Irradiance on a tilted surface that is reflected off the ground, , is calculated as a function of the irradiance on the ground, usually assumed to be , the reflectivity of the ground surface, known as albedo, and the tilt angle of the surface,  : The model for ground reflected irradiance develops from the following assumptions:

1. The array is infinitely long.
2. Irradiance on the ground is uniform and equal to , i.e., horizon blocking and near-field shading by the array is ignored.
3. Irradiance reflects from the ground equally in all directions, i.e., the ground is a diffuse or Lambertian reflector.
4. The ground is visible to the array from the point of intersection of the array’s slope projected to the ground, to the infinite horizon.

With these assumptions the model for  can be derived using a view or configuration factor. The view factor quantifies the fraction of diffuse reflected irradiance from one surface  that impinges on a second surface . In the equation above for , the term  is the view factor from surface , the ground, to surface , the module.

To derive this model, consider an infinite strip  on the ground of differential width   that is parallel to the array. Denote the array’s face as , and the view factor from  to   as . The irradiance per unit length (W / m) reflecting from the strip  is .  The contribution to irradiance per unit length (W / m) on  from reflected irradiance from  is

Let  be a coordinate axis on the ground with origin under the lower, forward edge of the array, parallel to the rear-facing normal vector to the array, with negative direction toward the horizon behind the array. Consider  to be the half-plane on the ground defined by ,  and   to be the rear-facing side of an infinitely long strip of width  above the half plane with edges parallel to the ground. The total irradiance on  per unit area (W/m2) from irradiance reflected from  is The view factor  is given by the formula

Rewriting the terms in the equation for   as

Substituting and evaluating the integral  obtains

When the full half plane is visible to the rear facing side of the array,  which reduces the above expression to

When  is taken to be the front-facing surface and  is the half-plane , the view factor  is calculated in a similar manner to obtain

Content contributed by Sandia National Laboratories