Single scattering, albedo for

FIGURE 24.3 Single-scattering albedo for (NH4)2S04 particles as a function of wavelength (RH = 50%). 

FIGURE 24.11 Single-scattering albedo for internal versus external mixture of soot and (NH4)2S04. 

Determination of single-scattering albedos for this problem is very sensitive to measurement errors. Even for d = 0, with no errors at all, (consequently, the measurements were made to machine accuracy) we could not obtain good results even for small r. However, in Fig. (1) we see that the accuracy was much better when A 1 and the measurements were made deep inside the atmosphere. For example, if (5 = 0.05 we could obtain A to an accuracy of 0.001 for A = 1 and r = 5.0. 

Because the single-scattering albedo depends sensitively on the imaginary part of the refractive index there has been keen interest in determining optical constants of atmospheric particles. These are used to calculate the important parameters in the heat balance problem for present and predicted aerosol... 

We now use several approximations discussed in previous chapters to estimate for the two model aerosols their single-scattering albedo 0, where... 

Figure 6. From figure 11 of Kylling et al. 1998. The ratio between simulated Brewer and Bentham UVB dose rates with and without aerosols as a function of the aerosol optical depth at 355 nm. Ratios of model results with aerosol single scattering albedo of (0.95 solid line), 0.87(dotted line) and 0.80 (dashed line) versus aersosol free model results are shown for solar zenith angle of 10° and an ozone column of 340 DU.

The correlation between photolysis rates and optical depths is obvious for the JN02 case in the UV-A region, it is not clear for JO( D). The model sensitivity study supports the expectation that aerosol optical depth and single scattering albedo are the two decisive parameters to describe the radiative effects of aerosols. 

Total effect not equal to sum of individual effects due to interactions. Cloud cover changes unknown. Effects shown for either an increase or a decrease. Specifically aerosols with high single scattering albedos (e.g., sulfates) which refiect UV radiation back to space. Specifically aerosols with low single scattering albedos (e.g., black carbon) which absorb UV radiation. Madronich and Granier (1992) and Krol et al. (1998). 

Consider a direct solar beam impinging on the layer shown in Figure 24.1. Assume, for the moment, that the beam is directly overhead, at a solar zenith angle of 0o = 0°. The fraction of the incident beam transmitted through the layer is e x, where x is the optical depth of the layer. The fraction reflected back in the direction on the beam is r = (1 — < T)a>P, where to is the single-scattering albedo of the aerosol, and p is the upscatter fraction, the fraction of light that is scattered by a particle into the upward hemisphere. 

This means that if we measure the specific intensities at optical depths T > 0 and T = 0 (preferably doing this at Legendre-Gauss nodes for better integrations) we find the single-scattering albedo. 

Our calculations have shown that the single-scattering albedo can be obtained from Eq. (36) even if the error amplitude is d 0.25—0.3. The results for A in Fig. (3) with /tq = 0.5 are very nearly the same as for /tq = 01 reported earlier [24]. After having found A from Eq. (36) we use it in Eq. (37) first to determine the number of possible values of the depolarization factor c. If there are two or three roots we have to use each c-value in our model to determine which minimizes the quadratic form... 

As shown, the quadratic integrals Q and R of Rybicki for unpolarized radiation and the quadratic integrals Sq and of Siewert and McCormick for polarized radiation are closely related. These integrals of radiative transfer provide us with a convenient tool for solving some elementary inverse problems. Numerical experiments have shown that for these problems the single-scattering albedo can be derived with great accuracy even when the measurements are not so accurate. The determination of other characteristics of the medium is much more complicated. 

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