NPZ-model/Biological-Processes.md

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 # DINuptake
@@ -22,7 +23,7 @@ It is assumed that about 50% of the light is photosynthetic active radiation (PA
 $`DIN_{upt}`$ is calculated from the maximum specific uptake rate [d<sup>-1</sup>] at ambient temperature and the algal concentration. Limitations by light and nutrients are described by Monod formulations.
  
 ```math
-DIN_{upt} = DIN_{upt,max} \cdot T_{fac} \cdot Phyto \cdot (\frac{PAR}{PAR+ks_{PAR}}) \cdot (\frac{DIN}{DIN+ks_{DIN}})
+DIN_{upt} = DIN_{upt,max} \cdot T_{fac} \cdot Phyto \cdot \left(\frac{PAR}{PAR+ks_{PAR}}\right) \cdot \left(\frac{DIN}{DIN+ks_{DIN}}\right)
 ```
 
 Where $`DIN_{upt,max}`$ is the maximum DIN uptake rate of algae at 10&deg;C [d<sup>-1</sup>], $`ks_{PAR}`$ and $`ks_{DIN}`$ are the half-saturation coefficients for light and DIN, respectively.
@@ -31,7 +32,7 @@ Where $`DIN_{upt,max}`$ is the maximum DIN uptake rate of algae at 10&deg;C [d<s
 # ZooGrazing
 The phytoplankton is grazed by zooplankton in the water column. The rate is depending on the  phytoplankton (Phyto) and zooplankton (Zoo) biomass and is influenced by the water temperature. The grazing rate is calculated from the maximum specific grazing rate ($`ZooGrazing_{max}`$) [d<sup>-1</sup>] at ambient temperature using a Holling type-II functional response for the phytoplankton, with $`ks_{ZooGrazing}`$ as the half saturation coefficient for zooplankton grazing on phytoplankton (mmolN m<sup>-3</sup>). 
 ```math
-ZooGrazing = ZooGrazing_{max} \cdot T_{fac} \cdot Zoo \cdot (\frac{Phyto}{Phyto+ks_{ZooGrazing}})
+ZooGrazing = ZooGrazing_{max} \cdot T_{fac} \cdot Zoo \cdot \left(\frac{Phyto}{Phyto+ks_{ZooGrazing}}\right)
 ```
 
 [top](NPZ model/Biological Processes)
@@ -63,7 +64,7 @@ ZooMortality = M_{Zoo} \cdot Zoo^{2} \cdot T_{fac}
 The mortality rate ($`Mort_{i}`$, mmol N m-2 d<sup>-1</sup>) of shellfish species $`i`$ (Mus, Oys and Coc) assumed to be density dependent, with $`M_{i}`$ is the specific mortality rate when the biomass of the shellfish species equals the carrying capacity ($`CC_{i}`$). $`DensM_{i}`$ indicates the importance of the density dependent mortality and FF_{i} is the density of shellfish species $`i`$.
 
 ```math
-Mort_{i} = M_{i} + DensM_{i} \cdot (\frac {FF_{i}}{CC_{i}}-1)) \cdot FF_{i}
+Mort_{i} = M_{i} + DensM_{i} \cdot \left(\frac {FF_{i}}{CC_{i}}-1\right) \cdot FF_{i}
 ```
 
 [top](NPZ model/Biological Processes)
@@ -81,18 +82,19 @@ $`DIN_{upt,MPB}`$ is the primary production by microphytobenthos [mmolN m<sup>-2
 ```math
 PAR_{b} = 0.5 \cdot I_{0}
 ```
-When the local biomass of microphytobenthos at the intertidal flats becomes too high, the primary production can be inhibited. The effective microphytobenthos concentration is calculated by:
+When the local biomass of microphytobenthos at the intertidal flats becomes too high, the primary production can be inhibited. The effective microphytobenthos concentration ($`MPB_{eff}`$)[mmolN m<sup>-2</sup>] is calculated by:
 
 ```math
-MPB_{eff} = MPB \cdot (1 - \frac{PAR_{b}}{PAR_{b} + ks_{PAR,MPB}}) 
+MPB_{eff} = \left(1 - \frac{MPB}{CC_{MPB} \cdot f_{int}} \right) \cdot MPB 
 ```
+where $`CC_{MPB}`$ is the maximum concentration of microphytobenthos at the intertidal area [molN m<sup>-2</sup>] and $`f_{int}`$ is the fraction of intertidal area within a compartment [-].
 
-$`DIN_{upt,MPB}`$ is calculated from the maximum specific uptake rate ($`MPB_{upt,max}`$) [d<sup>-1</sup>] at ambient temperature and the microphytobenthos biomass. Limitations by light and nutrients are described by Monod formulations. 
+$`DIN_{upt,MPB}`$ is calculated from the maximum specific uptake rate ($`MPB_{upt,max}`$) [d<sup>-1</sup>] at ambient temperature and the effective microphytobenthos biomass. Limitations by light and nutrients are described by Monod formulations. Primary production of the microphytobenthos only takes place when mudflat is exposed (fraction $`Exp `$ of the time). $`DIN_{upt,MPB}`$ is described by:
 
 ```math
-DIN_{upt,MPB}= MPB_{upt,max}  \cdot Exp \cdot MPB \cdot (\frac{PAR_{b}}{PAR_{b} + ks_{PAR,MPB}}) \cdot (\frac{DIN}{DIN + ks_{DIN,MPB}}) \cdot T_{fac}
+DIN_{upt,MPB}= MPB_{upt,max}  \cdot Exp \cdot MPB_{eff} \cdot (\frac{PAR_{b}}{PAR_{b} + ks_{PAR,MPB}}) \cdot (\frac{DIN}{DIN + ks_{DIN,MPB}}) \cdot T_{fac}
 ```
-Where $`MPB_{upt,max} `$ is the maximum DIN uptake rate [d<sup>-1</sup>] of microphytobenthos at 10&deg;C, $`ks_{PAR,MPB}`$ and $`ks_{DIN,MPB}`$ are the half-saturation coefficients for light and DIN, respectively. $`Exp`$ is the fraction of the time that the intertidal areas are exposed and $`T_{fac}`$ is the correction for the ambient water temperature.
+Where $`MPB_{upt,max}`$ is the maximum DIN uptake rate [d<sup>-1</sup>] of microphytobenthos at 10&deg;C, $`ks_{PAR,MPB}`$ and $`ks_{DIN,MPB}`$ are the half-saturation coefficients for light and DIN, respectively. $`Exp`$ is the average fraction of the time that the mudflats are exposed and $`T_{fac}`$ is the correction for the ambient water temperature.
 
 [top](NPZ model/Biological Processes)
 # MortMPB
@@ -102,7 +104,6 @@ In the model, the microphytobenthos is not grazed by filterfeeders. The mortalit
 Mort_{MPB} = M_{MPB} \cdot MPB^{2} \cdot T_{fac}
 ```
 
-
 [top](NPZ model/Biological Processes)
 # BotMin
 The mineralization of bottom detritus ($`Bot\_Det_{Min}`$) [mmolN m<sup>-2</sup> d<sup>-1</sup>] is described as a first-order function with  constant $`r_{Bot\_Det}`$. The mineralization rate increases with water temperature.