This model is a classic simulation of the production cycle in the ocean, including the effects of the thermocline in switching off advection of dissolved nutrients and detritus to the surface layer.

It illustrates a number of interesting features including the coupling of three state variables in a closed cycle, the use of time to control the duration of advection, and the modulus function for cycling annual temperature data over multiple years.

The model state variables are expressed in nitrogen units (mg N m-3), and the calibration is based on:

Baliño, B.M. 1996. Eutrophication of the North Sea, 1980-1990: An evaluation of anthropogenic nutrient inputs using a 2D phytoplankton production model. Dr. scient. thesis, University of Bergen.
 
Fransz, H.G. & Verhagen, J.H.G. 1985. Modelling Research on the Production Cycle of Phytoplankton in the Southern Bight of the Northn Sea in Relation to Riverborne Nutrient Loads. Netherlands Journal of Sea Research 19 (3/4): 241-250.

This model was first implemented in PowerSim some years ago by one of my M.Sc. students, who then went on to become a Buddhist monk. Although this is a very Zen model, as far as I'm aware, the two facts are unrelated.

Simple model to illustrate Michaelis-Menten equation for nutrient uptake by phytoplankton.

The equation is:

P = Ppot S / (Ks + S)

Where:

P: Nutrient-limited production (e.g. d-1, or mg C m-2 d-1)
Ppot: Potential production (same units as P)
S: Nutrient concentation (e.g. umol N L-1)
Ks: Half saturation constant for nutrient (same units as S)

The model contains no state variables, just illustrates the rate of production, by making the value of S equal to the timestep (in days). Move the slider to the left for more pronounced hyperbolic response, to the right for linear response.

Simple model to illustrate Steele's equation for primary production of phytoplankton.

The equation is:

Ppot = Pmax I/Iopt exp(1-I/Iopt)

Where:

Ppot: Potential production (e.g. d-1, or mg C m-2 d-1)
Pmax: Maximum production (same units as Ppot)
I: Light energy at depth of interest (e.g. uE m-2 s-1)
Iopt: Light energy at which Pmax occurs (same units as I)

The model contains no state variables, just illustrates the rate of production, by making the value of I equal to the timestep (in days). Move the slider to the left for more pronounced photoinhibition, to the right for photosaturation.

This model implements a very simple shellfish carrying capacity simulation for tidal creeks with freshwater input.

Physics

The model implements the one-dimensional version of the advection-dispersion equation for an estuary. The equation is:

dS/dt = (1/A)d(QS)/dx - (1/A)d(EA)/dx(dS/dx) (Eq. 1)

Where S: salinity (or any other constituent such as chlorophyll or dissolved oxygen), (e.g. kg m-3); t: time (s); A: cross-sectional area (m2); Q: river flow (m3 s-1); x: length of box (m); E: dispersion coefficient (m2 s-1).

For a given length delta x, Adx = V, the box volume. For a set value of Q, the equation becomes:

VdS/dt = QdS - (d(EA)/dx) dS (Eq. 2)

EA/x, i.e. (m2 X m2) / (m s) = E(b), the bulk dispersion coefficient, units in m3 s-1, i.e. a flow, equivalent to Q

At steady state, dS/dt = 0, therefore we can rewrite Eq. 2 for one estuarine box as:

Q(Sr-Se)=E(b)r,e(Sr-Se)-E(b)e,s(Se-Ss) (Eq. 3)

Where Sr: river salinity (=0), Se: mean estuary salinity; Ss: mean ocean salinity

E(b)r,e: dispersion coefficient between river and estuary, and E(b)e,s: dispersion coefficient between the estuary and ocean.

By definition the value of E(b)r,e is zero, otherwise we are not at the head (upstream limit of salt intrusion) of the estuary. Likewise Sr is zero, otherwise we're not in the river. Therefore:

QSe=E(b)e,s(Se-Ss) (Eq. 4)

At steady state

E(b)e,s = QSe/(Se-Ss) (Eq 5)

The longitudinal dispersion simulates the turbulent mixiing of water in the estuary during flood and ebb, which supplies salt water to the estuary on the flood tide, and make the sea a little more brackish on the ebb.

You can use the top slider to turn off dispersion (set to zero). If the variable being simulated is (a) salinity, you will see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system; (b) POM, then the ocean (which typically has less POM) will not contribute a flushing effect and the concentration of POM in the tidal creek or estuary will be higher.

The second slider allows you to simulate a variable river flow, and understand how dispersion compensates for changes in freshwater input.

Biology

Two biological functions are implemented in CREEK, both extremely simplified.

