Upscatter fraction

The influence of aerosols on radiative forcing depends on the balance between three essential quantities single-scattering albedo, upscatter fraction, and optical depth—all are sensitive functions of the aerosol chemical composition and size distribution in the 0.1 to 1.0 pm range [1,14]. Aerosol climate forcing, AF, depends on geophysical and aerosol parameters and can be expressed as... 

Angstrom exponent scattering efficiency of substance X (m g ) upscatter fraction axial angle (rad) solar zenith angle (rad) wavelength (nm)... 

Upscatter fraction pm Dimensionless Fraction of light scattered in upward direction. Property of aerosol in atmosphere evaluated by... 

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. 

Fq = incident solar flux, W m-2 Ac = fraction of the surface covered by clouds Ta = fractional transmittance of the atmosphere Rs = albedo of the underlying Earth surface tt) = single-scattering albedo of the aerosol (3 = upscatter fraction of the aerosol x = aerosol optical depth... 

The single-scattering albedo to depends on the aerosol size distribution and chemical composition and is wavelength-dependent. The upscatter fraction (3 depends on aerosol size and composition, as well as on the solar zenith angle 0o- Aerosol optical depth depends largely on the mass concentration of aerosol. 

This equation was first derived by Haywood and Shine (1995). We will now consider explicitly how upscatter fraction and optical depth may be calculated. 

Radiative transfer theory to calculate the upscatter fraction p as a function of particle size and solar zenith angle 0o was developed by Wiscombe and Grams (1976). Figure 24.5 gives p as a function of p0 = cos 0q and particle radius. For Sun at the horizon... 

FIGURE 24.4 Schematic of the relationship between upscatter fraction and hemispheric backscatter ratio as a function of solar zenith angle for two particle sizes. 

FIGURE 24.6 Diurnal (24-h) average upscatter fraction for (NH4)2S04 particles averaged over the solar spectrum, for three seasons and several latitudes (°N) as a function of particle radius (Nemesure et al. 1995). Here winter = December 21, spring = March 21, and summer = June 21. The bottom panel represents the global annual average p. 

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