## 6 Conclusions  
In this study, three new deep learning architectures that are applicable to the field of solar forecast have been presented, namely the spatio-temporal dilated convolutional neural network (ST_Dilated_CNN) and spatio-temporal convolutional neural network versions 1 and 2 (ST_CNN_v1 and ST_CNN_v2). These artificial neural networks were evaluated against three scenarios with different sets of input features, including irradiance data, astronomical variables, and a combination of astronomical and meteorological features. For each of the scenarios evaluated, the proposed networks were proven to be superior to the baseline models, outperforming them by up to 3 percentage points in some cases. A dataset available to the scientific community was used for the study. It was a dataset from the Spanish region of Castile and Leon that has records from 37 meteorological stations. It has a temporal resolution of 30 min and covers a region of up to 1000 km\({}^{2}\). The results show that the best combinations of input characteristics for the models included astronomical variables. Scenarios 2 and 3 benefited the most when assessing the forecast skill of the models, achieving significantly better FS values than Scenario 1, where only irradiance data were modelled. \begin{table}
\begin{tabular}{l l c c} \hline \hline
**Scenario** & **Performance Metric** & **F-Statistic** & \(p\)**-Value** \\ \hline \multirow{3}{*}{Scenario 1} & MAE & 11.43 & 3.23 \(\times\) 10\({}^{-5}\) \\  & RMSE & 14.50 & 2.75 \(\times\) 10\({}^{-6}\) \\  & R2 score & 14.13 & 3.67 \(\times\) 10\({}^{-6}\) \\ \hline \multirow{3}{*}{Scenario 2} & MAE & 13.18 & 7.81 \(\times\) 10\({}^{-6}\) \\  & RMSE & 9.02 & 0.0002 \\  & R2 score & 8.15 & 0.0005 \\ \hline \multirow{3}{*}{Scenario 3} & MAE & 7.03 & 0.0014 \\  & RMSE & 8.87 & 0.0003 \\ \cline{1-1}  & R2 score & 7.42 & 0.0010 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: F-statistics and \(p\)-values computed by applying the ANOVA test to the considered performance metrics, grouped by scenario. The \(p\)-values computed with the ANOVA test were highly statistically significant (lower than 0.001) for all metrics and all the evaluated scenarios, suggesting that there was a significant difference in performance. This reinforces the validity of the improvements in performance achieved by the proposed models, and suggests that the models evaluated performed significantly differently in terms of MAE, RMSE, and R2 score. In terms of future work, the evaluation of the models with public datasets from other regions is proposed to study if changes in location (and, therefore, atmospheric conditions) affect the prediction quality of the models. Additionally, variables of physical models, such as atmospheric visibility, 200 hpa geopotential, cloud liquid condensation (CLC), and cloud ice condensation (CIC), could also be added to the training and evaluation of the proposed models. Subsequent works could also explore the application of feature selection algorithms to reduce the dimensionality of the input and ultimately minimize the computational cost of training the models. Another line of research may be associated with finding the distance at which neighbor data are no longer correlated, and therefore create noise instead of providing relevant information. Conceptualization, L.B.C., C.-I.C. and M.-A.M.-C.; methodology, L.B.C. and M.-A.M.-C.; software, L.B.C. ; validation, L.B.C., M.-A.M.-C. and C.-I.C. ; investigation, L.B.C. ; resources, M.-A.M.-C. and C.-I.C. ; data curation, L.B.C. ; writing--original draft preparation, L.B.C. ; writing--review and editing, L.B.C., M.-A.M.-C. and C.-I.C. ; visualization, L.B.C. ; supervision, M.-A.M.-C. and C.-I.C. All authors have read and agreed to the published version of the manuscript. This research received no external funding.