Energy flux, solar radiation

Both these effects require knowledge of the spectral and spacial radiation distributions of the radiation flux on a surface. The determination of both these distributions at a given location is a difficult instrumentation problem. In this paper, the effect of scattering processes in the atmosphere on the available energy of solar radiation on a surface is examined. Both the spectral and spacial effects of Rayleigh scattering are demonstrated. 

To examine the available energy of solar radiation, let us briefly examine the thermodynamic results for blackbody radiation within an insulated cavity. There is no net flux of... 

The sun radiates approximately as a blackbody, with an effective temperature of about 6000 K. The total solar flux is 3.9 x 10 W. Using Wien s law, it has been found that the frequency of maximum solar radiation intensity is 6.3 x 10 s (X = 0.48 /rm), which is in the visible part of the spectrum 99% of solar radiation occurs between the frequencies of 7.5 X 10 s (X = 4/um) and 2 x 10 s (X = 0.15/um) and about 50% in the visible region between 4.3 x 10 s (X = 0.7 /rm) and 7.5 X 10 s (X = 0.4 /Ltm). The intensity of this energy flux at the distance of the earth is about 1400 W m on an area normal to a beam of solar radiation. This value is called the solar constant. Due to the eccentricity of the earth s orbit as it revolves around the sun once a year, the earth is closer to the sun in January (perihelion) than in July (aphelion). This results in about a 7% difference in radiant flux at the outer limits of the atmosphere between these two times. 

Fig. 17-1 The global climate system, (a) Energy fluxes, including incoming solar radiation, reflected radiation, emitted longwave radiation (from an effective altitude of ca. 6 km), and atmospheric and oceanic heat flux toward the polar regions, (b) The atmospheric circulation corresponding to part (a). Refer back to Fig. 7-4 and associated text for a discussion of the general circulation.

Solar radiation consists of photons of different energies E. Of particular interest is the spectral distribution n(E), which describes how the photons are distributed over the different energy values. The quantity n(E) indicates the number of photons of specific energy E per unit surface area per unit energy per unit time. From this distribution we define the total photon flux as... 

The properties of solar radiation have been established from measurements from a satellite, thus eliminating all influences from the earth s atmosphere. From the measured Planck s spectrum and by fitting Equation 17.3, it can be concluded that the sun is a black body [5], that its emissivity e = 1, and that its temperature is Ts = 5762 K. The sun emits a photon energy flux s, arid... 

Press ( 3) makes a similar approximation, comparing the closed system available energy of a volume of radiation in a cone compared to that in a full spherical space. His results translated into flux terms indicate that approximately 38% of the available energy flux in a solar solid angle is retained if the energy is uniformly scattered over a full 4vsolid angle. 

The principal result being that the available energy to energy flux ratio for uniform solar radiation is from 0.5 to 0.7. 

Figure 5. Available energy to energy flux ratio for solar radiation if scattered uniformly over the sky. Reproduced with permission from Ref.O) Copyright 1980, Pergamon Press Inc.

In the calculations of the available energy flux reported In this paper for Rayleigh scattered solar radiation, the following assumptions and procedures have been utilized. 

Table I. Available Energy to Energy Flux Ratio for Rayleigh Scattered Solar Radiation as a Function of Wavelength...

The computational procedure for the calculation of energy flux per unit frequency per unit solid angle eV(0 due to Rayleigh scattered solar radiation is outlined in this section. 

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