# Visibility Assessment of New Photovoltaic Power Plants in Areas with Special Landscape Value
## 2 Methodology
### Accumulated Perception Time
#### 2.1.2 Calculation Process  
Suppose that along a given route, \(k\), there are \(n\) nodes or arranged observation points. The value \(APT_{i,k}\) corresponds to the sum of the values of the \(APT\) variable for all the \(n\) observation points of route \(k\), considering a new PV plant placed in cell \(i\). The stages that define the process of assessing the value of the \(APT_{i,k}\) variable are described below:  
1. Generation of the set of positions of observation points. The positions of the observation points are generated by taking equidistant nodes along the route at a distance equal to the size of the cell selected to represent the values of the \(APT\) variable. The nodes, stored in a vector layer, have an associated attribute table containing the information required for each point: the geographical coordinates, the height of the eyes of the observer above the ground, the height of the observed object above the ground, the elevation of the observation point (\(z\)-coordinate), the slope of the terrain in the direction of travel, the average speed of the observer as he/she moves from one node to the next one, and the average observation time in each node. These last values are calculated in the next two stages;
2. Evaluation of the walking speed of the observer. An observer walking along delimited routes over different types of terrain does not have a constant speed, as may occur when walking on flat terrain clear of obstacles. The observer's speed will generally be slower when walking over rough terrain with steep slopes. In order to take into account the difficulty of walking routes in rough terrain, the Modified Tobler's Function proposed by [PERSON] et al. in [36] has been used. It consists of an exponential function that provides the walking speed depending on the slope of the route section by which the potential observer is walking. This function is shown in (2), where \(ws_{n}\) is the walking speed (km/h) in node \(n\) and \(\delta_{n}\) is the angle of the terrain slope, in degrees, in the usual direction of the linker, in that node. \[ws_{n}=4.8\cdot e^{-5.3\;|0.7\tan\delta_{n}+0.03|}\qquad(\rm km/h)\] (2)  
To determine the angles of the terrain slopes \(\delta_{n}\) in the direction of travel associated with each node, the following steps are performed:  
* To each node the value that collects the DTM cell with the same coordinates is assigned. Let us call this value the \(z\)-coordinate of the node, which is stored in the attribute table;
* Knowing the difference between the values of the \(z\)-coordinate of nodes \(n\) and \(n+1\) and the distance \(d_{n}\) between them, it is easy to obtain the angle of the slope \(\delta_{n}\), when the observer moves from node \(n\) to \(n+1\). If \(\delta_{n}\) has a positive value, it is an upward slope, while if it is negative, it is a downward slope. The value obtained is stored in the register corresponding to node \(n\) in the attribute table;
* All the nodes of route \(k\) are analysed in the direction of travel, obtaining the values \(\delta_{n}\) of each node;
* The value of the real distance (\(D_{n}\)) separating nodes \(n\) and \(n+1\) is determined. The value of the distance \(d_{n}\) corresponds to the projection on the horizontal plane of the real distance \(D_{n}\);
* Then, applying the hiking function (2), the values of the observer's velocity \(ws_{n}\) at each node \(n\) are obtained and stored in the attribute table. 3. Calculation of the average observation time \(t_{n}\) in node \(n\). This corresponds to the travel time used by the walker to travel from node \(n\) to node \(n+1\) along the route k. The time \(t_{n}\) is calculated as the distance between consecutive nodes \(D_{n}\) divided by the velocity of observer \(ws_{n}\) assigned to node \(n\); \(t_{n}=D_{n}/ws_{n}\). The value of \(t_{n}\) obtained for each node \(n\) is stored in the attribute table;
4. Determination of the distance between the new PV plant and the observation point.