# Visibility Assessment of New Photovoltaic Power Plants in Areas with Special Landscape Value
## 2 Methodology
### Accumulated Perception Time  
#### 2.1.1 Required Data  
The calculation of the hours per year, represented by the _APT_ variable, takes into account increasing or decreasing factors. These factors include the distance between the observation point and the cell in which the proposed PV plant is located, the fraction of the PV plant that can be seen from the observation point, and the fraction that can be seen above the skyline. For the evaluation of the _APT_ variable, it is necessary to consider aspects such as:  
* Orography: Hills and depressions ensure that PV power plants remain hidden from the eyes of observers. In other areas, PV power plants can be fully or partially visible and some of their elements can be seen above the skyline, which increases their visibility. The orography is considered in a GIS using the digital elevation model (DEM) of the study area. The DEM is the digital representation of the elevation of the earth's surface with respect to a reference. Specifically, DEMs are a set that include digital terrain models (DTMs) and digital surface models (DSMs). DTMs represent the elevation of bare ground, while DSMs represent the elevation of the land surface, including obstacles not exclusively associated with terrain orography such as trees, vegetation, buildings, and other natural or artificial objects [30]. In this work, in order to consider visual obstacles on the ground, we have used a DSM of the analysed area. Different DSMs could also be used, as the density of vegetation can change over the seasons;
* Observation points: These represent the places where potential observers in motion can be located at a given time. These points are represented in a vector layer and have an associated attribute table containing the following data: geographic coordinates, height of the observer's eyes above the ground, height of the observed object above the ground, observation point elevation (\(z\)-coordinate), slope of the terrain in the direction of travel, and travel speed of the observers. From the speed value, it is possible to calculate the average observation time of the observers, as will be discussed in detail later in this section;
* Average annual number of observers travelling along the observation points of a given route;
* Colour contrast of the observed object with respect to the background. According to [31], objects with a higher colour contrast will have greater visibility than objects with a low contrast, therefore it is necessary to introduce a weighting factor as a function of this colour contrast of the facility;
* Distance between the observer and the observed object (proposed PV plant). According to [32], the visual acuity of the human being decreases with distance, therefore it is necessary to enter a weighting factor as a function of this distance. Some works published in the scientific and technical literature consider this distance in models of viewshed analysis. [PERSON] in [33] proposes the use of fuzzy functions, the values of which decrease with the distance between observer and observed object. In the methodology used in this work, we have taken a similar approach, but we use a weighting function, shown in (1), with factors that have been adjusted taking into account both the height of the observed object and the loss of human visual acuity with distance, using logarithmic functions. This weighting function was used by [PERSON] in 2007 [34], improving the proposal of [PERSON] in 2004 [35]. The weighting factors are limited by distance in three different perception zones as:  
\[\left\{ \begin{array}{c}w=0.3\;\;for\;\;d\leq 57.5\\ w=\frac{-0.0638\cdot\ln(d)+0.59}{1.105}\;\;for\;\;57.5<d<10,000\\ w=0\;\;for\;\;d\geq 10,000\end{array} \right. \tag{1}\]  
where \(w\) represents the weighting factor, which can take values between 0 and 0.3, and \(d\) represents the distance, in meters, between the observer and the observed object. In this work, we have assumed that the potential observers are moving at the average speed of a walking human being.