Modeling Solar Radiation at the Earth’s Surface

A Method for Determining the Solar Global and Defining the Diffuse and Beam Irradiation on a Clear Day

Amiran Ianetz and Avraham Kudish

1 Introduction

The terrestrial solar irradiation is a function of solar altitude, site altitude, albedo, atmospheric transparency and cloudiness. The atmospheric transparency is a func­tion of aerosol concentration, water vapor as well as other factors. The presence of aerosols in the atmosphere attenuates the beam component, whereas it increases the diffuse component of the solar global irradiation. In essence, the beam component is converted to diffuse irradiation. Consequently, it may have a relatively small ef­fect on the total solar global irradiation. Water vapor, on the other hand, attenuates both the beam and diffuse components and, thereby, decreases the total solar global irradiation.

The determination of the magnitude of the solar irradiation on a clear day is contingent on the criteria used to define a clear day. A priori a clear day is char­acterized by a perfectly cloudless sky assuming an average transparency state of the atmosphere (Sivkov 1971). The degree of cloudiness can be quantified by hu­man observation of cloud cover and/or sunshine duration measurements. It should be noted that (a) cloud cover observations are usually made only intermittently, i. e., varies between hourly or a number of times per day, and (b) there is an inherent uncertainty in utilizing sunshine duration measurements to define a clear day, viz., the existence of clouds in the sky that are not in the optical path between the sun­shine duration measuring device and the sun are not observed by the instrument. The atmospheric transparency can be quantified by determining either a turbidity coefficient or aerosol optical thickness (AOT). It is also reasonable to expect that a clear day will be associated with a measured maximum of the solar global irra­diation intensity, i. e., relative to some time interval, e. g., a month. Nevertheless, it

Amiran Ianetz

Ben-Gurion University of the Negev, Beer Sheva, Israel, e-mail: amirani@zahav. net. il Avraham Kudish

Ben-Gurion University of the Negev, Beer Sheva, Israel, e-mail: akudish@bgumail. bgu. ac. il is conceivable that such a relative maximum may be observed under special cloud cover conditions, viz., the existence of clouds in the vicinity of the sun, but not di­rectly blocking the sun, which create a funneling-effect on the solar irradiation. In practice, the criteria used to define a clear day at the particular site under considera­tion will be contingent on the database of measured parameters available. Databases consisting of measured solar global irradiation on a horizontal surface are available from most meteorological stations, whereas the existence of cloud cover and/or sun­shine duration measurements concurrent with solar global irradiation measurements is much less common. Atmospheric transparency measurement databases are also quite rare. Consequently, the following analysis to determine the solar global irra­diation on a clear day will be limited to the criterion based upon the most readily available database, viz., that consisting of solar global irradiation.