Modeling Solar Radiation at the Earth’s Surface

Recent Advances in the Relations between Bright Sunshine Hours and Solar Irradiation

Bulent G. Akinoglu

1 Introduction

It seems quite a realistic view to state that the data of bright sunshine hours are the only long term, reliable and readily available measured information that can be used to reach highly accurate estimates of solar irradiation values on the Earth sur­face. Kimball at 1919 demonstrated for the first time the existence of the relation between the average daily irradiation obtained by means of phyroheliometric and photometric measurements and the duration of sunshine measured by a Marvin sun­shine recorder. He presented the relations graphically and included also the relation between the solar irradiation and cloudiness. Using the data of several locations in USA he came to a conclusion that: “In fact, the radiation-ratio and sunshine data plot very nearly on the straight line connecting 100% sunshine and 0% sunshine radiation intensities” (Kimball 1919).

Alternatively, one might exclaim that the history started at 1924, with a sim­ple empirical linear relation proposed by Angstrom (1924). Since then hundreds of articles appeared in the literature from all over the world which made use of this well-known Angstrom’s linear correlation in the same, similar and/or modified manner. The correlation derived by Angstrom from measured data of Stockholm, in its original form, was:

H = Hc (0.25 + 0.75^ (5.1)

where H and Hc are the total irradiation income on horizontal surface for a day and for a perfectly clear sky, respectively while n/N is the time of sunshine expressed as the fraction of greatest possible time of sunshine. One of the chief results that Angstrom reached was “A clear conception of the radiation climate... cannot be obtained without a detailed experience of the amount of energy furnished by the diffuse radiation” (Angstrom 1924).

Bulent G. Akinoglu

Middle East Technical University, Ankara, Turkey, e-mail: bulent@newton. physics. metu. edu. tr

It is rather hard to define a perfectly clear sky which barely depends on the ge­ographical parameters and the climate of the locality that is mainly the air mass, atmospheric constituents and the cloud amount and type. Another untidiness is the records of sunshine which is not only dependent on the instrument calibration and the burning paper strip type but also on the climate conditions and sun’s altitude. Nevertheless, sunshine records evidently possess very valuable surface measured information, are already used in too many applications and will certainly be used in future applications.

In 1940 Prescott replaced the clear sky reference value by a rather more gener­alized ‘Angot’s value’ that is the radiation on a horizontal surface with a transpar­ent atmosphere. He used the only available measured solar irradiation data in the continent to obtain the regression constants and utilize them to estimate the solar income for Acton, Canberra close to Mount Stromlo. The formula was then named as Angstrom-Prescott correlation and the correlations and/or models which use the bright sunshine hours to estimate solar irradiation were named as sunshine-based models. The regression coefficients were named as Angstrom coefficients.

This chapter starts with a brief description of the measuring instruments and some information on the available data. The physical basis of Angstrom-Prescott relation is discussed especially with reference to the recent advancements on the subject matter. Some of the recent successful models are discussed in details empha­sizing especially a broadband hybrid model and the quadratic form. Finally, model comparisons and validation techniques are summarized which is followed by a dis­cussion and conclusion section together with a future prospect.