Optical depth

Here B is the world average burden of anthropogenic sulfate aerosol in a column of air, in grams per square meter. The optical depth is then used in the Beer Law (which describes the transmission of light through the entire vertical column of the atmosphere). The law yields I/Iq = where I is the intensity of transmitted radiation, Iq is the incident intensity outside the atmosphere and e is the base of natural logarithms. In the simplest case, where the optical depth is much less than 1, (5 is the fraction of light lost from the solar beam because of... 

The error of this approximation is less than 0.01% for relevant global mean temperatures (see the Appendix). The thickness of the atmospheric layers, which is increasing with the altitude, is correlated to the optical depth of the... 

The bulk of stellar radiation comes from the surface layers or atmosphere of a star, more particularly the photosphere , which is defined as the region having optical depths for continuum radiation between about 0.01 and a few. The optical depth ti is measured inwards from the surface and represents the number of mean free paths of radiation travelling vertically outwards before it escapes from the star. It is related to the geometrical height z above some arbitrary layer by... 

At moderate optical depths, only the Gaussian part of the profile is significant ... 

A form of the curve of growth more relevant to stellar (as opposed to interstellar) absorption lines is derived from work by E. A. Milne, A. S. Eddington, M. Min-naert, D. H. Menzel and A. Unsold. In the Milne-Eddington model of a stellar photosphere, the continuum source function (equated to the Planck function in the LTE approximation) increases linearly with continuum optical depth rA and there is a selective absorption i]K, in the line, where rj(Av), the ratio of selective to continuous absorption, is a constant independent of depth given by... 

With 0 the quantum yield, e the molar absorption coefficient, d the optical depth, and k a constant account for the fact that only a small fraction of emission can be observed. 

Light Scattering Technique. Properties of the light scattered by a large number of droplets can be used to determine droplet size distribution. Dobbins et al. 694 first derived the theoretical formulation of scattering properties of particles of arbitrary sizes and refractive indices in polydispersions of finite optical depth. Based on... 

TABLE 3.14 Calculated Enhancements or Depressions of Actinic Fluxes above and below Perfectly Light-Diffusing Clouds of Different Optical Depths"... 

Conditions Cloud optical depth Above cloud Below cloud... 

The cloudless case shown first for a small solar zenith angle and typical summertime conditions shows an enhancement due to reflections from the surface. The cloud with an optical depth of 8 corresponds to a total of 67% transmission of the light through the cloud, but essentially all of it is diffused by the cloud and is therefore not directly transmitted light. The cloud with an optical depth of 128 only transmits a total of 9% of the light, essentially all of which is again diffuse. 

Hegg, D. A., J. Livingston, P. V. Hobbs, T. Novakov, and P. Russell, Chemical Apportionment of Aerosol Column Optical Depth Off the Mid-Atlantic Coast of the United States, J. Geophys. Res., 102, 25293-25303 (1997). 

FIGURE 12.27 Zonally averaged optical depth at 19.5°N and derived from the satellite-based Advanced Very High Resolution Radiometer (AVHRR) (adapted from Russell et al., 1996). 

Stamnes, K., J. Slusser, and M. Bowen, Biologically Effective Ultraviolet Radiation, Total Ozone Abundance, and Cloud Optical Depth at McMurdo Station, Antarctica, September 15, 1988 through April 15, 1989, Geophys. Res. Lett., 17, 2181-2184 (1990). 

FIGURE 14-32 Typical contributions of aerosol liquid water, carbonaceous compounds, and sulfate in the lower troposphere of the east coast of the United States to the total aerosol optical depth. The contribution of light absorption is also shown. The different bars represent different sets of measurements during different flights (adapted from Hegg et al., 1997). 

Jayaraman et al. (1998) measured the aerosol optical depth, aerosol size distribution, and the solar flux close to the coast of India, over the Arabian Sea, and then... 

The seasonal cycle of CCN has also been shown to be correlated with that of cloud optical depth in one remote marine area (Boers et al., 1994), and the isotope composition of non-sea salt sulfate over remote regions of the southern Pacific Ocean has been shown to be consistent with a DMS source (Calhoun et al., 1991). 

Boers, R., G. P. Ayers, and J. L. Gras, Coherence between Seasonal Variation in Satellite-Derived Cloud Optical Depth and Boundary Layer CCN Concentrations at a Mid-Latitude Southern Hemisphere Station, Tellus, 46B, 123-131 (1994). 

Loeb, N. G., and R. Davies, Observational Evidence of Plane Parallel Model Biases Apparent Dependence of Cloud Optical Depth on Solar Zenith Angle, J. Geophys. Res., 101, 1621-1634 (1996). 

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