*3.1. Analysis of Weather Inputs*

Figure 4 compares solar irradiation values from the monitoring and GDAS datasets, for each of the two manually picked weeks included in the test samples. For each time period, both the real (monitoring) and estimated (GDAS) signals, and the difference between those signals, are represented. Temperature graphs for manual weeks, and both temperature and irradiation graphs for random days, are omitted for the sake of brevity.

Table 2 shows the MBE, RMSE, and nRMSE metrics results for temperature and solar irradiation in the GDAS dataset. Errors are computed using the corresponding values from the monitoring dataset as a reference. The results are computed for three different periods: the entire temporal span of the study, the 22 random chosen days from the second test sample, and the two manually picked weeks from the third test sample. Individual error values are calculated for each day of each period, and then the mean and standard deviation values of those errors are computed.

**Figure 4.** Comparison of solar irradiation inputs for manually chosen weeks.



It is clear that GDAS has a moderate tendency to underestimate both mean air temperature and solar irradiation variables for the studied location and temporal interval. However, MBE values are much closer to zero than their RMSE counterparts for the entire study span and the 22 randomly chosen days, especially for solar irradiation. For the two manually chosen weeks, which cover similar dates of 2012 and 2013, distances towards zero are not so divergent between both metrics. This behaviour shows that underestimations and overestimations of weather variables for individual days tend to almost compensate one another for periods of time that comprise a larger variety of weather conditions. Mean and standard deviation values of nondimensional errors for solar irradiation are lower than their temperature equivalents on all temporal samples.

Key instants on the daily behaviour of irradiation curves, namely, dawn and dusk hours and the hour of maximum value, match closely between the monitoring and GDAS variables, as can be seen in Figure 4. The same behaviour is found for the randomly picked days; for almost all days, the GDAS estimations and the monitoring data have their maximum value at the same hour or with a one-hour difference, while dawn and dusk hours both match for most days with maximum differences of one hour.

When comparing sample periods, errors for the randomly chosen days are more similar to those of the entire study span when placed against errors for the manually chosen weeks. This indicates that the former sample is more representative of the global behaviour of both weather variables for the study span. Although the sample of two weeks provides an efficient way of visualising specific features of the solar irradiation inputs, numerical error metric values for said sample should be treated as examples, and should not be generalised.

The main objective of the present study is related to the prediction of PV power outputs, and not to air temperature or solar irradiation. However, both of these weather variables are key inputs of the ANN model used for predicting photovoltaic power, particularly solar irradiation. As the GDAS dataset contains interpolated weather values for every two out of three hours, it is sensible to compare the error values in this dataset with those of similar studies. For example, [31] uses an ANN model trained with the LMA algorithm to forecast surface irradiation from extraterrestrial solar irradiation in the South of China, among other inputs, using both historical data series and statistical feature parameters to feed the models. Their RMSE results are ~43 W/m<sup>2</sup> for sunny days, and ~85–255 W/m<sup>2</sup> for cloudy days (using statistical parameters or historic series as inputs). The RMSE irradiation errors from Table 2 are larger than the statistical-based-predictions from [31], but lower than historic-based-predictions, which are more comparable.

It must be highlighted that GDAS is a NWP model, meaning that the derived meteorological data are estimated (forecasted) values. For the particular case of GDAS, this estimation includes the interpolation of scattered real observations into a regular grid of points, and also a very-short-term forecasting of future weather conditions. These spatial interpolations and temporal extrapolations imply a certain level of uncertainty. In addition, GDAS forecasts have a three-hour resolution. Instantaneous air temperature and solar irradiation values at each three hours are taken from GDAS outputs and interpolated to a one-hour temporal resolution using second order B-splines. This means that short-term phenomena cannot be captured by the GDAS model (e.g. transient shadows due to passing clouds). Even though these issues with GDAS data remain, the resulting weather values (particularly solar irradiation) are shown to have a reasonably good match with the monitored data. The nRMSE errors for temperature and irradiation are lower than a 17% and 12%. RMSE errors for solar irradiation are in accordance to those found in related bibliography, and estimated key instants of the daily behaviour of these variables (dawn, noon, and dusk) closely match those of the monitored data.
