# Estimation of Direct Normal Irradiance at Antarctica for Concentrated Solar Technology
## 2 Materials and Methods
### Data Analysis and Model Development  
The solar-metric instrumentation control unit was programmed to perform a measurement of the three solar components, DNI, GHI and Diff.HI, each minute, while the data acquisition was recorded with a frequency of one record every five minutes. In particular, every five minutes, for each of the three irradiation components, the average and the mean standard deviation values (MSD) of the five consecutive measures in the interval were recorded. In the model construction of the DNI estimation starting from the GHI, only the averages value were used, while the MSD were used to check (and potentially discard) those average values that seemed far-fetched. Throughout 65 days of constant observations, 18,709 specific data elements were recorded which corresponds to 288 records per day. 18,545 of the recorded data elements from the entire data set are related to diurnal intervals that can be used for the estimation of the DNI. The reason the records of daily observations with respect to the total observations are so preponderant is that beyond the parallels of the polar circles, the day duration increases considerably in the summer season. The Sun in this area remains uninterruptedly beneath the horizon (the polar night). At the latitude where the Mario Zucchelli base is located, sunrise and sunset are present until 3 rd November; then, from 4 th November until 7 th February, the Sun remains above the horizon for the entire 24 h period. Figure 2: Photo of Solar-metric station of the instrument at Mario Zucchelli Station. Conversely, it should be noted that although the days are long, in reality the Sun rises relatively little above the horizon during the day and this effect is much more pronounced as we move towards latitudes close to the poles. The phenomenon can be shown by calculating the Sun's maximum elevation during the day ([PERSON], 2016), for all the days of the year (Figure 3). The three observed components by solar-metric instrument are linked by the following relationship:  
\[I=I_{\text{bn}}\cos\theta_{\text{z}}+I_{\text{d}} \tag{1}\]  
where, \(I\) is global horizontal irradiance, \(I_{\text{bn}}\) is the direct normal irradiance on the normal plane, \(\theta_{\text{z}}\) is the solar zenith angle and \(I_{\text{d}}\) the diffuse solar irradiance on the horizontal plane. The availability of the three observed solar components therefore makes it possible to validate the individual measurements. The solar zenith angle is the angle that the direction of the solar beams forms with the normal to the horizontal plane at a fixed location. The zenith angle is calculated according to the latitude and longitude, day number of the year and the time of day. The exact Sun position and the moment of acquisition are essential to Equation (1). The product of the Ibn with the cosine of the zenith angle is the direct irradiance referred not to the normal, but rather to the horizontal plane, for which the symbol \(I_{\text{b}}\) will be used from this point in the text:  
\[I_{\text{b}}=I_{\text{bn}}\cos\theta_{\text{z}} \tag{2}\]  
The Equation (2), translated into the following relationship between the three irradiance components (GHI, DNI and Diff.HI), where all are referred to the horizontal arrangement is the sequent:  
\[I=I_{\text{b}}+I_{\text{d}} \tag{3}\]  
The dispersion graph covering the 65 days of the observed and calculated DNI values from Equation (3) is presented in Figure 4. Following the relationship in Equation (3), we could validate our observations and calculate one of the needed values if measurements for the other two are available. Figure 3: Daytime duration during the year at the MZS. To begin with, all the observed data set must be validated. The good planning and execution of the observations certainly enables the elimination of the majority of systematic errors in the dataset. In the dataset, random errors inevitably occur, which are intimately connected to the observational process itself and can never be completely eliminated or prevented.