# Advances in Simulating Radiative Transfer in Complex Environments
## 3 Results and Discussion
As solar radiation at 13:00 originates from the south being at the left-hand side of the model area, shortwave reflected radiation coming from upper wall parts is modeled to be received in urban canyons at pedestrian level on the left-hand side of glass-facade buildings. The total amount, however, is comparatively low, as solar radiation is mostly reflected upwards from soil or roof surfaces and is, thus, included in the lower hemisphere values. Besides the primary reflection from wall surfaces, secondary reflected radiation can be found in Central Park, where primary reflected solar radiation from soil surfaces and grass is secondarily reflected downwards by tree canopies. In contrast to the massively differing radiation patterns, at first glance, we only find small discrepancies in potential air temperature results for a horizontal cut at pedestrian level at 13:00 between AVF and IVS (Figure 8a). In general, IVS features slightly lower values of around 0.2-0.4 K. However, we find distinct differences between AVF and IVS in parts where high discrepancies of secondary radiation fluxes were observed. Especially the cooler regions in the southern/left part of the model area are more pronounced in IVS, as they receive less emitted longwave and less reflected shortwave radiation due to the shadows of larger skyscrapers next to them. Figure 5: Comparison of proof-of-concept simulation results between AVF and IVS for longwave radiation received from the lower hemisphere at 13.00 in a height of 1.5 m (**a**) and in a height of 82.5 m (**b**), respectively. Analysis of MRT corroborates that by showing even larger deviations between AVF and IVS for the same height and timestep (Figure 8b). According to the radiation patterns the MRT is based on, MRT also features a wider range of values in IVS. To address the magnitude of urban heat stress and the effects of mitigation strategies properly, thermal comforts indices are often used as holistic indicators in urban environments. These indices take several parameters such as air temperature, humidity, wind speed, and MRT into account [54; 55]. In this study, the thermal comfort index PET is used representing a commonly used index for outdoor environments of temperate climate zones [56; 57; 58]. When analyzing PET in Figure 8c, we find that major patterns are the same between AVF and IVS. However, the range is again wider and more differentiated in IVS simulation. As discrepancies in wind field and humidity are assumed to be marginal by the use of different radiation schemes and as temperatures are shown to be only slightly different in Figure 8a, deviations are mainly based on the differences in MRT patterns, which are in turn a key factor for thermal comfort and, thus, PET calculation. These findings agree with the analysis of nighttime results shown in Figure 9. Long-wave radiation emissions are based on the object temperatures. During nighttime, these surface temperatures of soils, buildings, and plants are influenced by their thermal properties, which specify their behavior in storing and releasing heat, as well as the amount of solar radiation that has or has not been received during daytime. As both of these parameters vary massively over the model area, simulated surface temperatures and, hence, longwave radiation patterns should differ as such. However, only in IVS, these very  
Figure 6: Comparison of proof-of-concept simulation results between AVF and IVS for reflected shortwave radiation received from the lower hemisphere at 13.00 in a height of 1.5 m (**a**) and in a height of 82.5 m (**b**), respectively. fine and distinct patterns of emitted longwave radiation from the lower hemisphere are recognized for both urban canyons as well as Central Park in the horizontal cut in 1.5 m height at 03:00 (Figure 9a). AVF, in contrast, shows a uniform distribution of values around 415 W/m\({}^{2}\) for all parts of the model area.