Modeling Solar Radiation at the Earth’s Surface

Analysis of Solar Irradiation Distribution Types

The analysis of the frequency distribution and distribution type of a particular solar irradiation database are very important parameters in the design of solar irradia­tion conversion systems. The conversion system size and type (non-concentrating/ concentrating) are functions of the magnitude and distribution of the solar irradiation (global/beam). The ability to perform a meaningful economic feasibility analysis of such systems is contingent on the availability of such information.

3.2 Distribution Types

The values for the skewness (As) and kurtosis (K) can be utilized to define the fre­quency distribution type for a particular database, viz., to describe the breadth of the distribution curve, its degree of asymmetry and its shape relative to that for a normal distribution curve. This following discussion is based upon generally ac­cepted rules of statistical analysis, cf., Brooks and Carruthers 1953. The frequency distribution types as a function of the skewness and kurtosis values are defined in Table 4.8.

The preferred types of distribution, viz., most suitable for solar energy conversion systems, in descending order are as follows: V > IV > I > VI > II and III. The reasoning behind this order of preference of the distribution types is as follows.

• Statistically, a type V distribution frequency has a higher occurrence of values greater than the average value, 35-40%, relative to a normal distribution (type I);

• A type IV also has a higher occurrence of values greater than the average value, 25%, relative to a normal distribution (type I).

• Consequently, if types V and IV possess the same average value as a normal distribution, they will both afford a greater number of days with values in excess of the average value relative to that afforded by a normal distribution. Type V is

Table 4.8 Definition of frequency distribution types as a function of the range of the kurtosis and skewness values

Distribution Type No.

Distribution Curve

Skewness (As)

Kurtosis (K)



-0.4 < As < 0.4

-0.8 < K < 0.8


almost normal with positive tail

As > 0.4

-0.8 < K < 0.8


narrow peak with positive tail

As > 0.4


О CO 1 О



almost normal with negative tail

As < -0.4

-0.8 < K< 0.8


narrow peak with negative tail

As < -0.4

K > 0.8


bimodal, symmetrical with flat peak

-0.4 < As < 0.4

K <-0.8

preferred because it has a higher occurrence of values greater than the average value;

• Types II and III are both characterized by a relatively low average value and are, therefore, much less preferred for solar conversion systems. Their preference will be dictated by the relative magnitude of their average value.

• Type VI is rated, with regard to preference, between types V/IV and types II/III since it is characterized by a peak value that exceeds the average value.

Obviously, the average solar irradiation intensity at a site, either global and/or beam, is of the utmost importance when designing a solar conversion system but the distribution of the irradiation intensity is also a critical parameter.

Modeling Solar Radiation at the Earth’s Surface

Quality Assessment Based Upon Comparison with Models

Many models based on the physics of radiation transfer through the clear atmo­sphere have been developed (Lacis and Hansen 1974; Atwater and Ball 1978; Hoyt 1978; Bird and Hulstrom 1981a, …

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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