*2.3. Study Area and Data*

Our study area is located in the central part of the city of Košice (Figure 1). The city of Košice is the second largest city in Slovakia with a population of approximately 240,000 inhabitants and an area of 242.77 km2. It is part of an agglomeration with more than 367,000 inhabitants and the Košice-Prešov agglomeration with 555,800 inhabitants is one of the largest urbanized areas in Slovakia. The city of Košice is a typical example of an urban area in a temperate climate in Central Europe. The eastern part of Slovakia, where the city of Košice is also located, is characterized by warm and relatively dry summers and cold, slightly humid winters, with average daily temperatures ranging from −2 ◦C in January to 21 ◦C in July. The average annual number of clear-sky and overcast days for the city Košice is 48 and 126, respectively [29]. Based also on this factor, an area of 4 km2 was selected, where different types of buildings are located, from administrative to residential buildings.

**Figure 1.** Location of the study area in the city of Košice, Slovakia.

The geometric 3D model of the city of Košice was derived from photogrammetric data collected by PHOTOMAP, s.r.o. company Košice. The model represents a level of detail 2 (LoD2) [30], which means that the model contains information about the basic geometry of buildings, including roofs. The 3D model itself was processed by combining data from aerial surveying and airborne laser scanning. The aerial survey imagery was photogrammetrically mapped in the PHOTOMOD software and the aerial laser scanning data were vectorized in the Ustation software. The 3D city model is stored in a shapefile vector format and consists of 61,766 polygons. A DTM with a cell size of 0.2 m was derived from LIDAR (light detection and ranging) data collected in late summer 2016 using the LEICA ALS70 airborne laser scanner.

Pyranometer MS-60 [31,32] produced by the EKO-INSTRUMENTS company was used to measure solar irradiances. The pyranometer's response time is 95% less than 18 s; the measured irradiance values are in the range of 0–2000 W/m2; and maximum measuring error is +/−18 W/m2. Measurements were taken at selected locations around 9:00 a.m., 12:00 p.m., and 4:00 p.m., local time. Two minute measurements at five s intervals were taken at the given location, then the values were averaged.

#### *2.4. Calculation of Solar Radiation*

Urban zones can be distinguished on the basis of their morphological and functional characteristics, which are often associated with specific socio-demographic and cultural features [33]. These factors play an important role in the use of solar energy, so it is important to analyze the different aspects of solar radiation distribution in urban environments. Based on these factors, 5 locations in the city of Košice were selected to demonstrate the use of the r.sun and v.sun modules, and then these locations were compared with the data from the pyranometer measurements (Figure 2). These include two buildings in the city centre (the State Theatre and the Greek-Catholic Church) and three buildings from the wider city centre of Košice, namely the Municipal Swimming Pool, the apartment house, and

the residential house. The actual measurements were carried out on the selected vertical facades of the buildings. We opted for south-facing facades at the selected locations in most cases; in one case, it was the east-facing facade. Subsequently, the measured values were compared with the calculated irradiance values by the v.sun and r.sun models. In case of the v.sun model, it can be easily identified as an attribute value for the specific polygon representing the facade. In case of the r.sun model, the identification of the site on the steeply inclined surface approximating the facade is more complicated, essentially it is a matter of a specific cell identification within the DSM. The positions of pyranometer measurements were measured by the global navigation satellite system (GNSS) using the Topcon HiPER HR. The point measurements were performed for 30 s using the real-time kinematic (RTK) positioning via weighted averaging with an overall accuracy of the fixed solution between 1 and 2 cm.

**Figure 2.** Positions of the selected locations in the city of Košice: Apartment house, Ceskoslovensk ˇ á Street (**1**); Residential house, Muránska Street (**2**); State Theatre, Hlavná Street (**3**); Municipal swimming pool, Protifašistických bojovníkov Street (**4**); and Greek-Catholic Church of the Nativity of the Virgin Mary, Moyzesova Street (**5**).

#### **3. Results**

The selected buildings have different architectures and different types of facades. We selected four south-facing and one east-facing facade. The day during which the measurements took place represents a typical summer day (23 June 2021). The measurements took place at approximately 9:00 a.m., 12:00 p.m., and 4:00 p.m., local time. Since we only had one pyranometer, we had to conduct the actual measurement between 8:30 a.m. and 9:30 a.m., since it was not possible to be at all selected locations at the same time. This was also performed for the 12:00 p.m. and 4:00 p.m. measurements. The exact times of measurements were recorded by the pyranometer. We then computed irradiances by solar models for these exact times of measurements. Using the r.sun module, we calculated raster

maps for the selected time horizons for the center of the city of Košice, which are shown in Figure 3. The calculation of solar radiation by the r.sun model is based on the DSM representing terrain and buildings. The facades are only approximated by steeply inclined surfaces. To compare the model with pyranometer measurements for the selected locations, we used their GNSS positions and identified raster cells containing the modeled solar irradiance values. The 3D distribution of solar irradiance by the v.sun model is shown in Figure 4. The model calculates solar irradiance only for polygons of the 3D city model. This means that it is much easier to identify solar irradiance for a particular facade represented by a polygon than by raster cells.

**Figure 3.** Solar irradiance from the r.sun model in the city center of Košice on 23 June 2021 (W/m2).

**Figure 4.** Solar irradiance from the v.sun model in the city center of Košice on 23 June 2021 (W/m2).

Since the real time of measurement is always recorded by the instrument, we could use the solar radiation models for these exact times to ensure the correct comparison between the values. In the following subsections, we present the results for the particular locations.
