# Evaluation and Comparison of Spatial Clustering for Solar Irradiance Time Series
## 1 Introduction
To ensure broader variation in cloud movements, neighboring stations were used that were selected by using a dynamic time warping (DTW)-based similarity score. The method is very interesting, although complex. The proposed model achieved 19.74% less nRMSE compared to the benchmarks. The majority of the papers presented above propose methods and modes of validation crucial for the clustering of solar radiation; however, they are limited, for the most part, to a single-criterion study most often relating to a geographical criterion and daily and monthly data (time step not really interesting in practice for solar applications). In order to address these limitations, we propose to develop a new methodology, particularly by studying non-geographical parameters and statistical parameters revealing the dynamics of each hourly or intra-hourly clear-sky index time series. Various techniques of clustering [30] are applied to group the meteorological stations by \"solar radiation affinities\", i.e., to group by similarity or proximity criteria according to the static and dynamic characteristics of the time series. Clustering is not an exact science; totally contradictory results can be linked to the use of poor-quality measures. It is therefore essential, in the field of solar engineering, in addition to stating this characteristic, to identify, quantify, and correct possible problems. The various steps of this work are as follows (rarely are all of these steps studied in the same paper):  
* To evaluate the quality of the data provided by the meteorological stations because the measure of solar irradiation is often accompanied by errors due to pyranometer calibration, surrounding effects, or data-acquisition-system failure;* To determine the best descriptors of static (e.g., descriptive statistics measures) and dynamic (e.g., Hurst exponent (H), forecastability coefficient (F), etc.) characteristics of the series and to determine the redundancy of these descriptors;
* To implement clustering algorithms such as k-mean, k-medoids, spectral, and hierarchical clustering;
* To compare the clusters obtained by each method with each other and the well-known Koppen classification, characterizing the areas according to climate, solar irradiation, precipitation, and temperatures. The paper continues as follows: Section 2 implements tools that analyze the accuracy and quality of the measured data; Section 3 evaluates the best criteria to characterize solar time series; Section 4 presents the Koppen climatic classification and the clustering methods that are implemented on the solar irradiance time series; Section 5 implements some clustering algorithms and compares the clustering results; at last, in Sections 6 and 7, the perspectives of the work are described and conclusions are drawn, respectively. The major contributions of the paper are as follows:  
* The objective of the clustering is to improve the efficiency of the forecasting of the solar radiation; the objective was found only in one reference [29];
* The utilization of several parameters to characterize each site;
* The utilization of dynamic parameters to characterize each meteorological station: Hurst exponent already used for other meteorological time series but not for solar irradiances, and mainly the forecastability coefficient, which is a new concept--the utilization of several clustering methods and their comparison between them and with the well-known Koppen classification (upgraded for Spain).