1. Introduction
Solar radiation is a general term for the electromagnetic radiation emitted by the Sun [
1]. It is a source of energy and significantly affects the environment, as well as geological and natural processes and the health and vitality of humans, animals, and plants [
2,
3,
4,
5]. It is also an important renewable energy source that helps sustain life on Earth. Solar energy can be actively used to generate electricity in power plants but also passively to generate electricity using photovoltaic systems on the roofs and facades of buildings. To optimize the distribution of these devices, it is necessary to know the distribution of solar radiation in the country. Because solar radiation is essential for plant growth, knowledge of its distribution also helps, for example, in planning the cultivation or protection of sun-demanding plants. In the mountain environment, it is specifically a matter of forest protection. Another application in the mountain environment, where it is necessary to know the distribution of solar radiation, is the prediction of avalanche hazards.
Solar radiation that hits the georelief is the result of a complex interaction between the atmosphere and the Earth’s surface. Its amount depends on many factors, for example, geographic location, season, time of day, local landscape, cloud cover, and other optical properties of the atmosphere [
6]. In the case of considerable vertical fragmentation of the area, direct measurements are insufficient to express the spatial and temporal variability of solar radiation incidents on the surface of the georelief [
7,
8]. Although there are thousands of solar radiation monitoring stations around the world, for most geographic areas, there is no accurate data available on solar radiation [
9]. Management of measurements in a mountain environment is even more problematic due to difficult access to rugged terrain. In situ measurements are also demanding and require a dense network of sensors. Therefore, in addition to the available measurements, it is necessary to use existing knowledge and create suitable models of solar radiation. Because modelling the influence of local weather on solar radiation modelling is very demanding and inaccurate, potential solar radiation is often calculated based on digital elevation models (DEMs) [
10,
11]. This is also due to the fact that many analyses require modelling of potential solar radiation with sufficient positional accuracy, albeit with lower temporal accuracy. In addition, for many spatial analyses, the value of solar radiation at a certain point in relation to its surroundings is often more important than absolutely accurate values in the whole area. A suitable parameter that meets these requirements is potential annual solar radiation calculated at high spatial resolution in geographical information systems (GIS).
The main spatial distribution factor of potential solar radiation is georelief, especially elevation, slope, and aspect. This paper is therefore devoted to determining the effect of the used DEM resolution, as well as the above-mentioned terrain parameters, on the calculation of potential solar radiation in GIS.
Currently, the most used software tools for the calculation of potential solar radiation are the Solar Radiation toolset implemented in ArcGIS [
12,
13] and r.sun [
14], which was designed for the GRASS GIS [
15]. Selected studies that describe the implementation of calculation of solar radiation based on 3D data are also presented in [
9]. The article [
9] states that one of the main models created in a GIS tool is Solar Analyst, developed by Fu and Rich [
16,
17,
18,
19,
20] based on a theory called SolarFlux. The model was created as a module in ArcView 3.0 software created by ESRI (Environmental Systems Research Institute) and later implemented in the ArcGIS 10 extension known as the Solar Radiation toolset [
12,
13].
Many articles have been devoted to the calculation of potential solar radiation. Some of them focus on fundamental research of the calculation of potential solar radiation [
5,
21,
22,
23,
24]; others focus on its use in various applications [
8,
25,
26,
27,
28,
29,
30,
31,
32,
33]. For example, [
8] is devoted to the calibration and validation of the ArcGIS Solar Radiation tools for photovoltaic potential determination, focusing mainly on the input atmospheric parameters, diffusivity, and transmissivity but also pointing to the importance of spatial resolution in the calculation of potential solar radiation. According to [
8], most GIS-based methods for calculating solar radiation are based on some form of geographic data, such as DEMs [
10,
11,
21,
22] or light detection and ranging (LiDAR) data [
5,
24,
25,
26,
27,
28]. These methods also use different assumptions and therefore differ in terms of accuracy and performance [
8]. For example, refs [
5,
24,
25,
28] describe tools for calculating potential solar radiation from 3D LiDAR data.
In the field of applications and uses of calculated potential solar radiation in mountain areas, the effect of solar radiation on forest damage by bark beetle attacks was described in some papers [
34,
35,
36,
37,
38,
39,
40,
41]. Specifically, in [
30,
39,
40], potential solar radiation was applied as one of the site characteristics in the determination of the probability of bark beetle attack in the Tatra Mountains. In [
30], the authors stated that potential solar radiation calculated based on the DEM better identified beetle infestations than commonly used meteorological variables. However, it should be emphasized that DEM at a resolution of 30 m (e.g., based on shuttle radar topography mission (SRTM) [
41,
42,
43]) was mostly used in those analyses.
Although the influence of the DEM resolution on the calculation of potential solar radiation is known to be significant [
8,
10,
11], it has not yet been quantified how accurate the input DEM should be or which error in the calculation of potential solar radiation would result from using a lower-quality DEM. The authors mostly point to different DEMs, which means that the results also show a difference resulting from another data source. In this study, we used only one data source and aggregated it by the average function to different resolutions. This leads to a real indication of the influence of the DEM spatial resolution on the calculation of potential solar radiation. We used an available DEM derived from LiDAR data.