1. Primary production - a constant primary production rate is considered in gC m-3 d-1

2. Oyster filtration - a constant clearance rate (CR) is considered in L ind- 1 h-1, scaled to a certain stocking density S (ind m-3)

Units are normalized, and food depletion is CR * S * POM, in g POM m-3 d-1

The third slider allows for adjustment of different aquaculture densities.

Wild filter-feeding species are included in the model, using an identical clearance rate to the cultivated oysters. Wild species can be turned on or off in the model using the fourth slider.

The model provides three outputs:
1. POM concentration in mg L-1
2. Equivalent in chlorophyll (ug L-1)
3. Total oyster biomass in kg for the whole system

Simple model to illustrate   algal  ,   growth based on primary production of Phytoplankton as a state variable, forced by light and nutrients, running for a yearly period.

Phytoplankton growth based on on Steele's and Michaelis-Menten equations), where: 

Primary Production=(([Pmax]*[I]/[Iopt]*exp(1-[I]/[Iopt])*[S])/([Ks]+[S]))

Pmax: Maximum production (d-1)
I: Light energy at depth of interest (uE m-2 s-1)
Iopt: Light energy at which Pmax occurs (uE m-2 s-1)
S: Nutrient concentration (umol N L-1)
Ks: Half saturation constant for nutrient (umol N L-1).

Further developments:
- Nutrients as state variable in cycle with detritus from phytoplankton and oyster biomass.
- Light limited by the concentration of phytoplankton.
- Temperature effect on phytoplankton and Oyster growth.

  Biogas, model  as well birefineray option to seperate c02 , chp from bogas model are proposed

This model is a classic simulation of the production cycle in the ocean, including the effects of the thermocline in switching off advection of dissolved nutrients and detritus to the surface layer.

It illustrates a number of interesting features including the coupling of three state variables in a closed cycle, the use of time to control the duration of advection, and the modulus function for cycling annual temperature data over multiple years.

The model state variables are expressed in nitrogen units (mg N m-3), and the calibration is based on:

Baliño, B.M. 1996. Eutrophication of the North Sea, 1980-1990: An evaluation of anthropogenic nutrient inputs using a 2D phytoplankton production model. Dr. scient. thesis, University of Bergen.
 
Fransz, H.G. & Verhagen, J.H.G. 1985. Modelling Research on the Production Cycle of Phytoplankton in the Southern Bight of the Northn Sea in Relation to Riverborne Nutrient Loads. Netherlands Journal of Sea Research 19 (3/4): 241-250.

This model was first implemented in PowerSim some years ago by one of my M.Sc. students, who then went on to become a Buddhist monk. Although this is a very Zen model, as far as I'm aware, the two facts are unrelated.

Simple model to illustrate oyster growth based on primary production of Phytoplankton as a state variable, forced by light and nutrients, running for a yearly period.

Phytoplankton growth based on on Steele's and Michaelis-Menten equations), where: 

Primary Production=(([Pmax]*[I]/[Iopt]*exp(1-[I]/[Iopt])*[S])/([Ks]+[S]))

Pmax: Maximum production (d-1)
I: Light energy at depth of interest (uE m-2 s-1)
Iopt: Light energy at which Pmax occurs (uE m-2 s-1)
S: Nutrient concentration (umol N L-1)
Ks: Half saturation constant for nutrient (umol N L-1).

Further developments:
- Nutrients as state variable in cycle with detritus from phytoplankton and oyster biomass.
- Light limited by the concentration of phytoplankton.
- Temperature effect on phytoplankton and Oyster growth.

Simple model to illustrate Michaelis-Menten equation for nutrient uptake by phytoplankton.

The equation is:

P = Ppot S / (Ks + S)

Where:

P: Nutrient-limited production (e.g. d-1, or mg C m-2 d-1)
Ppot: Potential production (same units as P)
S: Nutrient concentation (e.g. umol N L-1)
Ks: Half saturation constant for nutrient (same units as S)

The model contains no state variables, just illustrates the rate of production, by making the value of S equal to the timestep (in days). Move the slider to the left for more pronounced hyperbolic response, to the right for linear response.

This model is a classic simulation of the production cycle in the ocean, including the effects of the thermocline in switching off advection of dissolved nutrients and detritus to the surface layer.

It illustrates a number of interesting features including the coupling of three state variables in a closed cycle, the use of time to control the duration of advection, and the modulus function for cycling annual temperature data over multiple years.

The model state variables are expressed in nitrogen units (mg N m-3), and the calibration is based on:

Baliño, B.M. 1996. Eutrophication of the North Sea, 1980-1990: An evaluation of anthropogenic nutrient inputs using a 2D phytoplankton production model. Dr. scient. thesis, University of Bergen.
 
