# Efficient Machine Learning-Based Prediction of Solar Irradiance Using Multi-Site Data
## 3 Results and Discussion
### Feature Impacts with SHAP  
The SHAP (Shapley Additive Explanations) explainer is a method used to interpret the output of machine learning models by breaking down and attributing the contribution of each feature to the model's predictions. SHAP values are based on cooperative game theory and the concept of Shapley values, which provide a way to fairly allocate the \"payout\" (in this context, the prediction) among all features (players) by considering all possible combinations of features [30]. In this context, this explainer was used to understand the impact of features within each station and how they contribute to the model's performance in predicting the targeted GHI. In each station, the features were analyzed for the 30-min shift, as it was the best horizon for prediction and had the least RMSE observed. Figures 18 and 19 provide the analysis in each station. Analyzing the impactful features reveals that, for all stations, the lagged version of GHI up to 30 min is the most significant feature. While most stations show that only two or three features have the most noticeable impact, the UNLV station stands out with at least six impactful features. These features primarily include the shifted values of global UVA up to 1 h, airmass, the GHI shifted values up to 1 h, and the zenith and azimuth angles. This indicates that including these feature values at the UNLV station could be beneficial for the trained models. Another observation from the SHAP explanations is that it is not necessary to use data from periods far in the past. The explanations show that a maximum lag of 1.5 to 2 h is sufficient for accurate predictions.  
Figure 17: Model-free benchmark: (**a**) with SARIMAX and (**b**) without shift.  
In addition, from a logical and physical standpoint, it is well-established that features correlated with GHI are inherently linked to both DNI and DHI, given their mutual dependence on solar geometry and atmospheric conditions. However, based on our station-specific analysis, it is evident that the available features vary significantly across different stations. This heterogeneity poses a challenge in establishing a consistent and robust set of predictors for GHI across all sites. While some features, such as the solar zenith and azimuth angles, may be common across stations, their relative contribution to GHI prediction appears limited when compared to that of the lagged GHI values. Our analysis shows that the predictive importance of lagged GHI values decreases as the lag duration increases, which is consistent with the autocorrelation and partial autocorrelation patterns observed in our preliminary time-series analysis. To this end, we primarily rely on the first two lagged values of GHI (i.e., GHI\({}_{l-1}\) and GHI\({}_{l-2}\)) as key features for forecasting. This decision is further supported by the SHAP analysis illustrated in Figure 20, which clearly shows a strong contribution from the first lag, with a noticeably diminished impact from the second lag. These findings are aligned with the earlier SHAP-based feature importance assessments. Moreover, other meteorological variables, such as airmass, though considered in the initial set of features, were found to have minimal influence relative to the lagged GHI values. For this reason, and to reduce model complexity while maintaining interpretability and generalizability across stations, we focused exclusively on using lagged GHI values as predictors in our modeling approach.  
Figure 19: SHAP feature effects on predictions: (**a**) UNLV, (**b**) NWTC, and (**c**) RAZON.  
Figure 18: SHAP feature effects on predictions: (**a**) NELHA, (**b**) ULL, and (**c**) HSU.