NPZ-model/Physical-Processes.md

@@ -13,7 +13,23 @@ Where T is the ambient water temperature and $`Q_{10}`$ indicates the relative i
 
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 # Underwater light conditions
-The underwater light conditions is depending on the 
+The underwater light conditions is depending on the the irradiation and the extinction of the light in the water. Mean daily irradiation at the water surface  ($`I_{0}`$) [W d<sup>-1</sup>] is derived from the file KNMI measurements (stored in “./DataOS/KNMI/”). The underwater-light conditions are calculated from the daily irradiation at the water surface and the extinction coefficient ($`k_{d}`$):
+
+```math
+I_{z} = I_{0} \cdot e^{-k_{d} \cdot z}
+```
+
+The extinction coefficient ($`k_{d}`$) is depending on the amount of Total Particulate Matter in the water.  
+Los and Wijsman (2007) use the relation from Van Gils and Tatman (2003)  
+
+
+The average light ($`I_{avg}`$) is calculated by integration of the function over the whole water column divided over the waterdepth. 
+
+```math
+I_{avg} = \frac{ \int_{z=0}^{z=Depth} \cdot I_{z} \cdot dz}{Depth}
+```
+
+It is assumed that about 50% of the light is photosynthetic active radiation (PAR) $`PAR = 0.5 \cdot I_{avg}`$