<< Click to Display Table of Contents >> The Hay transposition model 

The Hay transposition model applies differently to the different components of the irradiance.
The Beam component results of a pure geometrical transformation (no model  no intr4insic error):
BeamInc = BeamHor * sin Hsoli / sin Hsol
The Diffuse component is supposed to be mainly constituted of an isotropic distribution, and a circumsolar contribution proportional to Kb
DiffInc = DiffHor * [ (1Kb) * (1 + cos i) / 2 + Kb * sin HsolI / sin Hsol ]
The Albedo component is the irradiance reflected by the ground "seen" by the plane :
AlbInc = ρ * GlobHor * (1  cos i) / 2
where
i = Plane tilt
Hsol = Sun height on horizontal plane
Hsoli = Sun height on the plane (= 90°  incidence angle)
Kb = Clearness index of beam = BeamHor / (Io * Sin Hsol)
Io = Solar constant (depends on the day of year)
ρ = Albedo coefficient (usual value 0.2)
The expression (1 + cos i) / 2 is the mathematical result of the spherical integral of a constant irradiance, coming from all directions "seen" by the plane (i.e. the orange slice between the plane and the horizontal).
NB: All transposition models are highly dependent on the diffuse component. The higher diffuse, the lower transposed irradiance in monthly or annual values.
This is usually evaluated from another model (LiuJordan or Erbs) and represents the main uncertainty in the transposition result.