# Evaluation and Comparison of Spatial Clustering for Solar Irradiance Time Series
## 7 Conclusions and Perspectives  
The objective of this paper was to cluster several sites located in Spain according to solar radiation characteristics (quantitative and qualitative), with an objective to improve the forecasting of the solar irradiations. The novelties of this paper are not in the clustering methods, because the four methods used are well-known, but in the used parameters to qualify each meteorological station. Particularly, the use of the Hurst coefficient, and mainly the forecastability one, is original. Each cluster groups the stations not according to the solar radiation potential only, as this has been already achieved for some sites over the World and is useful, as an example, for agricultural applications, but, and above all, it regroups the stations from the solar-radiation-variability point of view, i.e., from the qualitative viewpoint. It is essential to know that this variability in energy studies and this clustering will be useful for the elaboration of forecasting model based on time series and machine-learning methods. The quality control of solar irradiation data provided by almost a hundred meteorological stations used in irrigation works was first realized during the study period 2017-2020. It allows us to be sure that the numerous data (more than 5 million GHI data) used in this work are relevant. After this quality control, 76 stations were then selected. In calculating the clearness index to know the clear-sky solar irradiance, the [PERSON] McClear model was used and previously verified; it appeared that its accuracy, when applied to our data, was high. Firstly, each station was characterized, from a solar-radiation-variability point of view, by six parameters, including both static and dynamic ones: mean, standard deviation, skewness, Kurtosis, Hurst exponent, and forecastability coefficient. The dependence between these six parameters was then studied by using [PERSON]'s Rank Correlation  
Figure 20: Various steps of the methodology. Coefficient, and the results showed a high dependency between some of them; consequently, based on the parsimony principle and to avoid the redundancy of the information, only the mean, Hurst exponent, and forecastability coefficient were used to characterize each meteorological station. From these descriptors, the stations were grouped by similarity (the shortest distance between descriptors), using the following algorithms: k-means, k-medoids, and spectral and hierarchical clustering to identify geographical areas with similar solar irradiation characteristics at a low time step (half an hour). The clusters were compared with each other and the well-known Koppen-Geiger climate classification. The possible relationship between the Koppen classification and the number of clusters in which these time series can be grouped was analyzed. For both cases (five classes and three classes), the hierarchical clustering algorithm is the closest to the Koppen classification. However, it is probably not the most interesting to test, as it is a more complex method with the same (similar) results as a naive clustering method. When evaluating the performance of the clustering algorithms, it can be concluded that there is no interest in simultaneously implementing k-means and spectral clustering since the results are similar in more than 90% for classes three and five. The results shown in this study could be used to improve GHI prediction through the time-series formalism and machine learning in the following cases:  
* To select to predictor considering that a method efficient on a meteorological site can be applied with the same efficiency of all the sites of the same cluster (i.e., with the same solar radiation variability or evolution);
* To make a forecast on a site where a GHI measurement device has just been installed.