- DINuptake
- ZooGrazing
- ZooFaeces
- ZooExcretion
- ZooMortality
- MortShellfish
- Mineralization
- DINupMPB
- MortMPB
- BotMin
- N-loss due to denitrification
DINuptake
DINuptake is the production of phytoplankton (primary production) [mmol-N m-3 d-1] and is depending on the underwater-light conditions (PAR), water temperature, the nutrient concentration (DIN) and the phytoplankton concentration.
Mean daily irradiation at the water surface (I_{0}
) [W d-1] 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}
):
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.
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}
DIN_{upt}
is calculated from the maximum specific uptake rate [d-1] at ambient temperature and the algal concentration. Limitations by light and nutrients are described by Monod formulations.
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°C [d-1], ks_{PAR}
and ks_{DIN}
are the half-saturation coefficients for light and DIN, respectively.
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-1] 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 (mmol-N m-3).
ZooGrazing = ZooGrazing_{max} \cdot T_{fac} \cdot Zoo \cdot \left(\frac{Phyto}{Phyto+ks_{ZooGrazing}}\right)
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.
ZooFaeces = p_{FaecesZoo} \cdot ZooGrazing
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.
ZooExcretion = Resp_{Zoo} \cdot Zoo \cdot T_{fac}
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. M_{Zoo}
is the mortality rate of the zooplankton (mmol-N-1m-3d-1).
ZooMortality = M_{Zoo} \cdot Zoo^{2} \cdot T_{fac}
MortShellfish
The mortality rate (Mort_{i}
, mmol-N m-2 d-1) 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
.
Mort_{i} = M_{i} + DensM_{i} \cdot \left(\frac {FF_{i}}{CC_{i}}-1\right) \cdot FF_{i}
Mineralization
The mineralisation of detritus (Det_{Min}
), in units of mmol-N m-3 d-1is described as a first-order function with a first-order rate constant r_{Det}
The mineralisation rate increases with water temperature.
Det_{Min} = r_{Det} \cdot Det \cdot T_{fac}
DINupMPB
DIN_{upt,MPB}
is the primary production by microphytobenthos [mmol-N m-2 d-1]. It is assumed that production only occurs at the intertidal areas during exposure. DIN_{upt,MPB}
is depending on the irradiation at the surface (I_{0}
), the water temperature, the nutrient concentration (DIN) and the microphytobenthos concentration. Mean daily irradiation at the water surface [W d-1] 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). The photosynthetic active radiation at the intertidal flats (PAR_{b}
) [W d-1] can be expressed as:
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 (MPB_{eff}
)[mmol-N m-2] is calculated by:
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 [mol-N m-2] 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-1] 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:
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-1] of microphytobenthos at 10°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.
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.
Mort_{MPB} = M_{MPB} \cdot MPB^{2} \cdot T_{fac}
BotMin
The mineralization of bottom detritus (Bot\_Det_{Min}
) [mmol-N m-2 d-1] is described as a first-order function with constant r_{Bot\_Det}
. The mineralization rate increases with water temperature.
Bot\_Det_{Min}= r_{Bot\_Det} \cdot Bot\_Det \cdot T_{fac}
N-loss due to denitrification
Part of the detritus in the bottom is mineralized by denitrification. As a result part of the nitrogen is lost as N2 to the atmosphere (N_{loss}
) [mmol-N m-2 d-1].
N_{loss} = p_{Denit}\cdot Bot\_Det_{Min}