# Estimation of Direct Normal Irradiance at Antarctica for Concentrated Solar Technology
## 3 Results  
### Analysis of the Estimated Monthly and Annual DNI from GHI  
Next, having validated our fine-tuned model based on 65 consecutive observations of all three radiations components, the following step is to extrapolate the presented model onto the entire observed GHI dataset at and near MZS. The Eneide observation site hosts a control unit that has acquired all the GHI data from 1987. In this study, the GHI observations from Eneide station are used to construct the time series of the DNI at the same location using the estimation model described in Section 2.4. To this purpose, the time series covered by the interval from 1999 until 2013 was considered, with a series of 15 years of data.  
This long dataset includes GHI hourly data observations, where the corresponding hourly value of the DNI is estimated using the following algorithm:  
\[\begin{array}{l}\text{Input}:\text{GHI}\\ K_{\text{T}}=\frac{\text{GHI}}{\text{EHI}}=\frac{\text{GHI}}{\text{ENI}\cos \theta_{z}}\\ \text{Correlation}:\text{$K_{\text{bn}}$}=\frac{K_{\text{T}}}{1+\text{e}^{- \alpha-\beta K_{\text{T}}}}\left[\text{model Boland}\right.\left.-\text{Ridley} \right.\left.-\text{ENEA}/\text{Antarctica}\right]\\ \text{DNI}\right.=\left.K_{\text{bn}}.\text{ENI}\end{array}\]  
In the above formulas we need certain already known quantities: ENI is the normal extra-atmospheric irradiance, EHI is the horizontal extraterrestrial irradiance (EHI = ENI-cos \(\theta_{z}\)), and, finally, \(\alpha\) = -9.18 and \(\beta\) = 14.28 (15) the Boland-Ridley coefficients estimated by ENEA for the Antarctica.  
The final summary of the average daily monthly and annual daily DNI at Eneide station, relative to the 1998-2013 periods, is shown in Table 3 and the annual trends are plotted in Figure 11. The presented data show that the validated observations of GHI and estimated DNI start from November 1999. In the last row of Table 3, mean monthly values for all years are calculated, except 1998 and 1999 where annual trend was observed as unlikely and 2002 and 2008, where the data was incomplete. The results show the annual DNI at Eneide varied between a minimum value of 1794 kWh-m\({}^{-2}\) year in 2005 and a maximum of 2223 kWh-m\({}^{-2}\) in 2013, with an average of 2014 kWh-m\({}^{-2}\).  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c} \hline \hline
**Year** & **Jan.** & **Feb.** & **Mar.** & **Apr.** & **May** & **June** & **July** & **Aug.** & **Sept.** & **Oct.** & **Nov.** & **Dec.** & **Year** \\ \hline
1998 & 4.162 & 1.812 & 0.608 & 0.082 & 0.001 & 0 & 0 & 0.088 & 0.885 & 2.239 & 5.066 & 5.101 & 609.9 \\
1999 & 3.571 & 1.628 & 0.522 & 0.122 & 0.001 & 0 & 0 & 0.269 & 1.011 & 2.5  
In Figure 11, the annual and mean trends of average monthly DNI values at Eneide station are presented, with respect to the Antarctic seasons. On the horizontal axis, intervals equal to one year starting from July and ending in June of the following calendar year are considered, in order to reproduce the familiar \"bell\" trend of the radiation over the year observed at others latitude. In Figure 11, we have omitted those annual period with missing or invalid data (2002-2003 and 2008-2009).