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PHY2505 - Lecture 5

Interaction of solar radiation and the atmosphere

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Extinction Source (scattering)

Where and z defined upwards from surface

LAST TIME we looked at the variability of the solar constant S(,t) ~ Io (,t)cos (t)(t.

• Systematic variability due to orbit: cos (t)(t.

• Long term variability due to solar cycles.

• Short term variability on order of measurement time??

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deJeII

o

o

Interaction of the sun and atmosphere

RECALL

z

kdz

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• How constant is Io(t,)?

– From satellites we don’t know the absolute value of S(t,) better than ±4Wm-2 (~0.3%)

Short term variability of Io(t,)

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Variability of S(t,)– On top of this is a day to day variability

of order 0.1% – how significant is this? Will return to this when we look at remote sensing and retrieval.

– This variability is explained by magnetic disturbances: sunspots, flares, prominences. A successful theory predicting change in magnitude of S(,t) due to disturbances has not yet been developed. The figure shows a decrease of 0.1% in the solar constant apparently due to presence of a cluster of sunspots

– New satellite missions will provide new information on variability of Io(,t): SOHO mission provides first continuous observations from L1 point

Sunspot blocking:

Figure from Hoyt & Schatten (1997)

Short term variability of Io(t,) (cont.)

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This time: Solar absorption and scattering terms

ABSORPTION:RECALL: energy exchange in the UV/VIS region produced mainly by ionization (UV continuum) and electronic transition processes.Some transitions are also produced by coupling of vibrational modes with electronic transitions

To quantify atmospheric absorption we need:

– the composition of the atmosphere

– the distribution of atmospheric constituents

– the strength of their absorption coefficients in the solar region

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Atmospheric composition

+ aerosol and cloud

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Solar absorption bands

Absorption below 120nm considered to be insignificant as solar output so low in EUVStrongest absorptions:H2O overtonesO2 coupled vib-electronic transitionsO3 electronic transitions (see fig)

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Atmospheric structure

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Absorption with altitude

Plot shows height at which optical depth =1

Indicates no solar radiation reaches the surface at wavelengths lower than about 300nm

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Scattering

The absorption component of I(*) can be calculated using a good line-by-line model (later..)

In some regions of the solar spectrum the scattering interaction results in a reduction of incoming radiation as great as due to absorption…

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Scattering

Qualitatively,

If a plane wave meets a particle small compared to its wavelength we expect that

most of the wave energy is transmitted forward

with a small amount of energy lost in the form of a scattered wave centred on the particle

Represent scattered energy Is=IoCsca

Thus defining the scattering cross section, Csca. Can also define absorption cross section Cabs and extinction cross section Cext in the same way.

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),(

k

P

r

II o

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Consider the vector nature of the electric field:

Assume applied field, Eo, induces a dipole moment, po in a small homogeneous charged particle, radius r <<poEo where =polarizability

The applied electric field generates oscillations in the induced dipole which in turn produces plane polarised EM: the scattered wave.From electromagnetic theory:

where we can write

Substituting the expressions for P and Po into E we get the expression for scattered field in terms of incident field

Scattering: quantitative approach

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The scattering matrix comes about due to the phase between scattered and incident light.

Can express Eo as parallel Eol

and perpendicular Eor to scattering plane

In the atmosphere these components are

related by a random phase:

the incident solar radiation is unpolarised.

Relate the incident and scattered components by (see fig)

And rewrite in matrix form, where is the scattering angle:

Scattering: the scattering matrix

Scattering matrix – an important part of scattering problems

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RECALL: Intensity of radiation per solid angle (radiance) Io= |Eo|2

Can express the two components of the electric field in terms of radiances:

and the total scattered intensity of the unpolarised sunlight incident on a molecule in the direction as

For unpolarised light, Ior=Iol=Io/2, and using k=2/ we get Rayleigh’s scattering formula

Scattering: Rayleigh scattering formula

1/4 dependence

polarizability

distance,r

Scattering angle

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For vertically polarized light, Er, scattering is isotropic, independent of andfor horizontally polarised light, Eol, the scattered intensity depends on cos2

The angular dependence of the Rayleigh scattering patterns for Eor, Eol and Eo is shown:

For more complex problems we define the PHASE FUNCTION, P(cos ) to represent this angular distribution. This is a normalised non-dimensional parameter integrated over and

for Rayleigh this integral givesand

Scattering: Phase function

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Scattered flux, f, is found by integrating the scattered intensity over solid angle:

giving

We can define the cross section per molecule, , by f/Fo

Scattering: cross section

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Polarizability, Derived in Liou Appendix A

Where Ns= number of particles per unit volume

m= mr+imi is the refractive index of the particle – notoriously difficult to measure!

For air, the real part of the refractive index is approximated by

- basis of formulae quoted for Rayleigh scattering optical depth

Scattering: polarizability

Real part imaginary partAbsorption scattering