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 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.

Units don't really work, not sure what to do regarding flow units (can't divide units and the conversion part doesn't make any sense)

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 modern carbon cycle model for use in virtual education modules.

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.

Model created by Scott Fortmann-Roe.  This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

Experiment with adjusting the initial number of moose and wolves on the island.

Simple model to illustrate a simple simulation of the microalgae biomass production, focusing on the dependent variables such as light, nutrients and other factor that is running for a yearly period.

The biomass model uses an example, Phytoplankton growth based 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).

Once this is understood, it looks upon the viability of biogas production from the microalgae biomass.

This story contains a conceptual model of phosphorus cycling in a dune-lake system in the Northland region of New Zealand. It is based on the concept of a stock and flow diagram. Each orange ellipse represents an input, while each blue box represents a stock. Each arrow represents a flow. A flow involves a loss from the stock at which it starts and an addition to the stock at which it ends.

This model illustrates predator prey interactions using real-life data of bison and wolf populations at Yellowstone National Park.

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.

Dissolved oxygen mass balance in a tide pool, forced by tides and light.

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.

In Chile, 60% of its population are exposed to levels of Particulate Matter (PM) above international standards. Air Pollution is causing 4,000 premature deaths per year, including health costs over US$8 billion.

A storytelling of the nitrogen cycle.

In Chile, 60% of its population are exposed to levels of Particulate Matter (PM) above international standards. Air Pollution is causing 4,000 premature deaths per year, including health costs over US$8 billion.

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.

This model simulates the growth of carp in an aquaculture pond, both with respect to production and environmental effects.

Both the anabolism and fasting catabolism functions contain elements of allometry, through the m and n exponents that reduce the ration per unit body weight as the animal grows bigger.

The 'S' term provides a growth adjustment with respect to the number of fish, so implicitly adds competition (for food, oxygen, space, etc).

 Carp are mainly cultivated in Asia and Europe, and contribute to the world food supply.

Aquaculture currently produces sixty million tonnes of fish and shellfish every year. In May 2013, aquaculture production overtook wild fisheries for human consumption.

This paradigm shift last occurred in the Neolithic period, ten thousand years ago, when agriculture displaced hunter-gatherers as a source of human food.

Aquaculture is here to stay, and wild fish capture (fishing) will never again exceed cultivation.

Recreational fishing will remain a human activity, just as hunting still is, after ten thousand years - but it won't be a major source of food from the seas.

The best way to preserve wild fish is not to fish them.

Simple mass balance model for lakes, based on the Vollenweider equation:

dMw/dt = Min - sMw - Mout

The model was first used in the 1960s to determine the phosphorus concentration in lakes and reservoirs, for eutrophication assessment.

This story presents a conceptual model of nitrogen cycling in a dune-lake system in the Northland region of New Zealand. It is based on the concept of a stock and flow diagram. Each orange ellipse represents an input, while each blue box represents a stock. Each arrow represents a flow. A flow involves a loss from the stock at which it starts and an addition to the stock at which it ends.