Angular Distribution of Sky Diffuse Radiance and Luminance
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Angular Distribution of Sky Diffuse Radiance and Luminance Jos´e Luis Torres and Luis Miguel Torres
1 Introduction As a rule, available global irradiance data in weather stations are referred to the horizontal plane. On the other hand, the different solar systems are generally placed on sloping surfaces. Therefore, it is necessary to establish procedures for calculating the existing irradiance on tilted planes in which direct, diffuse and ground reflected irradiances are evaluated in separated ways. The importance of the diffuse fraction of the global radiation is commonly underestimated. However, it must be pointed that in latitudes from 40 to 60◦ N, this fraction may become 40% to 60% of the yearly radiation received on a horizontal plane. Although this fraction can be lower on a sloping plane, it still supposes an important percentage that should be calculated in the most exact way, especially, in climates with frequent covered skies. Estimation of the diffuse component has been tackled in most cases by means of models that calculate the radiation on a tilted plane from radiation data on the horizontal plane. Existing models basically differ in the treatment each of them makes of the sky diffuse radiation. In fact, diffuse radiation is caused by a number of complex processes due to the interaction of solar radiation with the molecules and particles of the atmosphere, i.e., simple and multiple scattering and absorption phenomena, which may take place simultaneously or not at every wavelength, modify the intensity and the spectrum of the incident radiation in the high part of the atmosphere and redistribute the energy in different directions until it reaches the Earth surface. The physical bases of the aforementioned phenomena have been known for a long time since J.W. Strutt (later known as Lord Rayleigh) in 1871 set the physical laws that govern the light dispersion for very small particles and later in 1908, Mie proposed his theory for bigger spherical particles. All the described phenomena cause that the Jos´e Luis Torres Public University of Navarre, Pamplona, Spain, e-mail: [email protected] Luis Miguel Torres Public University of Navarre, Pamplona, Spain, e-mail: [email protected]
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diffuse radiation has an anisotropic nature, highly non-uniform, and that the energy received from the different areas of the sky vault may be different. The newest models for calculating radiation on the tilted plane from radiation on the horizontal plane provide approximations for this physical reality. Three areas of brightness more or less differentiated depending on the insolation conditions are considered. An alternative to this procedure consists of carrying out the calculation of the diffuse radiance on a sloping plane by integrating the sky radiance distribution coming from the part of the sky that is “seen” by the said plane. This alternative is particularly interesting for estimating the radiation on planes placed in urban environments or complex terrains. In these situati
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