Modeling Solar Radiation at the Earth’s Surface

Models for Determining the Global Irradiation on Clear Day

The clear day solar global irradiation intensity at a particular site is also an inherent function of the day for which it is determined, since the extraterrestrial irradiation varies from day to day. The latter parameter sets an upper, although unattainable, limit on the magnitude of the solar global irradiation.

A number of models, essentially empirical correlations, have been developed and reported in the literature that calculate the clear sky solar global irradiation, Gc, based exclusively on site location and astronomical parameters, i. e., the solar zenith angle 0z. A priori, it is to be expected that such simple empirical correla­tions will be best suited to sites having similar meteorological parameters. A list­ing of some of these previously reported empirical clear sky regression equations, where the clear sky global solar irradiation is given in units of W/m2, includes the following:

Haurwitz (1945, 1946)

Gc = 1098[cos0z exp(—0.057/cos0z)j, (4.1)

Daneshyar-Paltridge-Proctor (Daneshyar (1978); Paltridge and Proctor (1976); Gueymard (2007))

Gc = 950.0{1 — exp—0.075(90° — 0z)]} + 2.534 + 3.475(90° — 0z), (4.2)

Berger-Duffie (1979)

Gc = 1350[0.70cos0z ], (4.3)

Adnot-Bourges-Campana-Gicquel (1979)

Gc = 951.39cosL15(0z), (4.4)

Kasten-Czeplak (1980)

Gc = 910cos0z — 30, (4.5)

Robledo-Soler (2000)

Gc = 1159.24(cos0z)1179exp[—0.0019(n/2 — 0z)]. (4.6)

Badescu (1997) tested these empirical clear sky regression equations, viz., Eqs. (4.1-4.5), for the climate and latitude of Romania. He found that Eq. (4.4), based upon measurements made in Western Europe, best modeled clear sky global irradiation in Romania.

Lingamgunta and Veziroglu (2004) have proposed a universal relationship for estimating daily clear sky irradiation using a dimensionless daily clear sky global irradiation, Hdclv, as a function of the day of year, n, latitude, ф, a dimensionless altitude, A (which is local altitude divided by 452 m - height of Petronas Towers) and hemisphere indicator, i (which is i = 1 for northern hemisphere and i = 2 for southern hemisphere). They defined the dimensionless daily clear sky global irradiation as Hdclv = Hdc/(24 • 3600 • Gsc), where Hdc is the clear sky global irradiation (Wh/m2) at the site and Gsc is the solar constant, 1367W/m2. Their universal relationship is given as

Hdclv ={[0.123 + 0.016( — 1)і](Ф/90) 15 + (0.305 + 0.051[(90/ф)2 - і]1'5) (4.7) cos ф — 0.1(1 + A)—01}{1 + [0.975 + 0.075( —1)і] sin((72/73)(n — 81)) йи(3ф/4).

It should be noted that the solar zenith angle is not a parameter in Eq. (4.7), as opposed to the other models under discussion.