# Some Applications of ANN to Solar Radiation Estimation and Forecasting for Energy Applications
## 4 Estimation of GHI from Other Meteorological Data
### Results  
Figure 3 shows the average, minimum, and maximum values of nRMSE and the standard deviation versus the number of inputs. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline _Parameter_ & _GHI_ & \(\delta\) & \(\theta_{Z}\) & \(T\) & \  
The minimum nRMSE was obtained for the 10 inputs model with a value of 18.65% compared to 73.91% for the worst configuration (2 inputs: WD and WS). Table 3 presents the two best configurations for the same number of inputs; as an example, for 9 inputs, 10 combinations were possible, and only the two best ones (from an nRMSE point of view) are reported in Table 3. The models were classified in descending order of performance (ranking). Some models with a lower number of inputs can be better than models with a higher number of inputs. The declination, \(\delta\), appeared very rarely, WD and Pr never appeared, S was always present, and T, H, EHI, and p were often present; these 5 inputs had a relatively good R with GHI (but only 6% for temperature). Without S (strongly linked with GHI), the best nRMSE dropped to 32.07% compared with 18.65% for the best configuration with 10 inputs. Table 4 shows the results for the best configurations without S input. Figure 4 shows the average, minimum, and maximum nRMSE values and the standard deviation versus the number of input data without S input. The ANN reliability can be considered as correct, particularly when S was an input. Pr and WD had a low influence on GHI estimation (low correlation with GHI). The nRMSE of the 6-inputs model (T, H, p, WS, S, EHI) was 19.35% compared with the nRMSE of 10-inputs model with 18.65%; this combination had a good performance with a minimum of inputs. Estimated 5-min GHI is plotted versus the measured 5-min GHI for four architectures in Figure 5.  
ANN structure with 10 inputs;  
ANN structure with six inputs;  
Figure 5: Estimated 5-min GHI versus measured 5-min GHI for various ANN architectures (Bouzareah site); (**a**) using 10 inputs; (**b**) using 6 inputs (with S); (**c**) using 9 inputs (without S); (**d**) using 5 inputs (without S). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline
**Nbr** & **Rank** & \(\mathbf{\delta}\) & \(\  
+++ ==WARNING: Truncated because of repetitions==
bm{\theta_{z}}\) & **T** & **H** & **p** & **Pr** & **WS** & **WD** & **EHI** & **MAE** & **nMAE** & **RMSE** & **nRMSE** & **MBE** \\
**inputs** & **Rank** & \(\mathbf{\delta}\) & \(\mathbf{\theta_{z}}\) & **T** & **H** & **p** & **Pr** & **WS** & **WD** & **EHI** & **MAE** & **nMAE** & **RMSE** & **nRMSE** & **nRMSE** & **MBE** \\  
++  
ANN structure with nine inputs without sunshine duration; and best ANN structure with five inputs (without sunshine duration). Few differences appeared between the ANN structure with 10 and six inputs in term of reliability and data dispersion. Without S, it appears clearly a more important spread of data compared with the results obtained with ANN structures with S in the inputs set. The performances of the best ANN structures without S for 5-min data were correct with an nMAE between 28.5% and 31% and an nRMSE between 32% and 35%. The presence of some meteorological inputs in the \"best\" configurations seems sometimes surprising as WD and WS; it is difficult to understand the physical relations between GHI and other meteorological parameters. One of the major criticisms that could be levelled at the ANN model is that it is a black box model, allowing it to find some relations between data as often difficult to interpret, and ANN is a data driven method. Even if some estimated data are far away from the real values, we can consider that the performance of this model is satisfying because determining GHI with a time granularity of 5-min from other meteorological data is a very complex task (high variability phenomenon and anisotropic aspect); keeping in mind that such a method is generally applied only for daily average values [5].