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NPZ-model/State-Variables.md
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......@@ -37,111 +37,6 @@ The shellfish populations are controlled by a variable mortality (MortShellfish)
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# Biological processes
## DINuptake
DINuptake is the production of phytoplankton (primary production) [mmolN m<sup>-3</sup> d<sup>-1</sup>] and is depending on the underwater-light conditions, water temperature, the nutrient concentration (DIN) and the phytoplankton concentration.
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 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) $`PAR = 0.5 /cdot I_{avg}`$
DINuptake is calculated from the maximum specific uptake rate [dsup>-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}})
```
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.
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## 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.
```math
ZooGrazing = ZooGrazing_{max} \cdot T_{fac} \cdot Zoo \cdot (\frac{Phyto}{Phyto+ks_{ZooGrazing}})
```
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## ZooFaeces
A fraction ($`p_{FaecesZoo}`$) of the uptake of phytoplankton grazed by zooplankton is excreted as faeces into the detritus pool. The rest is used for assimilation.
```math
ZooFaeces = p_{FaecesZoo} \cdot ZooGrazing
```
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## ZooExcretion
Respiration of the zooplankton is described as a first-order response, with $`Resp_{Zoo}`$ as the first order rate constant, and is corrected for water temperature. The nitrogen is excreted in the water column as DIN.
```math
ZooExcretion = Resp_{Zoo} \cdot Zoo \cdot T_{fac}
```
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## ZooMortality
The mortality of the zooplankton is described as a second-order function on the zooplankton biomass. Mortality is also assumed to be temperature-dependent.
```math
ZooMortality = M_{Zoo} \cdot Zoo^{2} \cdot T_{fac}
```
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## MortMPB
In the model, the microphytobenthos is not grazed by filterfeeders. The mortality is described as a second-order function on the microphytobenthos biomass. Mortality is also assumed to be temperature-dependent.
```math
Mort_{MPB} = M_{MPB} \cdot MPB^{2} \cdot T_{fac}
```
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## MortShellfish
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.
```math
Mort_{i} = M_{i} + DensM_{i} \cdot (\frac {FF_{i}}{CC_{i}}-1)) \cdot FF_{i}
```
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## Mineralization
The mineralisation of detritus is described as a first-order function with a first-order rate constant $`r_{Det}`$ The mineralisation rate increases with water temperature.
```math
Mineralization = (r_{Det} \cdot Det \cdot T_{fac}
```
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## DINupMPB
DINupMPB is the production of microphytobenthos [mmolN m<sup>-2</sup> d<sup>-1</sup>]. It is assumed that microphytobenthos only occurs at the intertidal areas. DINupMPB is depending on the irradiation, water temperature, the nutrient concentration (DIN) and the microphytobenthos concentration.
Mean daily irradiation at the water surface [W d<sup>-1</sup>] is derived from the file KNMI measurements (stored in “./DataOS/KNMI/”).
It is assumed that about 50% of the light is photosynthetic active radiation (PAR)
```math
PAR_{b} = 0.5 \cdot I_{0}
```
DINupMPB 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,MPB}= MPB_{upt,max} \cdot MPB \cdot (1-\frac{MPB}{CC_{MPB} \cdot f_{int}}) \cdot (\frac{PAR_{b}}{PAR_{b} + ks_{PAR,MPB}}) \cdot (\frac{DIN}{DIN _\cdot + 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. Production of the microphytobenthos is limited by the carrying capacity ($`CC_{MPB}`$, mmol N m<sup>-2</sup>) at the intertidal flat. $`T_{fac}`$ is the correction for the ambient water temperature.
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## BotMin
The mineralisation of bottom detritus is described as a first-order function with a first-order rate constant $`r_{Bot\_Det}`$. The mineralisation rate increases with water temperature.
```math
Mineralization = r_{Bot\_Det} \cdot Bot\_Det \cdot T_{fac}
```
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# Shellfish scope for growth
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