# A holistic microclimate model

The absorbed longwave radiation is calculated using the following rules:

• The portion of the visible sky is calculated as sky-view factor (SVF, 1= full sky is visible). Only buildings are counted in the SVF.
• This fraction of visible sky (SVF) can either contain longwave radiation from the sky, from the vegetation or from both.
• The fraction of obstructed sky (1-SVF) can contain reflected longwave radiation of the surface or longwave radiation emitted from walls. The bigger one of the two is used in the calculation.

One might say, that vegetation can also be found in parts of the obstructed sky. This is true, but normally the vegetation is only effective for the longwave budget if it shelters the sky…

For the visible sky the fraction that is coming from the sky itself and the part that is coming from the vegetation is calculated using a transmission factor (trans_plant). If no plants are present, trans_plant is 1. Below very dense vegetation, trans_plant is 0.

So, we get for the longwave radiation from the free sky (LW_free):

LW_free= trans_plant*LW_sky+ (1-trans_plant)*LW_plant

where LW_sky is the atmospheric counter radiation and LW_plant is the radiation of the leafs (averaged over a vertical column)

For the obstructed sky (LW_obst), the rule is:

LW_obst= max(q_lw_envi,q_lwsurf)

where q_LW_envi is an averaged value over all facade temperatures in the model and q_lwsurf is the longwave radiation of the surface concerned itself. The “max” function ensures that the highest of the values is used (see above).

Finally, the total incoming longwave radiation is weighted between LW_free and LW_obst using the SVF:

LW_total= SVF*LW_free+(1-SVF)*LW_obst

The values found in the receptor files for radiation coming from the vegetation, the sky and from the environment are based on this calculation for the selected surface:

from vegetation = SVF*(1-trans_plant)*LW_plant
from sky=SVF*trans_plant*LW_sky
from environment= (1-SVF)*max(q_lw_envi,q_lwsurf)

They are NOT the total amount of longwave radiation emitted (e.g. from the plants) but the amount of radiation reaching the surface of interest!