Fransz, H.G. & Verhagen, J.H.G. 1985. Modelling Research on the Production Cycle of Phytoplankton in the Southern Bight of the Northn Sea in Relation to Riverborne Nutrient Loads. Netherlands Journal of Sea Research 19 (3/4): 241-250.

This model was first implemented in PowerSim some years ago by one of my M.Sc. students, who then went on to become a Buddhist monk. Although this is a very Zen model, as far as I'm aware, the two facts are unrelated.

Simple model to illustrate Michaelis-Menten equation for nutrient uptake by phytoplankton.

The equation is:

P = Ppot S / (Ks + S)

Where:

P: Nutrient-limited production (e.g. d-1, or mg C m-2 d-1)
Ppot: Potential production (same units as P)
S: Nutrient concentation (e.g. umol N L-1)
Ks: Half saturation constant for nutrient (same units as S)

The model contains no state variables, just illustrates the rate of production, by making the value of S equal to the timestep (in days). Move the slider to the left for more pronounced hyperbolic response, to the right for linear response.

Simple model to illustrate Michaelis-Menten equation for nutrient uptake by phytoplankton.

The equation is:

P = Ppot S / (Ks + S)

Where:

P: Nutrient-limited production (e.g. d-1, or mg C m-2 d-1)
Ppot: Potential production (same units as P)
S: Nutrient concentation (e.g. umol N L-1)
Ks: Half saturation constant for nutrient (same units as S)

The model contains no state variables, just illustrates the rate of production, by making the value of S equal to the timestep (in days). Move the slider to the left for more pronounced hyperbolic response, to the right for linear response.

This model explains the mussel growth (Mytillus Edulis) based on primary production of phytoplankton biomass.

Light, nutrients and temperature were used as forcing functions over a two year period.

Simple model to illustrate oyster growth based on primary production of Phytoplankton as a state variable, forced by light and nutrients, running for a yearly period.

Phytoplankton growth based on on Steele's and Michaelis-Menten equations), where: 

Primary Production=(([Pmax]*[I]/[Iopt]*exp(1-[I]/[Iopt])*[S])/([Ks]+[S]))

Pmax: Maximum production (d-1)
I: Light energy at depth of interest (uE m-2 s-1)
Iopt: Light energy at which Pmax occurs (uE m-2 s-1)
S: Nutrient concentration (umol N L-1)
Ks: Half saturation constant for nutrient (umol N L-1).

Further developments:
- Nutrients as state variable in cycle with detritus from phytoplankton and oyster biomass.
- Light limited by the concentration of phytoplankton.
- Temperature effect on phytoplankton and Oyster growth.

Ce modèle est une simulation classique du cycle de productivité dans l'océan, incluant les effets de la thermocline pour désactiver l'advection d'éléments nutritifs dissous et de détritus à la couche superficielle.  

Ce modèle est une simulation classique du cycle de productivité dans l'océan, incluant les effets de la thermocline pour désactiver l'advection d'éléments nutritifs dissous et de détritus à la couche superficielle.  

This model explains the primary production of phytoplankton, forced by light and nutrients over a year period.

This model is a classic simulation of the production cycle in the ocean, including the effects of the thermocline in switching off advection of dissolved nutrients and detritus to the surface layer.

It illustrates a number of interesting features including the coupling of three state variables in a closed cycle, the use of time to control the duration of advection, and the modulus function for cycling annual temperature data over multiple years.

The model state variables are expressed in nitrogen units (mg N m-3), and the calibration is based on:

Baliño, B.M. 1996. Eutrophication of the North Sea, 1980-1990: An evaluation of anthropogenic nutrient inputs using a 2D phytoplankton production model. Dr. scient. thesis, University of Bergen.
 
Fransz, H.G. & Verhagen, J.H.G. 1985. Modelling Research on the Production Cycle of Phytoplankton in the Southern Bight of the Northn Sea in Relation to Riverborne Nutrient Loads. Netherlands Journal of Sea Research 19 (3/4): 241-250.

This model was first implemented in PowerSim some years ago by one of my M.Sc. students, who then went on to become a Buddhist monk. Although this is a very Zen model, as far as I'm aware, the two facts are unrelated.

Simple model to illustrate an annual cycle for phytoplankton biomass in temperate waters.
Potential primary production uses Steele's equation and a Michaelis-Menten (or Monod) function for nutrient limitation. Respiratory losses are only a function of biomass.

Simple model to illustrate Michaelis-Menten equation for nutrient uptake by phytoplankton.

