**1. Introduction**

The majority of the human population is located in cities, where, in developed countries, about 80% of the population lives [1]. This contributes to problems associated with dense urban areas, such as urban heat island effects, which ultimately lead to a higher energy demand, but also to higher production of unwanted exhalants and emissions. Moreover, the use of solar energy helps to mitigate various environmental problems and improve the quality of life in the cities. Solar thermal or photovoltaic applications are very common around the world and have become an important factor in the overall energy production mix in many countries. Therefore, it is increasingly important to know the solar resource potential of urban areas.

Solar radiation in urban areas is a key input factor in many urban energy models and sustainable city designs. Examples include thermal and photovoltaic applications, passive heating systems, or urban microclimate designs [2–4]. The implementation of distributed photovoltaic systems transforms the urban environment from a place of energy consumption to a place of energy production. Distributed solar systems are scalable at a micro-scale and open up new investment opportunities for electricity production within the city, allowing consumers to become producers. The changes, associated with rapidly expanding solar benefits in cities, are expected to have disruptive impacts on urban electricity infrastructures and related institutions, and will require tools to evaluate and plan for future changes.

The increasing availability of three-dimensional (3D) city models and high-resolution geospatial data stimulated solar resource assessments for urban areas [2,5–7]. Currently, there are several well-developed models of solar radiation distribution, such as the r.sun

**Citation:** Koleˇcanský, Š.; Hofierka, J.; Bogl'arský, J.; Šupinský, J. Comparing 2D and 3D Solar Radiation Modeling in Urban Areas. *Energies* **2021**, *14*, 8364. https://doi.org/10.3390/ en14248364

Academic Editor: Marcin Kami ´nski

Received: 10 November 2021 Accepted: 9 December 2021 Published: 11 December 2021

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model by Hofierka and Šúri [8], the Solar Analyst model in the ArcGIS program [9], the Perez model [10], the SORAM model [11], SURFSUN3D [12], and the SOL model [6], often used for solar radiation assessments in urban areas. Hofierka and Zlocha [5] developed v.sun, a 3D version of the r.sun model for 3D city models. Freitas et al. [6] pointed out that 3D solar radiation modeling that includes vertical surfaces, such as facades, is very time consuming if applied to large cities. The data must include topologically correct 3D vector data that usually require manual editing and verification of 3D polygon orientation represented by a normal vector. A frequent solution to the problem is the use of a highresolution digital surface model (DSM) approximating vertical surfaces, such as facades, by quasi-vertical surfaces [13]. This introduces an error in solar radiation estimates for vertical surfaces. To date, no in-depth analysis has been published that assesses whether this approximation is acceptable.

Nevertheless, the previously predominant two-dimensional (2D) solar radiation models, such as the r.sun model [8], are gradually being augmented by 3D solar radiation models that allow a better representation of vertical surfaces (building facades) while facilitating interactive assessment of PV potential in complex urban environments [12,14–16]. Technological advances provide new opportunities for complex 3D approaches in solar modeling [17].

The main objective of this study is to compare the results of 2D r.sun and 3D v.sun solar radiation models implemented in GRASS GIS [18] with field measurements by a pyranometer for the city of Košice in eastern Slovakia to demonstrate the applicability of 2D vs. 3D approaches in assessing the solar resource potential in urban areas. Therefore, five locations are selected with morphologically diverse buildings still typical for this urban area. The measurements and solar radiation modeling were carried out during a typical summer day (23 June 2021) for three different time moments. The solar radiation values were calculated for the time of measurements using the r.sun and v.sun modules integrated in the open-source GRASS GIS software. By comparing the r.sun and v.sun models with the measurements, we demonstrate the accuracy of the models specifically for selected building facades.
