# Some Applications of ANN to Solar Radiation Estimation and Forecasting for Energy Applications
## 5 Estimation of Tilted Global Irradiation (GTI) from Horizontal Global Irradiation (GHI)
### Comparison between GHI and DNI Forecasts  
It is impossible to compare the performances of the models according to the solar component in terms of the absolute value of RMSE (or MAE) because the daily curve of GHI and DNI are very different in term of amplitude and form. Thus, we plotted in Figure 12 a comparison of the performances in term of nRMSE because it is the most common error metric used in the solar radiation prediction; in the case of Figure 11, as we compared two different solar radiations (GHI and DNI) with a different scale, the normalized value of RMSE seems to be the most adapted metric.  
\begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Metric** & **Model** & **h+1** & **h+2** & **h+3** & **h+4** & **h+5** & **h+6** \\ \hline \multirow{2}{*}{RMSE} & SP & **207.86** & 287.64 & 338.86 & 378.19 & 412.67 & 434.51 \\  & ANN & 212.33 & **270.10** & **297.73** & **321.59** & **336.98** & **344.00** \\ \hline \multirow{2}{*}{nRMSE} & SP & **37.42\%** & 51.77\% & 60.98\% & 68.04\% & 74.23\% & 78.16\% \\  & ANN & 38.23\% & **48.62\%** & **53.58\%** & **57.85\%** & **60.61\%** & **61.88\%** \\ \hline \multirow{2}{*}{MAE} & SP & **125.24** & **187.12** & **230.34** & **266.01** & 298.23 & 317.71 \\  & ANN & 168.14 & 223.27 & 244.91 & 274.60 & **283.68** & **299.16** \\ \hline \multirow{2}{*}{nMAE} & SP & **22.55\%** & **33.68\%** & **41.45\%** & **47.85\%** & 53.64\% & 57.15\% \\  & ANN & 30.27\% & 40.19\% & 44.07\% & 49.40\% & **51.02\%** & **53.82\%** \\ \hline \multirow{2}{*}{MBE} & SP & 2.28 & 2.10 & 1.28 & 0.63 & \(-\)0.58 & \(-\)2.66 \\  & ANN & 3.34 & 2.76 & \(-\)4.12 & \(-\)6.15 & \(-\)6.24 & \(-\)6.88 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Performance metrics (in Wh/m\({}^{2}\) for RMSE, MAE, and MBE) for DNI (in bold is the best predictor for each horizon and each error metric) (Odeillo site).  
Figure 11: Comparison of forecasting models for various horizons for hourly DNI (Odeillo site); (**a**) in terms of nRMSE; (**b**) in term of RMSE.  
As previously underlined, GHI was forecasted with a better accuracy compared with DNI. It is probably due to the fact that in GHI, the two components, diffuse one and beam one, have compensating effects (when diffuse increases, beam decreases) and the variation rate of GHI is less rapid than for DNI. With SP and ANN methods, DNI is predicted with an nRMSE nearly twice as high than for GHI, but this difference was reduced when the forecast horizon increased and for (h+6), the accuracy for DNI prediction was the same than for GHI prediction.  
[PERSON] et al. [50] reviewed the intra-day ahead forecast performances for PV production (using GHI as renewable resource) using different numerical prediction models. Various error metrics were used and calculated according to different definitions, moreover, the forecasting methods were applied in different meteorological stations; thus, it is very difficult to make a comparison of our results with the literature in these conditions.  
A short bibliographical study [60] on DNI forecasting concludes that the DNI forecasting is obtained with a lower accuracy than for GHI forecasting and that only a small number of articles are written on the DNI forecasting at short time horizons as confirmed by [PERSON] et al. [20].