Another issue is how terrain fragmentation affects the accuracy of the calculation, although we can assume that differences in potential solar radiation are more significant in mountainous environments. Therefore, the aim is also to determine the influence of terrain parameters on errors in the calculated potential radiation caused by the lower resolution of the input data. Because the values of solar radiation change most in rugged terrain, we focused mainly on the mountain environment, specifically on the Slovak side of the Tatra Mountains (the highest mountains of the Carpathians).
We assume that based on the results, we will be able to better determine in which areas it is important to use a DEM with higher resolution and where a lower resolution is sufficient to model potential solar radiation. In the experiment, we tested DEM resolutions of 5 m, 10 m, 30 m, and 90 m.
This paper is further organized as follows.
Section 2 describes the data and methods used, including a description of the study area, available data sources, the design of the experiment, and a description of the software tools used.
Section 3 presents the results of quantifying the effects of DEM resolution on the calculation of potential solar radiation, as well as correlations between terrain parameters and errors in the calculation of potential solar radiation caused by lower spatial resolution.
Section 4 provides a discussion of the results, and
Section 5 concludes the document.
4. Discussion
Based on the obtained results, we can state that the resolution of input data in the calculation of potential solar radiation in the GIS environment has a significant impact on the results, especially in areas with high absolute values of TPI calculated with small neighbourhoods (10 m–100 m). This is especially evident in high mountain areas, which contain rugged terrain. Consequently, in areas with a |TPI50| or |TPI100| greater than 10 m, we recommend applying a high-resolution DEM to calculate potential solar radiation. In this study, we used a model of potential annual solar radiation with a spatial resolution of 5 m. In addition, we calculated a model at a resolution of 2 m, which we did not include in the analyses in this study due to computational complexity and time-consuming calculations. However, it can be used for other follow-up analyses, especially in rugged terrain. The second reason is the fact that four different resolutions are sufficient to show the effect of resolution on the result. The authors of [
13] also stated that calculating insolation can be very time-consuming. Calculations for a large DEM can take several hours, and for a very large DEM, even days [
13]. Similarly, the authors of [
8] points to the high computational complexity of the calculation of potential solar radiation at a high raster resolution. In comparison, for a study area of about 1 km
2, the processing time was recorded with a standard model run of 01 m: 12 s, 06 m: 22 s, and 10 m: 7 s for 30 m, 5 m, and 0.50 m, respectively [
8]. The calculations were performed on a Windows computer with an Intel i5 processor with four cores and eight GB of RAM. It should also be emphasized that processing time increases when using shorter time intervals.
However, it should be noted that even a file size of more than 2 GB, in this case, is a significant limit. In this context, it is also important to note that the Area Solar Radiation tool is designed only for local landscape scales, where it is generally acceptable to use one latitude value for the whole area [
13]. With larger datasets, such as for states, countries, or continents, the results will differ significantly at different latitudes (greater than one degree). For this reason, it is not sufficient to use only a higher raster resolution for a calculation of a larger area. It is also necessary to divide broader geographical regions into smaller zones with different latitudes [
13]. Our analysis in the Tatra Mountains was related to the elongated shape of the area with a difference in latitude of 0.22 degrees, although with a range of longitude greater than 1 degree [
51]. In this case, the error caused by the latitude setting leads to a potential solar radiation error of as much as 4000 Wh/m
2.
The authors of [
8] argue that the default model values of diffusivity and transmissivity lead to a substantial underestimation or overestimation of solar radiation. The authors further claim that model validation is necessary because actual values cannot be defined from atmospheric data prior to model implementation [
8,
57]. The values of solar radiation from meteorological stations are certainly useful for a comparison of the values of the calculated potential solar radiation. However, even the values of the modelled potential solar radiation are sufficient to perform many spatial analyses, especially if it is not necessary to know the exact values of solar radiation but rather their local changes in the area. The values calculated based on the DEM in our study are suitable for this purpose.
Therefore, we recommend using the potential annual solar radiation model calculated in this study with a resolution of 5 m (
Figure 5a,
Supplementary Material File S1) or higher for analysis in the Tatra Mountains (see Data Availability Statement). In the case of analyses in which a lower resolution is sufficient, the values of the calculated model can be aggregated to the required lower resolution (rather than calculating potential solar radiation with a lower resolution). We would like to add that model values need to be aggregated through the average function, not resampled, as resampling leads to less reliable values.
5. Conclusions
We found and confirmed that the most significant differences in the calculation of potential solar radiation resulting from different raster resolutions are in areas with high absolute values of TPI, i.e., mountainous areas (for resolutions of 10 m, 30 m, or 90 m, values greater than 10 m lead to 4–6 times greater errors compared to errors in a flat area).
According to our analysis, more accurate values of potential solar radiation at the required resolution (e.g., 30 m) are obtained by calculation at higher resolution (e.g., 5 m) and subsequent aggregation of values by the average function.
Based on the results, we recommend:
In future research, it could be useful to compare our results with the potential solar radiation calculated on the basis of SRTM at a resolution of 30 m or other DEMs used in spatial analyses in the Tatra Mountains. Another open issue is the calculation of potential solar radiation with even higher resolution, mainly due to analyses in smaller localities requiring more detailed knowledge of solar radiation.
Although our analysis was performed in a specific area, the results may be applicable to other areas. A high-spatial-resolution model of potential solar radiation can help improve the accuracy of various geological and ecological spatial analyses.