# Efficient Machine Learning-Based Prediction of Solar Irradiance Using Multi-Site Data
## 2 Proposed Solution
### Exploratory Data Analysis
At the HSU site, the presence of outliers in diffuse irradiance, direct normal irradiance, and the airmass feature suggests sensitivity to atmospheric variability and measurement inconsistencies. Finally, the ULL station exhibited outliers in GHI, DNI, DHI, and CR1000 temperature readings, likely caused by sudden temperature fluctuations or sensor exposure to environmental factors. Understanding these causes is crucial for improving data accuracy and the reliability of solar irradiance forecasts. The UNLV station, in contrast, exhibited outliers in only two series: GHI and wind cloud temperature. This suggests the impact of these values on the model's performance in relation to the time-shifted values. Similar to the UNLV station, the RAZON station had outliers present in only two series, GHI and DNI, whereas the NWTC station was characterized by the absence of outliers. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Parameter** & **NELHA** & **ULL** & **HSU** \\  & **Units** & **Units** & **Units** \\ \hline Rel humidity & \(\checkmark\)(\%) & \(\checkmark\)(\%) & \\ Station pressure & \(\checkmark\)(mBar) & \(\checkmark\)(mBar) & \\ Diffuse (stdev) & & \(\checkmark\)(W/m\({}^{2}\)) & \\ Diffuse horizontal & & \(\checkmark\)(W/m\({}^{2}\)) & \(\checkmark\)(W/m\({}^{2}\)) \\ Direct (stdev) & & \(\checkmark\)(W/m\({}^{2}\)) & \\ Direct normal & & \(\checkmark\)(W/m\({}^{2}\)) & \\ Global POA (stdev) & & \(\checkmark\)(W/m\({}^{2}\)) & \\ Global POA & & \(\checkmark\)(W/m\({}^{2}\)) & \\ Wind direction (stdev) & & \(\checkmark\)(\({}^{\circ}\)) & \\ Airmass & & & \(\checkmark\) \\ Azimuth angle & & & \(\checkmark\)(\({}^{\circ}\)) \\ CR510 battery & & & \(\checkmark\)(VDC) \\ CR510 temp & & & \(\checkmark\)(\({}^{\circ}\) C) \\ Diffuse horizic (band corr) & & & \(\checkmark\)(W/m\({}^{2}\)) \\ Diffuse horizic (shadowband) & & & \(\checkmark\)(W/m\({}^{2}\)) \\ Direct normal (calc) & & & \(\checkmark\)(W/m\({}^{2}\)) \\ Zenith angle & & & \(\checkmark\)(\({}^{\circ}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._Figure 3: Outlier analysis for **(a)** NELHA, **(b)** ULL, **(c)** HSU, **(d)** UNLV, **(e)** RAZON, and **(f)** NWTC. * What does the correlation study reveal? Correlation analysis was conducted in parallel across all station features using the Kendall method due to its robustness against outliers, as shown in Figure 4. This analysis highlighted variability in feature correlations across different sites. For example, the features most correlated with the GHI series were global PAR, CR1000 temperature, solar PV temperature, and average wind direction, with all but wind direction showing correlations exceeding 50%. At the ULL station, the GHI series was highly correlated with DNI and DHI, with the CR1000 temperature and solar panel temperature also being notable factors, although solar panel temperature had a correlation of 50%. At the HSU station, the CR510 battery and temperature showed the strongest correlations with the GHI. From these observations, it can be inferred that the CR1000 temperature, components of the GHI, and solar panel temperature are key factors in predicting GHI across stations. These features exhibit positive correlations with the GHI. Conversely, negative correlations were noted for relative humidity, CR1000 battery, and zenith angle, suggesting these factors may inversely affect GHI predictions. The NELHA station is characterized by a high correlation between the global PAR and GHI, as well as the CR1000 and temperature measurements. The UNLV station exhibits the best feature correlations and is similarly characterized by values of GHI that are correlated with global UVA, UVB, and the components of GHI, which are DNI and DHI. Additionally, the airmass shows a good correlation with the target. For the RAZON station, the components of GHI, PR1, and PH1 temperatures, pressure, and the RAZON status with the azimuth angle all demonstrate a correlation with the target that exceeds 50%. It is also important to note the presence of negative correlations.