# Advances in Simulating Radiative Transfer in Complex Environments
## 2 Model Description
### The Averaged View Factor (AVF) Concept  
To describe the radiative situation and solve the interactions between different elements, ENVI-met version 4.4.5 and prior used a generalized visibility concept based on averaged view factors (AVF). In the AVF concept, first, a three-dimensional ray tracing analysis is performed for every cell. Starting from a grid cell's center, rays are being shot for every 10\({}^{\circ}\) height and 10\({}^{\circ}\) azimuth angle creating a sphere consisting out of 18 \(\times\) 36, thus 648 individual view facets. While calculating these 648 individual view facets for every grid cell can be very time consuming, it only needs to be performed once for a model simulation as the objects seen by a cell do not change over the course of a simulation. Based on the object type (sky, building, plant, ground surface) seen by the view facet/hit by the ray and the total number of view facets, averaged view factors of sky \(\sigma_{\text{Sky}}\), vegetation \(\sigma_{Vcg}\), buildings \(\sigma_{Bldg}\), and ground surfaces \(\sigma_{Grnd}\) were stored as single values for each grid cell. By only saving the view factors for the different object types instead of the actual facade elements, ground surfaces, and plant sections seen in the facets, a lot of memory can be saved. However, since no information is stored about which individual elements are in radiative exchange with the cell, the calculation of secondary radiative fluxes cannot take into account the radiation exchanges between actual objects seen but rather has to resort to an approximation. Instead of individual information about radiation received from particular objects, the secondary radiation is approximated by combining a grid cells' view factor for buildings, plants, and ground surfaces with averaged values of reflected and emitted longwave radiation for all buildings, plants, and ground surfaces over the entire model domain [19; 28; 37].  
The received secondary radiation of a cell--in this case, the received shortwave reflected radiation from buildings--is, thus, calculated by:  
\[Q_{surefl,in}(i,j,k)=\sigma_{Bldg}(i,j,k)\cdot Q_{Bldg,surefl} \tag{1}\]  
with \(\sigma_{Bldg}(x,y,z)\) as the building view factor (0 to 1) of cell \(i,j,k\) and \(Q_{Bldg,surefl}\) as the averaged reflected shortwave radiation from all buildings calculated by:  
\[Q_{Bldg,surefl}=\frac{1}{N}\sum_{a=1}^{N}\propto(a)\cdot Q_{sw}(a) \tag{2}\]  
with \(N\) being the total number of facades in the model, \(\propto\) the albedo of facade \(a\), and \(Q_{sw}\) the shortwave radiation in front of facade \(a\). The same calculations are carried out taking into account averaged surface temperature values of buildings, leaves, or ground surfaces for the estimation of received secondary longwave radiation.  
To account for changes in the radiative situation, these calculations (Equations (1) and (2)) and their respective counterparts for other object types and emitted longwave radiation need to be solved regularly, i.e., every 15 min by default in ENVI-met.  
The consequence of this simplification is that every point with an identical view factor for buildings, ground surfaces, or vegetation will receive the exact same amount of reflected shortwave and emitted longwave radiation.  
While this simplification does save memory, it also leads to very unrealistic results: Given the same view factors, a cell would receive the exact same amount of reflected shortwave and emitted longwave radiation independent of the actual radiative processes in its vicinity. This could lead to identical reflected shortwave fluxes in front of north and south facades or high-reflective facade materials or low-reflective facade materials.