1 PHY Lecture 5 Interaction of solar radiation and the atmosphere

2 Extinction Source (scattering) Where and z defined upwards from surface LAST TIME we looked at the variability of the solar constant S(,t) ~ I o (,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?? Interaction of the sun and atmosphere RECALL

3 How constant is I o (t, )? –From satellites we don’t know the absolute value of S( t, ) better than ± 4Wm -2 (~0.3%) Short term variability of I o (t, )

4 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 I o (,t): SOHO mission provides first continuous observations from L1 point Sunspot blocking: Figure from Hoyt & Schatten (1997) Short term variability of I o (t, ) (cont.)

5 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

6 Atmospheric composition + aerosol and cloud

7 Solar absorption bands Absorption below 120nm considered to be insignificant as solar output so low in EUV Strongest absorptions: H2O overtones O2 coupled vib-electronic transitions O3 electronic transitions (see fig)

8 Atmospheric structure

9 Absorption with altitude Plot shows height at which optical depth =1 Indicates no solar radiation reaches the surface at wavelengths lower than about 300nm

10 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…

11 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 I s =I o C sca Thus defining the scattering cross section, C sca. Can also define absorption cross section C abs and extinction cross section C ext in the same way.

12 Consider the vector nature of the electric field: Assume applied field, E o, induces a dipole moment, p o in a small homogeneous charged particle, radius r <<   p o  E o 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 P o into E we get the expression for scattered field in terms of incident field Scattering: quantitative approach

13 The scattering matrix comes about due to the phase between scattered and incident light. Can express Eo as parallel E ol and perpendicular E or 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

14 RECALL: Intensity of radiation per solid angle (radiance) I o = |E o | 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, I or =I ol =I o /2, and using k=2  / we get Rayleigh’s scattering formula Scattering: Rayleigh scattering formula 1/ 4 dependence polarizability distance,r Scattering angle

15 For vertically polarized light, E r, scattering is isotropic, independent of  and  for horizontally polarised light, Eol, the scattered intensity depends on cos  2 The angular dependence of the Rayleigh scattering patterns for E or, E ol and E o 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 gives  and Scattering: Phase function

16 Scattered flux, f, is found by integrating the scattered intensity over solid angle: giving We can define the cross section per molecule, , by f/F o Scattering: cross section   

17 Polarizability,  Derived in Liou Appendix A Where Ns= number of particles per unit volume m= m r +im i 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 partimaginary part Absorption scattering