The Hay transposition model

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The Hay transposition model

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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 circum-solar contribution proportional to Kb

    DiffInc  = DiffHor *  [  (1-Kb)  *  (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 (Liu-Jordan or Erbs) and represents the main uncertainty in the transposition result.