This empirical model for diffuse sky irradiance was developed at Sandia National Laboratories by David King and has been found to work quite well at the Sandia facility (better, in fact, than any of the other models that have been compared). The model determines the diffuse irradiance from the sky ($$E_{d}$$) tilted surface using the surface tilt angle ($$\theta_T$$), diffuse horizontal irradiance ($$DHI$$), global horizontal irradiance ($$GHI$$), and sun zenith angle ($$\theta_Z$$) as:
$$E_{d} = DHI\times \frac{1+\cos \left( \theta_{T} \right)}{2}+GHI \times \frac{\left( 0.012 \theta_{Z}-0.04 \right)\times \left(1-\cos \left (\theta_{T}\right)\right)}{2}$$.
Note that the first term is simply the isotropic sky diffuse model. The second term is an empirical correction term to account for the circumsolar and horizon brightening effects. All angles are in degrees.
Reference:
Lave, M., et al. (2015). “Evaluation of Global Horizontal Irradiance to Plane-of-Array Irradiance Models at Locations Across the United States.” IEEE Journal of Photovoltaics 5(2): 597-606.