# Visibility Assessment of New Photovoltaic Power Plants in Areas with Special Landscape Value
## 2 Methodology
### Accumulated Perception Time
#### 2.1.2 Calculation Process
\tag{4}\]  
where \(\theta f_{i,n}\) is the angle of elevation of the line of sight [38] between the observation point represented by node \(n\) and the maximum height \(H_{pv}\) of the PV facility placed in the cell \(i\), and \(\theta h_{i,n}\) corresponds to the angle of elevation of the line of sight connecting the position of the observer's eyes in node \(n\) to the global horizon beyond cell \(i\), as shown in Figure 1.  
The \(Isk_{i,n}\) index can take values between 0 and 1, and represents the value per unit of the height \(H_{pv}\) above the skyline, as seen by an observer located at node \(n\). When the whole facility (in terms of height) is below the skyline \(Isk_{i,n}\) takes a value of 0, on the other hand, when the entire facility is above the skyline \(Isk_{i,n}\) takes a value of 1. To evaluate \(Isk_{i,n}\) it is necessary to determine the elevation angles \(\theta h_{i,n}\) and \(\theta f_{i,n}\) beforehand, as follows:  
* First, we assume that observers can look in any direction, so it is necessary to determine the horizon line around each observation point or node \(n\), whose geographical coordinates are known. That is, the horizon height \(\theta h_{i,n}\) must be evaluated for observer azimuth values from 0 to 360 sexagesimal degrees. The observer's azimuth refers to the angle, measured on the horizontal plane, formed by the direction in which the observer is looking with respect to a reference direction. In our work, the azimuth value was 0 degrees when the observer was facing east and 90 degrees when facing north. After applying GIS tools, the result obtained, for each node \(n\), is a raster dataset in which each cell \(i\) contains the value of the elevation angle \(\theta h_{i,n}\) of the line of sight connecting the observer's eyes in node \(n\) to the global horizon beyond the area represented by the cell \(i\). Consequently, all cells with the same azimuth value, will also take the same value of \(\theta h_{i,n}\);
* To obtain the elevation angle \(\theta f_{i,n}\), visibility analysis GIS tools are applied at each node \(n\). As result, a raster dataset is obtained in which each cell \(i\) contains the value of the elevation angle \(\theta f_{i,n}\) of the line of sight connecting the observer's eyes in node \(n\) with the highest part of the possible PV facility placed in the cell \(i\);
* Subsequently, by means of raster data layer processing techniques (map algebra) the \(Isk_{i,n}\) index is determined using the expression (4). For a single observer in node \(n\), the value of \(APT_{i,n}\) in cell \(i\) will take the value resulting from the product of the visibility height factor \(fhy_{i,n}\), the weighting factor \(w_{i,n}\) as a function  
Figure 1: Lines of sight connecting the observer, in node n, to the PV facility and to the horizon. of distance \(d_{i,n}\), the average observation time \(t_{n}\), and the term \((1+Isk_{i,n})\). This last term has been introduced in order to give a higher degree of visibility to facilities that can be seen above the skyline. We have applied this methodology to routes that are mainly taken by walkers in periods of good weather with clear skies and high colour contrast (spring, summer and autumn seasons). Therefore, the visibility of the fraction of the PV plant that can be seen above the horizon line has received twice as much weight as the rest of the facility. The \(APT_{i,n}\) calculation process is shown in Figure 2.  
Taking into account the average annual number of observers that can circulate through node \(n\) of route \(k\) (\(NOY_{k}\)), the cumulative value of \(APT_{i,n}\) will be given by the expression (5). \[APT_{i,n}=NOY_{k}\cdot fhv_{i,n}\cdot w_{i,n}\cdot t_{n}\cdot(1+Isk_{i,n}) \hskip 28.452756 pt(\text{hours/year}) \tag{5}\]  
Figure 2: \(APT_{i,n}\) calculation flow-chart for PV plant placed in the area represented by cell \(i\), and observers in the position represented by node \(n\).