**4. Discussion**

The modeling and use of solar radiation in urban environments are an important area of study in various scientific fields and disciplines, especially for solar resource assessments, such as photovoltaic and thermal applications, as well as urban heat island effects. Over the last decade, several studies have focused on this matter [34–36]. In this study, we focused on the accuracy of 2D (r.sun) and 3D (v.sun) solar radiation models for facades in built-up areas in comparison with field measurements using a pyranometer.

We selected five different buildings in locations in the wider center of Košice, which are shown in Figures 1 and 2. The measurements were carried out during a typical summer day (23 June 2021) for morning, noon, and afternoon time horizons, using the EKO-INSTRUMENTS MS-60 pyranometer during 2 min measurements in 5 s interval. The averaged value for each location was used in a comparison with the predicted values by the r.sun and v.sun models.

The results showed relatively large differences in the measured and predicted values of solar irradiance. The mean error and mean absolute error of all predictions are −22 W/m2 and 103 W/m2 for v.sun, respectively, and −219 W/m2 and 345 W/m2 for r.sun, respectively. Evidently, the 3D v.sun solar radiation model predicted solar irradiances on vertical surfaces with much better accuracy. The 2D r.sun solar radiation model failed to accurately predict solar irradiances in most cases, mostly due to an improper geometric representation of facades by a DSM. High sensitivity of the solar radiation model to input parameters, such as slope steepness or aspect, explains poor results of the model. Nevertheless, the model can provide acceptable results for rooftops and areas between the buildings. However, our results clearly show that a DSM does not provide a sufficiently accurate approximation of vertical surfaces in urban areas to estimate their solar resource potential with an acceptable accuracy.

This study also showed that the morphological complexity of buildings can affect the solar assessments, even in a 3D approach, because currently many 3D city models are available in a LoD2 accuracy with missing morphological structures, such as terraces, casting shadows, especially when solar elevation is high (Figure 9).

It should be noted that this analysis was carried out for selected buildings only and we did not include a complex analysis of shadows cast by neighboring buildings nor trees. This could affect some of the predicted values, especially in the morning and afternoon that have lower solar elevations.

In the manner of every other model, the r.sun/v.sun models have their advantages and disadvantages. The v.sun module can compute a 3D solar radiation for buildings represented by a 3D city model, but the disadvantage is its complicated preparation in terms of structure and topology. Another disadvantage is that it cannot account for vegetation, and this is an area for future improvements. The advantage of the r.sun model is a very simple preparation of input data for raster map calculations, which is easier and faster than for the v.sun model. To conclude, the r.sun solar radiation model should be only used for 2D surfaces, such as roofs and areas between buildings, while the v.sun solar radiation model is more appropriate for buildings, including facades, or other vertical surfaces represented by 3D polygons.
