# Solar Irradiance Forecasting Using Dynamic Ensemble Selection
## 5 Experiments
### Data Description  
The databases are related to four major cities in Brazil: Florianopolis, Fortaleza, Salvador, and Sao Paulo.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Parameters** & **Option** \\ \hline ARIMA & \(p\)_A\({}_{\beta}\)_ & Hyndman Method [65] \\ \hline \multirow{4}{*}{MLP} & Algorithm & Backpropagation \\ \cline{2-3}  & Activation Function & Sigmoid \\ \cline{2-3}  & Number of Hidden Layer Nodes & 20, 50, 100 \\ \hline \multirow{4}{*}{ELM} & Algorithm & Moore-Penrose pseudo-inverse \\ \cline{2-3}  & Activation Function & Hyperbolic Tangent \\ \cline{2-3}  & Number of Hidden Layer Nodes & 20, 50, 100, 200, 500 \\ \hline \multirow{4}{*}{SVR} & Kernel & RBF \\ \cline{2-3}  & \(\gamma\) & 0.1, 0.01, 0.001 \\ \cline{2-3}  & C & 10, 100, 1000 \\ \cline{2-3}  & \(\epsilon\) & 0.1, 0.01, 0.001 \\ \hline \multirow{4}{*}{GB} & Number of estimators & 50, 100, 200 \\ \cline{2-3}  & Max depth & 5, 10, 15 \\ \cline{2-3}  & Max features & 0.6, 0.8, 1 \\ \cline{2-3}  & Sub sample & 0.6, 0.8, 1 \\ \cline{2-3}  & Learning rate & 0.1, 0.3, 0.5 \\ \hline \multirow{4}{*}{RF} & Number of estimators & 50, 100, 200 \\ \cline{2-3}  & Max depth & 5, 10, 15 \\ \cline{2-3}  & Max features & 0.6, 0.8, 1 \\ \hline \multirow{4}{*}{DBN} & Number of Hidden Layer Node & 100, 200 \\ \cline{2-3}  & Learning rate RBM & 0.01, 0.001 \\ \cline{1-1} \cline{2-3}  & Learning rate & 0.01, 0.001 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameter configuration of the models and algorithms used.  
Florianopolis is the capital of Santa Catarina state, located in the south of the country. It is a coastal town. Fortaleza is the capital of Ceara state, in the Brazilian northeast. It is also a coastal town relatively close to the equator line. Salvador is the capital of Bahia state, located in the Brazilian northeast region. Sao Paulo city is the major city in Brazil. It is almost on the Tropic of Capricorn. The red marks in Figure 3 represent the locations of these cities on a map of Brazil. Considering the cyclic behavior of solar irradiation, where maximum values are often achieved at 12:00 and minimum values at 6:00 and 18:00, all inputs were analyzed in a window size of 12. Moreover, this value can also be achieved through an autocorrelation plot.  
As can be seen, the longest distance is between Fortaleza and Florianopolis, almost 3400 km. Due to this, it is clear that the sunlight may present different magnitudes along the year considering all cities. All databases are composed of 4758 hourly samples of solar irradiation (kJ/m\({}^{2}\)). We considered the measures from 1 January 2020 to 31 December 2020, the whole year. However, we selected just the samples from 6:00 to 18:00 during each day.  
Table 2 presents the geographical location of the solar irradiation stations and the descriptive statistics of the corresponding series. Note the difference in the altitude of Sao Paulo among the others, the only city that is not a coastal town. The acronyms STD and CV represent the standard deviation and coefficient of variation, respectively.  
Figure 3: Locations of the solar irradiation meters in Fortaleza, Florianopolis, Salvador, and São Paulo. The satellite map is from Google Maps (Map data ©2020 Google; [[https://www.google.com/maps/place/Brazil/](https://www.google.com/maps/place/Brazil/)]([https://www.google.com/maps/place/Brazil/](https://www.google.com/maps/place/Brazil/)), accessed on 15 January 2022); the satellite is from Google Earth Pro (Mapdata ©2020 Google; [[https://www.google.com/maps/@-23.6815315,-46.8754814,102](https://www.google.com/maps/@-23.6815315,-46.8754814,102)]([https://www.google.com/maps/@-23.6815315,-46.8754814,102](https://www.google.com/maps/@-23.6815315,-46.8754814,102)), accessed on 15 January 2022). The maps were edited with Microsoft Power Point (version 16.28-19081202).