The equation is:

P = Ppot S / (Ks + S)

Where:

P: Nutrient-limited production (e.g. d-1, or mg C m-2 d-1)
Ppot: Potential production (same units as P)
S: Nutrient concentation (e.g. umol N L-1)
Ks: Half saturation constant for nutrient (same units as S)

The model contains no state variables, just illustrates the rate of production, by making the value of S equal to the timestep (in days). Move the slider to the left for more pronounced hyperbolic response, to the right for linear response.

This model is a classic simulation of the production cycle in the ocean, including the effects of the thermocline in switching off advection of dissolved nutrients and detritus to the surface layer.

It illustrates a number of interesting features including the coupling of three state variables in a closed cycle, the use of time to control the duration of advection, and the modulus function for cycling annual temperature data over multiple years.

The model state variables are expressed in nitrogen units (mg N m-3), and the calibration is based on:

Baliño, B.M. 1996. Eutrophication of the North Sea, 1980-1990: An evaluation of anthropogenic nutrient inputs using a 2D phytoplankton production model. Dr. scient. thesis, University of Bergen.
 
Fransz, H.G. & Verhagen, J.H.G. 1985. Modelling Research on the Production Cycle of Phytoplankton in the Southern Bight of the Northn Sea in Relation to Riverborne Nutrient Loads. Netherlands Journal of Sea Research 19 (3/4): 241-250.

This model was first implemented in PowerSim some years ago by one of my M.Sc. students, who then went on to become a Buddhist monk. Although this is a very Zen model, as far as I'm aware, the two facts are unrelated.

Simple model to illustrate Michaelis-Menten equation for nutrient uptake by phytoplankton.

The equation is:

P = Ppot S / (Ks + S)

Where:

P: Nutrient-limited production (e.g. d-1, or mg C m-2 d-1)
Ppot: Potential production (same units as P)
S: Nutrient concentation (e.g. umol N L-1)
Ks: Half saturation constant for nutrient (same units as S)

The model contains no state variables, just illustrates the rate of production, by making the value of S equal to the timestep (in days). Move the slider to the left for more pronounced hyperbolic response, to the right for linear response.

This model is a classic simulation of the production cycle in the ocean, including the effects of the thermocline in switching off advection of dissolved nutrients and detritus to the surface layer.

It illustrates a number of interesting features including the coupling of three state variables in a closed cycle, the use of time to control the duration of advection, and the modulus function for cycling annual temperature data over multiple years.

The model state variables are expressed in nitrogen units (mg N m-3), and the calibration is based on:

Baliño, B.M. 1996. Eutrophication of the North Sea, 1980-1990: An evaluation of anthropogenic nutrient inputs using a 2D phytoplankton production model. Dr. scient. thesis, University of Bergen.
 
Fransz, H.G. & Verhagen, J.H.G. 1985. Modelling Research on the Production Cycle of Phytoplankton in the Southern Bight of the Northn Sea in Relation to Riverborne Nutrient Loads. Netherlands Journal of Sea Research 19 (3/4): 241-250.

This model was first implemented in PowerSim some years ago by one of my M.Sc. students, who then went on to become a Buddhist monk. Although this is a very Zen model, as far as I'm aware, the two facts are unrelated.

Simple model to illustrate Steele's equation for primary production of phytoplankton.

The equation is:

Ppot = Pmax I/Iopt exp(1-I/Iopt)

Where:

Ppot: Potential production (e.g. d-1, or mg C m-2 d-1)
Pmax: Maximum production (same units as Ppot)
I: Light energy at depth of interest (e.g. uE m-2 s-1)
Iopt: Light energy at which Pmax occurs (same units as I)

The model contains no state variables, just illustrates the rate of production, by making the value of I equal to the timestep (in days). Move the slider to the left for more pronounced photoinhibition, to the right for photosaturation.

Simple model to illustrate oyster growth based on primary production of Phytoplankton as a state variable, forced by light and nutrients, running for a yearly period.

Phytoplankton growth based on on Steele's and Michaelis-Menten equations), where: 

Primary Production=(([Pmax]*[I]/[Iopt]*exp(1-[I]/[Iopt])*[S])/([Ks]+[S]))

Pmax: Maximum production (d-1)
I: Light energy at depth of interest (uE m-2 s-1)
Iopt: Light energy at which Pmax occurs (uE m-2 s-1)
S: Nutrient concentration (umol N L-1)
Ks: Half saturation constant for nutrient (umol N L-1).

Further developments:
- Nutrients as state variable in cycle with detritus from phytoplankton and oyster biomass.
- Light limited by the concentration of phytoplankton.
- Temperature effect on phytoplankton and Oyster growth.