## The monthly average solar radiation on inclined surfaces

Starting from the experimental values obtained on horizontal surfaces, Liu and Jordan have introduced a widely used method to calculate the monthly average solar radiation on inclined surfaces. This method is based on the division of radiation between its direct and diffuse components. Liu and Jordan discovered that the ratio between the monthly average diffuse radiation D and the global radiation H received on a horizontal surface can be correlated to a parameter called monthly clearness index K. This index is obtained by dividing the monthly average terrestrial radiation for every day by the monthly average extraterrestrial radiation for every day both received on a horizontal plane.

K=H/Hm (39)

To compute Hex the solar constant value used is 1394 W/m2 (instead of the more recent value of 1367 W/m2). For this reason, K values should be based on that value. As for the calculation of Hex, it has been suggested that eqn (38) be applied to a specific day of each month. That day must be chosen to get an extraterrestrial radiation Hex on a horizontal surface, which is equal to the monthly average extraterrestrial radiation Hex.

If B (= H — D) is the monthly average direct component received on a horizontal surface for each day and E is the monthly average global radiation on an arbitrary oriented surface, we have:

E=RbB+RiD+Rr(B+D) (41)

where ha’ is the hour angle calculated using eqn (22); ha and ha are expressed in radians and Rb is the monthly average factor of inclination by direct radiation [1].