7. Aerosols and Climate

I. Scattering1. When radiation impinges on a medium of small particles,

scattering of some of the radiation occurs in all directions.The portion scattered backward is called the albedo.

2. Single scattering implies only a single interaction between particle and radiation. If the incident radiation is travelling in the direction with angle θ with the vertical,the fraction which reaches the surface without being scattered or absorbed is:

= exp ( )I I0

0τ-cos θ

θ

Where τ0 is called the (normal) optical thickness of the layer

= exp ( )I I0

0τ-cos θ

Single scattering is applicable when the layer is optically thin,for many purposes when τ0 < 0.1. But when θ=> π/2,cos θ => 0 and no layer is optically thin.

3. Multiple scattering occurs when there are more than one interaction between radiation and particles in a layer.

4. Rayleigh scattering: particles (like molecules) that are smallcompared to the wavelength of the radiation produce Rayleighscattering. The radiation induces an electric dipole in the particlewhich then reradiates. With Io the incident radiation, the scatteredradiation is proportional to the volume2, so it increases rapidlywith size, and proportional to λ-4:

a=particle radiusλ=wavelengthr=scattering distance

Is ∝ (1+cos2θ)Ioa6

λ4r2

In the visible, λ=4x10-5 cm (blue) and λ=8x10-5 cm (red). The scatteringis therefore 16 times larger for blue than red. The scattering distribution is the same in the forward and backward directions, so all points of the sky are essentially sources of predominantly blue scattered light. At twilight, the longer ray path through the atmosphere (r) causes most of the scattered blue radiation to be dispersed from the beam before itreaches the observer, so light then reflected from clouds or scattered to the observer from the haze layer appears reddish.

5. Mie Scattering: when the particle dimensions are large comparedwith λ, it is no longer sufficient to consider merely an induceddipole. The effect is to increase the amount of scattering inthe forward direction. This is partly due to diffractionof photons around the particles. The maximum efficiencyfor Mie scattering occurs when a~ λ. For a>> λ, the efficiencygoes to 2 – one part of photons passing through the particle,while the other for photons diffracted around it.

r= λ

ScatteringEfficiency

Qe

2

r

6. If the particle absorbs radiation, the forward scattering is not greatlyaffected as the absorption first becomes > 0 (diffraction part isuntouched), while the backward radiation is diminished. However,when absorption becomes very large, the particle will act more likea reflector, and backward scattering will be greatly increased.

7. Define a size parameter X=2πa/ λ. Rayleigh scattering gives reasonable accuracy when X<0.3. In a particle-free atmosphere,single scattering theory with Rayleigh scattering results in a smallerror in the visible, but appreciable errors in the UV.

II. Atmospheric scattering1. Atmospheric aerosols: a solid or liquid particle that is small enough to

be suspended in a gaseous medium (small settling velocity).

2. Most aerosols lie between 0.1-10 µm, varying approximately as r-4, where r is the particle radius. There are about 1011g of aerosolsin the atmosphere, with 1014 g/yr produced, resulting in a lifetimein the troposphere on the order of hours to days – removed by rain, and fallout of large particles due to their faster settling speed.

Stoke’s Law for terminal velocity equates the buoyant force/unit mass to the viscous force/unit mass:

)’ρ-ρg(ρ’ = 6πηwr

ρ’4/3πr3

Where η=viscosity coefficient; r=particle radius; w= vertical (fall) velocity.

So as r increases, the settling velocity increases. By 10µm,Particles are falling at a speed of 2km/day.

w= 29

gr2 (ρ- ρ’)η

3. Total extinction due to atmospheric scattering depends on the crosssectional area of the particles, the scattering efficiency, and the number distribution:

n(r) is numberdistributionTotal extinction ∝ π r2 Qe ( ) n(r)r

λ

The result is that the total extinction varies as the scatteringefficiency- dominance by size range near that of the wavelength, because the more numerous small particles have much lower efficiency, and smaller cross-sectional areas.

4. As infrared radiation from the earth peaks near 10 µm, it is larger than most of the dry aerosols, so they act like Rayleigh scatterers with small effect. The effect on short wave radiation is somewhat greater,although even here more than 95% is scattered forward.

5. Aerosols are thought to be poor absorbers, a few % in the infrared, even less in the visible, but these values depend on the exact aerosolcomposition. For example, black soot particles from biomass burningcan be strong absorbers in the visible.

Global Aerosol distribution

Green - carbonaceous particles (biomass burning)Red – desert dust particlesBlue – sulfate aerosols (industrial air pollution)

FirstIndirect Effect

Ship Tracks

Second Indirect effect Rainfall production

III. Volcanoes and scattering

1. General levels for volcanic aerosol injection: 7-15 km (troposphere,short lifetime because soon washed out); 20-27km (stratosphere, longlasting); 40-50km (only a small amount ever gets this high.

El Chichon1982

Pinatubo1991

2. The residence time in the stratosphere is less than one year for 2-5µmparticles, 0.5-12 years for particles of 0.5-1 µ m.

El Chichon

3. For perhaps 6 months after a volcanic eruption, the stratosphere isdominated by silicate particles, 0.1-1 µm – basaltic glass, obsidian,Al2O3. These are good scatterers up to 10 µm (and thus 10x betterthan the normal scattering efficiency in the infrared), with 75% ofthe scattering being forward. They are also better absorbers in the visible. After large eruptions, the scattering optical thickness can be τ>0.1 (about 20x larger than normal in the visible).

4. After 6 months, increased sulfate production, presumably due to SO2emissions increases scattering in the visible, and slightly increasesabsorption in the infrared.

5. To assess the impact of volcanoes on the climate, it is necessary to know the ratio of absorption/backscatter for both short and long waveradiation, relative to the normal situation.

6. It is also necessary to compare these values to the surface albedo. Ifthe surface albedo is very high (snow), warming can occur ifabsorption approximately equals backscatter, because that which isnow being absorbed was previously lost to space. With a low surfacealbedo (oceans) most of the incident radiation was being absorbedanyway. So in this case the absorption needs to be greater than the backscatter to produce a net heating.

Stratospheric Temp change

So/4[1-A] = τσT4

GeoEngineering

Homework:

Rosenfeld et al., 2008: Flood or Drought: How do aerosolsaffect precipitation? SCIENCE, 321, 1309-1313.