This model calculates the diffuse solar radiation on a tilted surface after the isotropic sky model of Liu-Jordan and the total incident radation on a tilted surface.
IrrTotTil = IrrDirTil + 0.5 * (1.0 + cosAngleTil) * IrrDifHor + 0.5 * (1.0 - cosAngleTil) * rhoAmb * IrrTotHor
where IrrDirTil stands for the total direct radiation on the tilted surface.
cosAngleTil is the cosinus of the tilt angle, the angle formated by the tilted surface and
the horizontal ground. IrrDifHor is the total diffuse radiation on a horizontal surface,
IrrTotHor is the total radiation on the horizonal surface and rhoAmb
is the reflexion factor of the surroundings.
Nikolai. V. Khartchenko. Thermische Solaranlagen Grundlagen, Planung und Auslegung, Springer ISBN 3-540-58300-9