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Mathematical model for predicting the magnitudes of total, diffuse, and direct-beam insolation

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  • Grindley, P. C.
  • Batty, W. J.
  • Probert, S. D.

Abstract

The simple mathematical model presented assumes that: 1. (i) the characteristic diurnal distribution of the fraction of the incident solar radiation available outside the atmosphere that is received on a horizontal surface under clear-sky conditions can be expressed as a curve of the form [tau]gmr=Ae-cp[alpha]mr in which A is a scaling coefficient, mr is the relative air mass, and c[rho][alpha] is an attenuation factor which depends on the angle of incidence;2. (ii) the diffuse fraction can reasonably be described approximately as [tau]dmr[approximate]1-(Bmr+[tau]gmr) in which B is the broad-band absorptivity. Measured values for the solar irradiance recorded at 1 min time intervals at a rural location near Cambridge, UK, were used to examine the relationship between the fraction of the solar radiation received on a horizontal surface and the diffuse fraction. The measurements corroborate the predictions from the mathematical model, whose validity is thus supported.

Suggested Citation

  • Grindley, P. C. & Batty, W. J. & Probert, S. D., 1995. "Mathematical model for predicting the magnitudes of total, diffuse, and direct-beam insolation," Applied Energy, Elsevier, vol. 52(2-3), pages 89-110.
    • Handle: RePEc:eee:appene:v:52:y:1995:i:2-3:p:89-110
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    Cited by:

    1. Gutiérrez-Trashorras, Antonio J. & Villicaña-Ortiz, Eunice & Álvarez-Álvarez, Eduardo & González-Caballín, Juan M. & Xiberta-Bernat, Jorge & Suarez-López, María J., 2018. "Attenuation processes of solar radiation. Application to the quantification of direct and diffuse solar irradiances on horizontal surfaces in Mexico by means of an overall atmospheric transmittance," Renewable and Sustainable Energy Reviews, Elsevier, vol. 81(P1), pages 93-106.
    2. Cao, J.C. & Cao, S.H., 2006. "Study of forecasting solar irradiance using neural networks with preprocessing sample data by wavelet analysis," Energy, Elsevier, vol. 31(15), pages 3435-3445.

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