# Advances in Simulating Radiative Transfer in Complex Environments
## 1 Introduction  
Accurate modeling of radiative fluxes plays an important role in microclimatology. This is especially the case in urban areas, where large differences in radiative fluxes can be found due to complex structures, heterogeneous materials, and a multitude of different surface types [1; 2; 3; 4; 5]. While primary radiative transfer, i.e., incoming shortwave and longwave radiation, can be simulated quite easily using ray tracing algorithms and local sky view factors, simulating secondary radiative fluxes, which are emitted or reflected by objects of the environment (walls, roofs, the ground surface, or vegetation), are much more complicated to be modeled. The complexity in modeling these radiative fluxes lies in the multiple interactions between the different elements within the view range of the grid analyzed. For instance, radiation reflected by a surface will contribute to the incoming radiation received by other surfaces. These surfaces will again also re-reflect parts of this radiation and distribute in vicinity. Handling such complex conditions is a challenge that is common to all algorithms that involve simulating multiple reflections of radiation such as daylight simulation or image rendering in general [6; 7; 8; 9; 10]. Over the years, different approaches have been developed to tackle this problem using different kinds of numerical algorithms. The multiple reflections of shortwave radiation can, for example, be handled by tracing the reflected photons using a Monte Carlo approach [11; 12; 13; 14; 15]. For the analysis of more mono-directed rays originating from discrete light or radiation sources, raytracing algorithms can be used to follow the radiation on its path through the modeled environment, similar to the algorithms implemented in themicroclimate model ENVI-met to calculate the shadow casting [16; 17; 18; 19]. Another group of algorithms approaches the problem from the other side, by not tracing the radiation itself, but analyzing the view relations between the different emitting and receiving elements in a scene or environment. These types of algorithms are generally categorized as radiosity approaches, with several sub-groups depending on the way the individual interactions between the elements are solved (e.g., matrix radiosity, progressive radiosity, or wavelet radiosity) [20; 21; 22; 23; 24; 25; 26; 27]. While these methods give good results in smaller environments such as indoor spaces, they are hardly applicable for outdoor situations where an enormous number of elements and view relations between points in space need to be analyzed due to the larger and more complex geometries. Moreover, different to indoor environments, where the radiative fluxes are often calculated only once for a given setting, the situation in an outdoor environment is constantly changing due to movement of the sun and the resulting heating and cooling of surfaces. Hence, the radiative situation needs to be solved frequently--similar to the shadow casting, which is typically updated every few minutes [28]. Modern microclimate models such as the CFD-model ENVI-met that considers turbulence and is based on solving Reynolds-Navier-Stokes equations [28; 29; 30; 31], allow for a very precise representation of the urban environment: Besides the detailed plant model [32; 33], ENVI-met recently introduced an Accurate In-Canopy Radiation Transfer scheme, which accounts for scattering and attenuation of shortwave radiation within trees' canopies [34]. Buildings cannot only be digitized with a variety of different materials but also individual facades of the same building can consist of different materials [28; 35; 36; 35]. The same is possible with the ground surface, where different surface types can be assigned to every grid. Since the different objects, materials, and surface types carry their own physical parameters such as albedo, emissivity, heat transfer coefficient, etc., the possibility to accurately replicate the variety of the urban environment drastically increases the accuracy of the model results.