temperature would have this value.

Measured average temperature at the earth's surface 288K or +15oC.

The Natural Greenhouse increases the surface by 33oC and makes life on Earth possible.

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Mars and Venus Mars: Atmospheric pressure 0.7% of that on Earth, 80% CO2.

Greenhouse effect raises surface temperature by 24K above the equilibrium value of 216K.

Venus: Atmospheric pressures 90 times that on Earth, 90% CO2. Greenhouse effect raises surface temperature from the equilibrium value of 227K to 750K.

Venus has suffered a runaway greenhouse effect. Was once much cooler with seas and oceans as Solar constant ~ 30% smaller in early Solar system.

Increasing Solar power increased the surface temperature and the evaporation of water. Water vapour in the atmosphere created a strong greenhouse effect. Eventually all water was removed from surface. Dissociation of water molecules by UV radiation then led to CO2 formation.

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Structure of atmosphere

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Atmosphere: pressure, temperature, composition.

About 80% of the mass of atmosphere is in the region of the atmosphere called the troposphere that extends up to about 11km from the earth’s surface.

100

90

10

20

30

40

50

60

70

80

Hei

ght (

km)

Mesopause

Stratopause

Tropopause

THERMOSPHERE

MESOSPHERE

STRATOSPHERE

200 250 300

TROPOSPHERE

TemperatureT (K)

Pressurep (mb)

3x10-4

4x10-2

8x10-1

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250

1000

Density (kgm-3)

5x10-7

6x10-5

1x10-3

2x10-2

4x10-1

1.2

Atmospheric composition by weight,

78% N2 , 21% O , 0.9% Ar, 0.035% CO2

Plus a very variable amount of water vapour.

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Interaction of Solar radiation

with atmosphere

Incoming solar radiation, has a peak intensity close to 0.5 m.

It interacts quite strongly with gas molecules, water droplet and dust in the atmosphere.

On average only 25% of the incoming solar energy reaches the Earth’s surface directly.

25% is absorbed by the atmosphere and about 25% reflected. About 5% is reflected from the surface.

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Absorption of terrestrial radiation

by atmosphereThe outgoing terrestrial radiation has an, approximately, black body spectrum, with a peak intensity close to 10μm.

Absorption by molecules such as CO2 and H2O is extremely strong at

such wavelengths.

About 95% of the energy radiated from the Earth’s surface is absorbed by the atmosphere.

This gives rise to the greenhouse effect in which energy is trapped in the atmosphere.

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Estimating the Magnitude of the Natural

Greenhouse Effect

An estimate of greenhouse warming can be obtained by considering the atmosphere as a slab of absorbing material.

Consider the earth plus atmosphere to have a reflection coefficient of 30% so about 240Wm-2 is initially absorbed by the earth's surface.

Let the atmosphere have zero absorption for solar radiation and 100% absorption for terrestrial radiation.

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120Wm-2 is radiated downwards and 120Wm-2 is radiated upwards and lost to space.

The additional energy 120Wm-2 will then be absorbed by the surface, and on re-emission the process continues.

The 240 Wm-2 absorbed by the surface is re-emitted as Infra-Red radiation.

Assume that this is totally absorbed by the atmosphere.

The atmosphere re-emits this energy in all directions.

Wm480 = )2/1240(1 = 2

240 ... + 60 + 120 + 240 =Power 2-1-

n0=n

The net result is that the total power downwards is given by the sum of the geometrical series,

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Result for the equilibrium temperature in the simplest model

In this model the surface receives twice the energy it would have without the atmosphere.

At equilibrium the surface must therefore radiate 480Wm-2.

σTs4 = 480Wm-2 for a black-body earth.

This gives a surface temperature is 303K.

c.f. measured value of 288K.

SURFACE

Total absorbed energy 480Wm-2

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Improving the simple model of greenhouse warming

A slightly better treatment (see notes) gives an equilibrium temperature of 285K.

c.f. measured value 288K.

This model is very crude as it does not include the atmospheres vertical structure, clouds etc.

