# Simulation of Wind Speeds with Spatio-Temporal Correlation
## 4 Results
### Simulation
#### 4.2.2 Three Locations Relationship  
Once obtained the wind speed correlations for two locations, the behavior of the algorithm is evaluated for the case of three places. In this case, the algorithm calculation time in the simulation stage is 1 day, 23 h and 15.53 min in 3,999,039 iterations. As before, the calculation time in the simulation stage is much higher than the respective in the modeling stage, and, as occurs in the analysis of 3 locations in the modeling phase, the computation time is larger than in the case of 2 places.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Correlation** & **Cholesky Results** & **Iterative Algorithm Results** \\ \hline Pearson’s correlation & 0.2210 & 0.2240 \\ Autocorrelation 1 & 0.0097 & 0.9132 \\ Autocorrelation 3 & -0.0036 & 0.9131 \\ Cross-correlation 1–3 & 0.0006 & 0.2200 \\ Cross-correlation 3–1 & -0.0015 & 0.2166 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Obtained correlations in the simulation stage for the study with Fragavella, 1, and Lanzos, 3.  
Figure 8: Evolution of the data deviation to the real solution through time in the simulation stage: (**a**) study considering Fragavella and Labrada, (**b**) study considering Fragavella and Lanzos.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Correlation** & **[PERSON] Results** & **Iterative Algorithm Results** \\ \hline [PERSON]’s correlation & 0.8072 & 0.8218 \\ Autocorrelation 1 & -0.0083 & 0.9240 \\ Autocorrelation 2 & -0.0025 & 0.9235 \\ Cross-correlation 1–2 & -0.0041 & 0.7974 \\ Cross-correlation 2–1 & -0.0041 & 0.7967 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Obtained correlations in the simulation stage for the study with Fragavella, 1, and Labrada, 2.  
As can be seen in Figure 9, the behavior of the data deviation between the required solution and the calculated one in each iteration along the time is similar to that previously studied in the case of 2 sites, a few hours with a fast decrease in this case, up to 8 h, and then a refinement of the solution to the marked tolerance. On the other hand, comparing it with Figure 8, it can be seen that the initial solution is further away from the desired one in the case of 3 sites concerning any of the studies of 2 locations, this having an impact on both the calculation time and the number of iterations required to achieve the desired values.  
Table 11 shows the results of the correlations obtained with the application of the proposed algorithm for 3 locations. Like before, after the random series correlation given by Equation (16), the spatial correlations are very close to those corresponding to the objective solution. However, the temporal ones are around the value 0. The algorithm remains very precise with the consideration of 3 sites, so the differences between the objective results and those obtained with the simulation are lower than 5% in each of the cases.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Type of Correlation** & **Cholesky Results** & **Iterative Algorithm Results** \\ \hline [PERSON]’s correlation 1–2 & 0.8071 & 0.8219 \\ [PERSON]’s correlation 1–3 & 0.2222 & 0.2228 \\ [PERSON]’s correlation 2–3 & 0.3165 & 0.3161 \\ Autocorrelation 1 & 0.0031 & 0.9250 \\ Autocorrelation 2 & 0.0081 & 0.9245 \\ Autocorrelation 3 & 0.0050 & 0.9213 \\ Cross-correlation 1–2 & 0.0094 & 0.7974 \\ Cross-correlation 2–1 & 0.0033 & 0.7965 \\ Cross-correlation 1–3 & 0.0068 & 0.2202 \\ Cross-correlation 3–1 & 0.0058 & 0.2165 \\ Cross-correlation 2–3 & 0.0037 & 0.3101 \\ Cross-correlation 3–2 & 0.0056 & 0.3078 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Correlations obtained in the simulation stage for the study performed between Fragavella, 1, Labrada, 2, and Lanzós, 3.  
Figure 9: Evolution of the data deviation to the real solution through time in the simulation stage with the consideration of the locations of Fragavella, Labrada and Lanzós.