# Simulation of Wind Speeds with Spatio-Temporal Correlation
## 1 Introduction  
The electricity needs in daily life are assorted, and there are countless actions that consumers carry out daily, such as turning on lights, charging electronic devices or cooking [1]. Moreover, electricity production across the world has a growing perspective due to several causes, among which the new trend to use electric vehicles can be mentioned [2].  
The negative impact of fossil fuel gas emissions on human health and also on the planet health raises the awareness about the harmful effects of such emissions [3], and due to this, different countries have agreed to limit global warming to a value lower than 2 \({}^{\circ}\)C concerning preindustrial era [4]. To ensure the compliance of greenhouse gas emissions reduction into the atmosphere, the European Union has published a guide showing different scenarios [5]. All of them involve an increasing trend in the use of renewables, as all hypotheses show that most of the energy supply in 2050 will be generated using renewables, and the energy transition from fossil fuels to them constitutes a problem of world concern [6]. Specifically, wind energy prevails both in the current market and in the future production trends, foreseeing a doubling of installed capacity in the next ten years in the most conservative case [7], mainly due to the low cost of wind energy produced in large wind farms. This cost can be lower than 0.05 $/kWh in the locations with the highest mean wind speed values [8].  
Renewables depend on the variability of weather conditions. In the case of wind energy, the behavior of the primary resource, i.e., the wind, can be considered stochastic. However, in a given location, a set of measured wind speeds along a certain period can be described using some probability distribution [9], and the Weibull distribution is one of the most recommended and used for such a purpose [10, 11, 12].  
The characterization of wind speed is achieved by measurements, and there are factors that can make it difficult to proceed, such as the presence of adverse weather conditions,meter errors, lack of measurements due to maintenance periods or communication problems. In addition, it can happen that the accuracy of the measurement devices is not as good as expected, and this can result in an alteration of the values of the collected data [13; 14]. Additionally, in general, the wind speeds are measured at a given height that does not necessarily coincide with those of the wind turbine hubs [15; 16; 17]. These problems must be solved with the aim of accuracy since it is a critical factor when planning power generation [18; 19]. By studying wind speed simultaneity in different locations, it is possible to obtain the wind energy production at each period in an easier way using traditional methods [20; 21; 22]. Thus, from the dependence on the wind speeds between nearby places, the problem can be reduced to calculate the probability in each scenario [23].  
Analyzing the spatial correlations, the relationships between the wind speeds in different locations can be established. In this way, gaps that arise due to errors in the meter or in data capture can be covered, i.e., periods in which the data are not available, obtaining an accurate wind speed value in each moment and, in turn, of the power injected into the electrical network [24; 25]. If temporal correlations are also calculated, it is possible to characterize the resource in a later gap, being able to anticipate possible errors and assuring a reliable wind speed value [26; 27; 28].  
This paper is organized as follows: a methodology to solve the problem is presented in Section 2; the case study is described in Section 3; the results obtained are shown in Section 4, and the conclusions are outlined in Section 5.