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Absorption by molecules An electromagnetic wave, frequency and wavelength consists of photons of energy E =h =hc/ (c - speed of light)

 Wavelength Energy

U.V. <0.3μm >4eVEnergy > molecular binding energies. Can break bonds and cause ionisation

Visible 0.3-0.7μm ~2.5eV Energy ~ separation of electronic energy levels.

   Infra Red >1μm

Terrestrial spectrum peak

10μm 0.13eV

Energy ~ vibrational and rotational energies of molecules.

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Absorption UV by the ozone layer

The highest energy photons are absorbed in the upper atmosphere (mostly in the stratosphere).

Oxygen molecules (O2) have a binding energy of 5.1eV and are

strong absorbers for hv > 5.1 eV, i.e. λ < 0.24 μm

The free oxygen atoms produced react with other O2 molecules

to produce ozone O + O2 O3

O3 molecules have a binding energy of 4.3 eV and strongly

absorbs UV with λ < 0.29 μm.

O3 + hv O2 + O O3 + K.E.

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Absorption in the visible

Electrons in atoms occupy discrete energy levels.

Photons of the correct energy can promote an electron from a lower energy level to a higher level.

This produces weak absorption in narrow ranges of wavelength.

he-

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Absorption in the infra-red

Molecules can be modelled as masses (the atoms) connected by springs (the inter-atomic forces). The natural vibrational frequency is about 3 1013 Hz.

Light of frequency v0 can cause such a molecule to vibrate and absorbed energy for λ = c/v0 10 μm.

Complex molecules have more vibrational modes, and more polar molecules are stronger absorbers.

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Greenhousegases

The greenhouse effect is mainly due to CO2 and H2O but CH4, NO2 and CFCs also contribute. The relative importance of the same quantity of different gases released into the atmosphere is dependent on:

(a) The strength and number of absorption bands(b) The position of the bands relative to the terrestrial spectrum(c) The overlap of absorption bands with existing absorptions(d) The lifetime of the gas in the atmosphere.

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Atmospheric absorption

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Radiative forcingThe radiative forcing is the increase in the total downward flux of infra red, emitted by the atmosphere, due to the additional amount of gas to the atmosphere.

  CO2 CH4 CFCs N2O

Pre-industrial atmospheric concentration

280ppmv

0.8 ppmv

0 288ppbv

Current atmosphericconcentration (2001)

360ppmv

1.75ppmv

1ppb 308ppbv

Current annual rate ofatmospheric increase

0.5% 0.9% 2% 0.25%

Atmospheric lifetime (years)

50 - 200

10 65 - 2000

150

Radiative (Greenhouse) forcing (1765-2000 W m-2)

1.46 0.48 0.34 0.15

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Gases and radiative forcing

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Global warming potentialsThe relative contribution to global warming of a gas may be expressed as the Global Warming Potential (GWP)

ΔF additional radiative forcing due to adding of 1 kg of a gas to the atmosphere. c(t) is the fraction of the gas remaining in the atmosphere after time t. T is the integration period. ΔFCO2 and c(t)CO2 are the same quantities for CO2.

dt(t)C F

C(t)dt F = GWP

COCOTo

To

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Gas F GWP Half life (yrs)CO2 1 1 100

CH4 58 21 10N2O 206 290 150

CFC-11 3970 3500 65CFC-12 5750 7300 130

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The Enhanced Greenhouse Effect Equate the total energy incident m-2 of the Earth's surface to σT4 to obtain the surface temperature.

YEAR 1800 2000 2030 2100

ΔF(Wm-2) 0 2.5 5 10

Incident intensity (Wm-2) 397.5 400 402.5

407.5

TS (K) 288 288.451

288.9

289.8

ΔTS (K) - 0.45 0.90 1.8

ΔTS,WATER (K) - 0.73 1.44 2.9

ΔTS,IPCC (K) - 1.1 2.0 4.2

ΔF: change in radiative forcing. Ts: Equilibrium surface temperature.

ΔTs : increase in surface temperature. ΔTs,water includes effects of

increased water vapour levels. ΔTs,IPCC the prediction of the

Intergovernmental Panel on Climate Change (2001).

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Predictions of climate models, IPCC 2001

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Scattering by molecules

Consider light scattered by a particle in the atmosphere.

