Relation between the solar irradiation and bright sunshine hours is not a static occurrence but essentially a dynamic phenomenon. This is mainly due to our dynamic atmosphere because of its natural short and long term climatic cycles which was heavily affected by human-made hazards in the last 200 years. Hence, researches on solar irradiation and the atmosphere become more and more important not only to understand our environment but also to clarify its natural and man-made alteration upon intervention to its usual cycles.

Discussion of the static physical models as outlined in this chapter is still important as they aid to understand averaged behaviors of our environment, namely the atmospheric interaction of the solar rays in our case. This in turn helps to explain the dynamic activities of our atmosphere which are continuously monitored by the advanced technological satellites at least for the last several years (Mueller et al. 2006). Another important issue of course is the use of such models to estimate solar irradiation for the sites having no long term measurements so that short-term performance and long-term feasibility studies of all types of solar energy applications can be carried out.

Physical modeling of the transfer of solar radiation through the atmosphere is extremely important concept in this sense, and a part of it is the interrelations discussed in this chapter. In the search of these interrelations, physical properties of our atmosphere are mainly utilized and this will introduces new highlights to the interaction of solar rays and the atmosphere.

It might be desirable to construct accurate computations with simple equations; however, as stated by Gueymard (1993), the accuracy and simplicity are inversely proportional. In any case, the models should follow the physical mechanisms of atmospheric interactions of electromagnetic wave with matter as close as possible for a better radiation transfer modeling (Gueymard 1993).

Under the highlight of above considerations, some discussions and conclusions on the relationship between solar irradiation and bright sunshine hours are given in the followings. Discussions seem to start with Kimball’s and Angstrom’s pioneering works (Kimball 1919; Angstrom 1924) and Angstrom pointed that Angstrom- Prescott equation between H/H0 and n/N might depend also on the averaging time intervals. Hence, daily and monthly average daily values should correlate in a different manner as the averaging sweep out some of the information contained in the daily values. After reviewing the literature, a conclusion is reached by Gueymard et al. (1995) that the curvature of the quadratic form observed for daily values does not significantly remain for the monthly averages. In fact, some smoothing can be demonstrated using the second derivatives of the daily quadratic regression correlation, Eq. (5.27) and monthly expression, Eq. (5.29). That is the third coefficient in the monthly form, a2 have smaller value of 0.142 in magnitude than that of the daily expression, which is 0.25. Gueymard et al. (1995) also noted that the opposite trends in the variations of fractional diffuse and beam components with n/N cancel out to give almost perfectly linear variation between H/H0 and n/N.

The averaging procedure may indeed partly smooth out the quadratic nature in the daily values, however quadratic forms obtained for monthly average daily values have relatively better estimates of solar radiation as determined by Akinoglu and Ecevit (1990a, 1990b. 1993), Tasdemiroglu and Sever (1989) and Badescu (1999). In any case, non-linear nature of the relation between H/H0 and n/N for the monthly averages may still need further justifications using accurate and longer data set.

Essentially, it seems that there may be at least three reasons of the non-linearity. First one is the non-linearity in the daily values, basically quadratic form, results in a quadratic form for the monthly averages due to the quadratic dependence of the standard deviation on n/N. Second reason may be the bi-modal characteristics observed by Schuerke (2000) and some other researchers cited by Schuerke, give rise to a non-linear form. Finally, back-scatter effects may lead a non-linear term to the relation between H/H0 and n/N as discussed in section 4.3. Another fact is the variation of Angstrom coefficients with n/N imposed by quadratic correlation, namely Eq. (5.30), have similar trends as determined by Rietveld (1978). In addition, variation of a with b seems quadratic in nature which leads a quadratic relation between H/H0 and n/N as outlined in section 5.4.4. These conclusions however should be verified using accurate and longer data sets and starting from instantaneous considerations researches must be carried out for hourly, daily and monthly average daily values.

In fact, Eq. (5.33) seems to be under-estimating the monthly mean irradiation, at least for two Tibet sites with altitudes 2809 m and 3659 m (Yang 2007). In high altitude regions, due to the fact that the atmospheric parameters are less effective, the value of a0 + a1 + a2 for n/N = 1 of the quadratic form should be higher than those for the lower altitude regions (Yang 2007). Better estimations of the model of Yang et al. especially for the higher altitudes as presented in Table 6 of Yang et al. (2006) might be due to the fact that their model is taking into account some atmospheric parameters of the site under consideration.

The importance of hourly, daily and monthly average daily considerations are already discussed, yet a recent attempt on correlating the yearly average daily values of H/H0 and n/N for 38 years data of 51 locations resulted inalinear relation with a regression coefficient of 0.834 (Chen 2006).

Researches in the field of solar radiation should continue, particularly of works that present new and significantly improved ideas or concepts, and which enhance progress toward applications of solar energy (Kasten and Duffie 1993). Gueymard underlined this conclusion supporting the idea that the mere use of Angstrom’s equation to predict global irradiation from local sunshine data would not give significant progress (Gueymard et al. 1995). Following years, works on the simple use of Angstrom relation appeared rather frequently in the literature but researches on new ideas and concepts were not quite often.

Regional works on the subject may continue to reach local correlations between the solar irradiation and bright sunshine hours using the surface data, however it seems that new prospects of future research is strictly needed. Surface data should unquestionably continue to be collected but it is a must to use new instruments which also need frequent calibrations. Physical models of irradiative transmission through the atmosphere should be incorporated not only with the surface data but also with the data taken remotely by the satellites.

Another important future prospect is further achievements that can be obtained by constructing linkages between the surface data and those measured from satellites which will lead to new revenues in physical modeling of our atmosphere.

An important conclusion was reached by Gueymard (2003a, 2003b) which seems still valid: “No further improvements in current high performance models will therefore be necessary until more accurate fundamental data becomes available.” Another fact is that new validations and comparisons should use larger number of data sets but with higher accuracy and reliability which must be checked with the local organizations and with the existing available data. The future prospects given by Gueymard et al. (1995) seem still important research avenues to be carried out.

Models and the correlations presented in this chapter and of course others that could not be covered here necessitate further validations using accurate and longer surface data sets. Predictions and formalism of these models should be compared and linked by the models and observations obtained from the new generation satellites (Mueller 2004) to attain detailed information about solar irradiation on a spatially denser or even continuously on the surface of the Earth.

Acknowledgements Author would like to thank to Turkish State Meteorological Service for supplying data and to Mr. B. Aksoy for his valuable discussions. Valuable discussions with Dr. K. Yang and also his permission for the inclusion of the computer code of their model in the CD-ROM within the content of this chapter are also kindly acknowledged.