Modeling Solar Radiation at the Earth’s Surface

Solar Global Irradiation on a Clear Day

It is of interest to study the solar global irradiation on a clear day, which is a function of all the abovementioned parameters with the exception of degree of cloudiness, i. e., by definition there is a total absence of clouds. The analysis of the relative magnitudes of the measured solar global irradiation and the solar global irradiation on a clear day, as determined by a suitable model, provides a platform for studying the influence of cloudiness on solar global irradiation. Also, the magnitude of the solar global irradiation on clear day provides an estimate of the maximum solar energy available for conversion on a particular day.

1.1 Classification of Clear Days

There exist two, generally accepted, methods for classifying the day type as clear, partially cloudy or cloudy with regard to solar global irradiation. Barbaro et al. (1981) suggested that the classification of day type be based upon the degree of cloudiness. They defined day type as a function of degree of cloudiness, both in octas and tenths, as reported in Table 4.1.

Iqbal (1983) proposed utilizing the magnitude of the daily clearness index KT (the ratio of the solar global to the extraterrestrial solar irradiation) to define sky conditions, cf., Table 4.2.

Table 4.1 Classification of days according to cloud cover (Barbaro et al. 1981)

Day type






Partially cloudy






Table 4.2 Classification of days according to clearness index (Iqbal 1983)

Day type



0.7 < KT < 0.9

Partially cloudy

0.3 < KT < 0.7


0.0 < KT < 0.3

These two methods are essentially data filters that classify the day type on the basis of the magnitude of a related parameter. The authors have previously applied the latter definition to two sites in Israel, viz., Beer Sheva (Kudish and Ianetz 1996) and Jerusalem (Ianetz 2002). It is important to note that the monthly average daily solar global irradiation values on a clear day in the case of Beer Sheva reported in Kudish and Ianetz (1996) are very close to those reported in the present analysis despite the somewhat different KT criteria and different database, cf., section 2.3, Table 4.4. viz., the 1996 publication defined a clear day as that for which KT > 0.65 and the database consisted of the years 1982-1993, whereas the present analysis utilizes for most of the months a KT > 0.7 to define a clear day and the database consisted of the years 1991-2004. The close agreement between the two sets of clear day solar global irradiation values testifies to the stability of the Iqbal filters.

The advantage of the latter method lies in the fact that only solar global irradia­tion measurements are required, whereas the former method necessitates the avail­ability of a concurrent cloudiness observation database. In addition, as mentioned previously, the latter are usually made only intermittently, i. e., usually three times per day, whereas solar global irradiation data are monitored continuously and usu­ally reported on an hourly basis. The criterion based upon sunshine duration also has not been considered due to the limited availability of such data measured concur­rently with solar global irradiation and the abovementioned inherent error involved in such measurements.

It should be noted that two manuscripts treating the subject of clear sky so­lar global irradiation and its classification have been published recently. Lopez et al. (2007) presented a new model to estimate horizontal solar global irradiation under cloudless sky conditions, i. e., clear day, which requires the following input parameters: latitude, day of year, air temperature, relative humidity, Angstrom tur­bidity coefficient, ground albedo and site elevation along with solar elevation at sun­rise or sunset if the site has horizon obstructions. Younes and Muneer (2007) have proposed a clear day identification based upon the clearness index, diffuse ratio, turbidity and cloud cover limits. Once again, the method proposed in the following discussion has the distinct advantage that it requires a database consisting of a single parameter, viz., the solar global irradiation.

Modeling Solar Radiation at the Earth’s Surface

Quality Assessment Based Upon Comparison with Models

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Solar Horizontal Diffuse and Beam Irradiation on Clear Days

There exist a number of models to determine the solar horizontal diffuse irradia­tion on a clear day (Kondratyev 1969) but they are complex and have very stringent conditions. Similarly, there …


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