When the wavelength of the light, , is large compared with the diameter of the scattering particle, xo, the

scattered Intensity proportional to (x0/ )4. This is the Rayleigh scattering formula.

The molecules of the atmosphere, such as O2 and N2,

have sizes of order 510-10m which is very much smaller than the wavelengths of solar radiation ( ~5 x 10-7) so this equation is applicable.

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Blue Sky and red sunsetsScattered intensity proportional to (x0/ )4

The ratio of the scattered intensity of blue light ( ~ 0.4m) to red light ( ~ 0.7m) would therefore be ( 7/4 )4 which is about 10.

The sky usually looks blue because the scattered sunlight we are seeing when we ‘look at the sky’ is mostly from the blue end of the spectrum.

When we view a sunset we are seeing the light that has passed through a thick layer of atmosphere without scattering which is predominantly from the red end of the spectrum.

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Scattering by aerosols

Horizontal axis: particle radius over wavelength of light. Vertical axis: scattering cross section divided by the geometrical area /r2

In the atmosphere the important particles are water droplets, dust and H2SO4 crystals . Typical size is 0.110 microns ~ λ of visible light. 

Cross Sections: A particle of radius r0 >>l will simply block out an area πr0

2 ( geometrical area). For λ >> r0 the wave can 'flow around' the particle. In this case one has an effective 'cross-section' σ which is much smaller than πr0

2

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Once in a Blue Moon

If one had a high concentration of particles, all of a size just larger than 0.5μm, the red end of the spectrum would be scattered more strongly than the blue because σ α (xo/)n with n<0.

The last major occurrence of this type in Britain was in 1951 when smoke particles of a uniform size drifted over from huge forest fires in Canada.

The sky had a pinkish tinge by day and the Moon appeared blue.

Such events are very rare, hence the expression.

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Global CoolingAerosol particles injected into the atmosphere gradually precipitate out. Particles in the range 0.1μm to 1μm have half-lives of about one month in the upper troposphere and 1 year in the lower stratosphere. Smaller and larger particles have a significantly shorter half-life.

A typical long life particle, diameter 0.5μm, will scatter incoming solar radiation very strongly as the peak in the Solar spectrum is at λ ~0.5μm.

At the terrestrial radiation spectrum peak, 10μm, the scattered intensity will be reduced by a factor of order ( 10/0.5 )4 (Rayleigh Scattering).

Aerosols very effectively scatter incoming solar radiation but not outgoing terrestrial radiation: a reverse greenhouse effect.

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Volcanic Eruptions

Large Volcanic eruptions put huge amounts of material into the stratosphere. The aerosol level was about sixty times normal six months after the 1990 Pinatubo eruption.

Climate models predict that such eruptions should cause global temperature drops of ~0.5oC for a periods of about three years. Such short-term temperature dips are evident in the temperature records.

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Extreme cooling: Nuclear Winter

A Nuclear war could result in large amounts of dust and smoke in the stratosphere due to explosions and the resulting fires.

In 1984 Carl Sagan and co-workers predicted temperature drops of between 20o and 40o degrees lasting many months for a ‘plausible’ 5,000 megaton exchange. They coined the term ‘nuclear winter’ to describe this global disaster.

Better climate models now suggest a shorted period with a smaller temperature drop. The predictions depend crucially on the assumptions about the war.

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Death of the dinosaurs

This happened in less that 10,000 yrs, possible much quicker, but it is very difficult to measure shorter time periods.

One theory is that a very large asteroid hit the earth throwing a huge mass of material into the atmosphere. The mass extinction then resulted from the ensuing darkness and large temperature drop.

About 65 million years ago the Cretaceous period ended when about 70% of all species on earth became extinct. These included the dinosaurs leaving mammals to thrive.

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Theory supported by the presence of a rock layer, deposited around this time, rich in Iridium, which is 10,000 times more abundant in asteroids than in the earth’s crust.

The Iridium co-exists with fused and shocked quartz crystals consistent with such an impact.

Meteor impact?

Evidence is also emerging that suggests that other mass extinction may be related to meteor impact.

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Dinosaur extinction