# Efficient Machine Learning-Based Prediction of Solar Irradiance Using Multi-Site Data
## 3 Results and Discussion
### Hourly GHI Prediction and Link with Time-Lagged Versions
The stability of model performance across the majority of stations for the 1-h lagged version of GHI was confirmed through an analysis of hourly GHI values at \(t\), \(t+1\), and \(t+2\) for all stations, as depicted in Figure 14. The projection revealed a general correlation between these GHI values, as evidenced by the dense diagonal distribution observed in all stations. For example, the RAZON station displays a high concentration of GHI values, particularly in the lower GHI range, indicating consistency in the relationship between the time-lagged GHI values. At the HSU station, the distribution is more balanced across the three lagged versions, suggesting a steady relationship over time. The NWTC station, however, shows a noticeable spread, especially at higher GHI values, where the points become less concentrated. This suggests that as GHI increases, the relationship between consecutive GHI values becomes more variable. For the NWTC station, this indicates that while a forecasting model would likely perform well for lower GHI values due to the dense concentration of data, it may struggle with higher GHI values, where increased variability and potential non-linearities could challenge prediction accuracy. Similarly, the UNLV station exhibits a broader spread in the data points, particularly at higher GHI values, implying greater volatility in GHI, especially during periods of high irradiance. This volatility suggests that the UNLV station may require more sophisticated modeling approaches to account for the increased uncertainty at higher GHI levels. In contrast, the NELHA and ULL stations show similar distributions, with a higher concentration of values in the lower GHI range and more variability at higher GHI values. Particularly for NELHA, this increased variability at higher GHI suggests a potential challenge for forecasting models, requiring them to adapt to changes in the data distribution effectively. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & \multicolumn{6}{c}{**30-min shift**} \\ \hline
**Station** & **Model** & \(\mathbf{R^{2}}\) & **RMSE** & **MAE** & **Median AE** & \(\mathbf{D^{2}}\) \\ \hline NELHA & GradientBoosting & 0.96 & 63.61 & 28.88 & 3.17 & 0.88 \\ ULL & MLP & 0.95 & 62.09 & 26.63 & 3.21 & 0.86 \\ HSU & CatBoost & 0.97 & 45.87 & 18.94 & 1.56 & 0.88 \\ UNLV & MLP & 0.98 & 42.82 & 15.46 & 1.92 & 0.93 \\ NWTC & GradientBoosting & 0.99 & 71.26 & 34.00 & 11.85 & 0.89 \\ RAZON & GradientBoosting & 0.89 & 103.98 & 30.93 & 6.35 & 0.84 \\ \hline \hline \multicolumn{6}{c}{**1-h shift**} \\ \hline
**Station** & **Model** & \(\mathbf{R^{2}}\) & **RMSE** & **MAE** & **Median AE** & \(\mathbf{D^{2}}\) \\ \hline NELHA & MLP & 0.89 & 113.19 & 31.97 & 4.57 & 0.87 \\ ULL & MLP & 0.95 & 65.01 & 31.12 & 5.72 & 0.84 \\ HSU & CatBoost & 0.96 & 51.11 & 22.40 & 2.38 & 0.86 \\ UNLV & MLP & 0.98 & 46.81 & 19.71 & 4.37 & 0.92 \\ NWTC & ExtraTrees & 0.98 & 113.98 & 35.23 & 4.84 & 0.88 \\ RAZON & GradientBoosting & 0.94 & 74.10 & 33.63 & 6.22 & 0.83 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Model performance comparison for 30-min and 1-h shifts. Figure 14: The 3-D hourly GHI versus \(\text{GHI}(t+1)\) and \(\text{GHI}(t+2)\) for different stations: (**a**) NELHA, (**b**) ULL, (**c**) HSU, (**d**) UNLV, (**e**) RAZON, and (**f**) NWTC.