*3.1. Apartment House*

The first location is situated in the wider center of Košice in Ceskoslovensk ˇ á streetapartment house (Figures 1 and 2). The facade faces the east. At 8:26 a.m., we recorded a value of 663 W/m2, which is the highest value of all measured objects at that time (Table 1). This is evidently due to the fact that the facade itself is oriented to the east, so solar irradiance is higher than in other south-facing facades or even on horizontal surfaces. The v.sun model gave us a value of 581 W/m<sup>2</sup> (Figure 5A), and the r.sun model calculated a value of 40 W/m2. The value from the r.sun model was read on a nearly perpendicular building facade represented by a high-resolution DSM. However, the facade approximation in this relatively tall building, apparently, led to geometric deformations that prevented a correct calculation of solar irradiance. Figure 5A shows that in the morning facades receive more solar irradiance than flat, horizontal rooftops.

**Table 1.** Solar irradiance at the apartment house in Ceskoslovensk ˇ á street in W/m2 on 23 June 2021.


**Figure 5.** Solar irradiance at the apartment house from the v.sun model on 23 June 2021 (W/m2) at (**A**) 8:26 a.m., (**B**) 11:25 a.m., and (**C**) 3:13 p.m. The black circle represents the measurement location.

At 11:25 a.m., the measured facade value dropped to 249 W/m<sup>2</sup> compared to the morning measurement. A similar decrease can be observed in the v.sun value (396 W/m2). This decrease in solar irradiance is due to its facade orientation. The r.sun value still shows a low value due to an improper geometric representation of the facade by the particular raster cell. Figure 5B clearly shows that, at this time, solar irradiance is the highest at the rooftops as well as south-facing facades.

At 3:13 p.m., we recorded a value of only 72 W/m2. This indicates that the site was already shaded. With the v.sun model, we recorded a value of 180 W/m2, and r.sun calculated a value of 952 W/m2. The v.sun model probably records a small amount of beam irradiance, whilst the r.sun model shows a completely opposite value to the morning and noon values and confirms the problem with the accuracy of geometric representation of the facade. At this time, the rooftops receive a relatively large amount of solar irradiance (Figure 5C).

#### *3.2. Residential House*

The second analyzed location is a residential house in Muránska Street. It is a classic two-story house in the wider center of Košice. In this case, we selected a south-facing facade. The value measured by the pyranometer at 8:39 a.m. is 458 W/m2 (Table 2), which is more than 200 W/m<sup>2</sup> less compared to the previous location (Table 1). In the morning, east-facing facades receive more solar irradiance than south-facing facades. We recorded a value of 372 W/m2 with the v.sun model and 574 W/m2 with the r.sun model (Figure 6A). Both values vary from the measured value, but they are still reasonable.


**Table 2.** Solar irradiance at the residential house in Muránska street in W/m2 on 23 June 2021.

**Figure 6.** Solar irradiance at the residential house from the v.sun model on 23 June 2021 (W/m2) at (**A**) 8:39 a.m., (**B**) 11:34 a.m., and (**C**) 3:59 p.m. The black circle represents the measurement location.

The value recorded by the pyranometer at 11:34 a.m. is slightly higher (549 W/m2) than that recorded in the morning. In June, during the noon, the sun altitude is high, so the solar incidence angle is lower for facades than for rooftops, leading to lower solar irradiance values (Figure 6). Both the v.sun and r.sun models also show maximal values, albeit the v.sun estimate is very close to the measured value (514 W/m2). At 3:59 p.m., the value recorded by the pyranometer (188 W/m2) was significantly lower than that recorded in the morning, and a similar value was predicted by the v.sun model (164 W/m2). The r.sun prediction is almost four times higher than the actual value (709 W/m2).

#### *3.3. State Theatre*

The third location in our study is the State Theatre right in the center of the city of Košice on Hlavná Street. It is a building constructed in the Neo-Baroque style, which corresponds to its rather structured and complicated architecture (Figure 7). The value measured by the pyranometer at 8:57 a.m. was 413 W/m2, which is almost 260 W/m2 less compared to the first location facing to the east (apartment building), but similar to the residential house. The recorded value was quite accurately modeled by both models: v.sun (317 W/m2) and r.sun (456 W/m2) (Table 3).

**Figure 7.** Solar irradiance at the State Theatre on 23 June 2021 (W/m2) at (**A**) 8:57 a.m., (**B**) 11:50 a.m., and (**C**) 3:31 p.m. The black circle represents the measurement location.


**Table 3.** Solar irradiance at the State Theatre in W/m2 on 23 June 2021.

The value recorded by the pyranometer at 11:50 a.m. is 505 W/m2. This can also be attributed to the architecture of the building mentioned above, but also to the position of the Sun in the sky at that moment in time. The v.sun model showed almost an identical value. From this point of view, we can conclude that the comparison of the results is very accurate at this point in time at this location.

The measurement at 3:31 p.m. recorded a value of 87 W/m2. The v.sun model calculated a significantly higher value (293 W/m2) as did the r.sun model (287 W/m2). This can be explained by the fact that, during the measurement at the given place at 3:31 p.m., the sun was slightly shaded by a cloud.

### *3.4. Municipal Swimming Pool*

The fourth location that we will compare is the Municipal Swimming Pool in the Protifašistických bojovníkov Street. The building itself is a morphologically complex structure made up of the swimming pool itself, but also other institutions that are housed there. The measurement at 9:19 a.m. showed a value of 502 W/m2; the r.sun and v.sun models showed slightly different values (579 W/m<sup>2</sup> and 386 W/m2, respectively), which can be considered acceptable (Figure 8) (Table 4).

**Figure 8.** Solar irradiance at the Municipal Swimming Pool on 23 June 2021 (W/m2) at (**A**) 9:19 a.m., (**B**) 12:09 p.m., and (**C**) 3:47 p.m. The black circle represents the measurement location.


**Table 4.** Solar irradiance at the Municipal Swimming Pool in W/m2 on 23 June 2021.

The measurement recorded at 12:09 p.m. is much lower (155 W/m2) and in comparison to predicted values by the v.sun and r.sun models (513 W/m2 and 819 W/m2, respectively). However, this fact has a logical explanation. During the actual measurement at that time, we noticed that there was a terrace above the measured facade (Figure 9), which caused a shadow at the time of the measurement since the solar altitude was very high. However, the terrace is not present in our 3D city model and DSM, so the solar radiation models do not reflect this fact in the results. At 3:47 p.m., we have already measured a slightly lower value at this location than at noon (97 W/m2); a similar value was calculated by the v.sun (170 W/m2). The r.sun model again predicted a very high value (760 W/m2), probably due to a DSM distortion at this site.

**Figure 9.** Location of the terrace on the Municipal Swimming Pool building: (**A**) real state of the building with terrace (white rectangle); (**B**) geometric 3D model, missing the terrace (white rectangle). The black circle represents themeasurement location.
