Anisotropic sky radiance model based on narrow field of view measurements of shortwave radiance

Abstract A model for the average anisotropic sky radiance (or intensity) as a function of the position of the sun, the diffuse fraction k , and the atmospheric clearness index k 1 are presented in this article. The complete range of sky conditions from clear to turbid to overcast is covered. Analysis of the observed data indicates that the model can be used to estimate instantaneous sky radiance values with a mean bias error of −11% and a root mean square error of 65% of the mean. The model is shown to account for 83% of the deterministic part of the variance of the instantaneous sky radiance measurements. The formulation for the sky radiance L ( θ , F ) in the direction (θ, F) is L(θφ)=G d a 0 +a 1 cos θ+a 2 exp (−a 3 ·Ψ) π(a 0 + 2a 1 3 +2a 2 I(θ s ,a 3 ) where Ψ is the scattering angle from the solar beam, a 0 , a 1 , a 2 , a 3 are tabulated functions of k and k 1 , and I ( θ s , a 3 ) is a specific function of a 3 and the solar zenith angle θ s .

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