Quoted from: I. T. Toğrul and H. Toğrul.Global solar radiation over Turkey: comparison of predicted and measured data[J]. Renewable Energy, 2002, 25(1):55-67.https://www.sci-hub.ren/10.1016/s0960-1481(00)00197-x

In this study, various regression analyses were applied to estimate monthly mean solar radiation in Turkey, by using n / N and n / N nh parameters. Also, equations which represent two periods of the year, winter and summer, were developed by using these parameters. The equations developed by using n / N nh ratio showed good results for the whole country, but, those which included n / N ratio at different cities showed better results. Even better results were obtained when the equations were applied to the summer and winter. In addition to RMSE and MBE statistics, the t-test method and the harmonic analysis were employed to prove that the results are reliable.

Introduction

While solar energy data are recognised as very important, their acquisition is by no means straightforward. The measurement of solar radiation requires the use of costly equipment such as pyrheliometers and pyranometers. Consequently, adequate facilities are often not available in developing countries to mount viable monitoring programmes. This is partly due to the equipment cost and also the cost of technical manpower. Several attempts have, hovewer, been made to estimate solar radiation through the use of meteorological and other physical parameter in order to avoid the use of expensive network of measuring instruments.

The objective of this study is to develop some statistical relations in order to estimate monthly mean daily global solar radiation in Turkey. For this aim, the data obtained from the observation stations in Antalya, I˙zmir, Ankara, Yenihisar (Aydın), and Yumurtalık (Adana) and the measured values in Elazıg˘ were used. The global solar radiation was measured by CM11 model Kipp pyranometer in observation stations, and by CM6 model Kipp pyranometer in Elazıg˘.

 I. T. Toğural and H. Toğural suggested the relation for the estimation of global solar radiation in Turkey:

\( 𝐻/𝐻_0 = 0.318 + 0.449 𝑆/𝑆_0 . \)

I. T. Toğural and H. Toğural suggested the third-order relation for the estimation of global solar radiation in Turkey, as follows:

\( H/H_0 = 0.1796 + 0.9813S/S_0− 0.2958(S/S_0) ^2 − 0.2657(S/S_0)^3 \) 

\( H/H_0=0.1587+1.3652S/Snh−0.1175(S/Snh)^2 \) for winter

\( H/H_0 = 0.288 + 0.9874S/Snh − 0.6967(S/Snh)^2 \) for summer

Finally, these results clearly indicate that reliance on the RMSE and MBE used separately can lead to a wrong decision in selecting the best model from a suited of candidate models and that the use of the RMSE and MBE in isolation is not an adequate indicator of model performance. Therefore, the t-statistic should be used in conjunction with these two indicators to better evaluate a model’s performance.