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Additional info for Short-Wave Solar Radiation in the Earth's Atmosphere: Calculation, Observation, Interpretation
Sample text
55) q = µ0 BI0 , where I0 = I(0, µ, µ0 , ϕ) = πδ(µ − µ0 )δ(ϕ) is the extraterrestrial radiance. 57) where T is the linear operator and the problem of calculating the radiance is reduced to the finding of the operator. 57). The following relation is used for that: 2π I= 1 dϕ0 0 T(µ0 , ϕ0 )I0 (µ0 , ϕ0 )dµ0 . 57) is widely used in the modern radiative transfer theory including the applied calculations. It is especially convenient for describing the reflection from the surface that will be considered in the following section.
The observations some of them we will consider in detail in Chap. 3 indicate that the cloud and snow are the closest to the orthotropic surface, the water is the most mirror surface and others are mainly backward reflected surfaces. However, the reference to the observation is excessive because of the mirror reflection of the banks from the water that everybody has seen and the backward reflection maximum is clearly observed from the airplane board. The orthotropic surfaces are especially convenient for the theoretical analysis and practical calculations because they are characterized with only one parameter – the albedo and because of the simplicity of the mathematical description.
It has been shown, that it is possible to neglect the sphericity of the atmosphere with a rather good accuracy if the angle of solar elevation is more than 10◦ . Then the refraction (the distortion) of the solar beams, which has been neglected during the deriving of the transfer equation is not essential. Mark that the horizontal homogeneity is not evident. This property is usually substantiated with the great extension of the horizontal heterogeneities compared with the vertical ones. However, this condition could be invalid for the atmospheric aerosols.