**5. Conclusions**

Solar energy is one of the most important renewable sources of energy. Therefore, it is desirable to model solar radiation in detail, especially in urban areas. There are currently several models that seek to model more accurately the distribution of solar radiation. Such models include r.sun and v.sun, which we analyzed in our study. They have the advantage of choosing parameters for spatial modeling, while working with spatially differentiated input and output data in raster/vector format. Both models use the same solar radiation component; however, they treat the geometry of input data differently. The results of both models were validated by in situ pyranometer measurements. The comparison of the results of individual models and measurements took place in locations that represent a typical urban environment in the study area. In addition to apartment buildings, with a relatively simple surface geometry, there are often historic buildings in the center with a more complex morphology of facades. By selecting different types of structures, we identified the shortcomings of individual models as well as input data.

The comparison of models and in situ measurements showed relatively good estimates by the 3D v.sun model and poor estimates by the 2D r.sun model. This can be attributed to an improper geometric representation of vertical surfaces by a DSM, which has a strong impact on solar resource assessments of the model. We also found that the LoD2 3D city models can be problematic in case of complex buildings with morphological structures, such as terraces. These cast shadows on facades especially when solar altitude is high and thus assessments even by the 3D model are inaccurate.

Nevertheless, both solar radiation models can be used effectively for solar resource assessments when used properly. The drawback of the v.sun model is that it does not provide estimates of solar radiation for urban greenery, which is often important part of urban areas. Our results also showed that the r.sun model is not able to accurately represent the spatial distribution of solar radiation on vertical surfaces, but its simplicity and speed provide a major advantage in modeling horizontal surfaces, such as roofs of buildings. The vector solar model v.sun proved to be a more suitable alternative for use in a 3D environment, based on its vector-voxel approach and its ability to model even vertical surfaces.

Our analysis can be helpful for solar resource assessments in urban areas using these solar radiation models or other solar radiation models with implemented similar methodology based on DSM and 3D city models. We see a great potential in integration with other areas of research and industry, for example for thermal and photovoltaic applications. We also envisage the use of these models in urban planning, and also in addressing the issue of urban heat islands.

**Author Contributions:** Conceptualization, Š.K. and J.H.; methodology, Š.K. and J.H.; software, Š.K., J.H., J.B. and J.Š.; validation, Š.K., J.H. and J.Š.; formal analysis, Š.K., J.H., J.B. and J.Š.; investigation, Š.K., J.H., J.B. and J.Š.; writing—original draft preparation, Š.K. and J.H.; visualization, Š.K.; supervision, J.H.; project administration, J.H.; funding acquisition, J.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research was funded by the Slovak Research and Development Agency (APVV) under the contract No. APVV-18-0044 and by the Scientific Grant Agency of the Ministry of Education, Science, Research, and Sport of the Slovak Republic and the Slovak Academy of Sciences (VEGA), under the contract No. 1/0300/19.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy reasons.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

### **References**

