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.

The Streeter-Phelps oxygen dynamics model was originally developed in 1925, almost a century ago.

Play

You can explore the model by hitting the simulate button, and you can use the three sliders below to (i) switch the spill on or off (1 or 0); (ii) define the day when the spill occurs (0 to 15); and (iii) make the model use a constant water temperature (20oC) or a (pre-defined) variable one.

A variable temperature affects oxygen saturation, and therefore also the oxygen deficit and oxygen concentration.

Every model element shows an = sign when you hover over it, and if you click the sign you can view the underlying equation.

If you want to edit the model, you need to create an account in InsightMaker and then clone the model and adapt it to your needs.

Study

Below is a detailed explanation of the model concept.

The model calculates the oxygen deficit (D), defined as Cs-C, where Cs is the saturation concentration of dissolved oxygen (based on temperature, and salinity if applicable), and C is the dissolved oxygen concentration.

Since D = Cs-C, it follows that:
dD/dt = -dC/dt

The rate of change of oxygen concentration with time (dC/dt) depends on two factors, organic decomposition and aeration.

dC/dt = Ka.D - Kd.L

The first term on the right side of the equation is aeration (which adds oxygen to the water), calculated by means of the temperature-dependent aeration parameter Ka.

Ka is also a function of Kr, which depends on wind speed (U) and water depth (z).

The sink term represents oxygen consumption through mineralization (bacterial decomposition) of organic matter.

The organic load L decays in time (or in space, e.g. along a river) according to a first order equation, i.e. dL/dt = -Kd.L

This equation can be integrated to yield L = Lo.exp(Kd.t), where Kd is the decay constant.

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 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.

Simple Model of the Food Chain

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.

Working Draft of a model to simulate the effect on ecosystem service values of planting 10 billion oysters in the Chesapeake Bay by the year 2025.

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 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.

This model implements a very simple proxy for vertical dispersion of heat in a lake based on the equation:

dT/dt = 1/A d(EA)/dz (dT/dz)

where: T: temperature (oC); t: time (days); z: depth (m); A: cross-sectional area (m2); E: vertical dispersion coefficient (m2 d-1)

If we consider that E is constant (it is in this model), then the equation becomes dT/dt = (EA/A)(d^2T/dz^2) = E(d^2T/dz^2), the classic diffusion equation

The model is simplified by exchanging temperature as a state variable, rather than executing  the full heat balance. This would require a computation of fluxes of atmospheric longwave and shortwave radiation, water longwave radiation, water conduction and convection, and water evaporation and condensation.

The vertical dispersion coefficients are adjusted artificially so that mixing increases at lower temperatures, thus quickly homogenizing the water column in colder months of the year.

Diagrams on generalized knowledge claims and workflow processes from Magliocca 2018 Global Environmental Change article

FORCED GROWTH GROWTH GOES INTO TURBULENT CHAOTIC DESTRUCTION 
 BEWARE pushing increased growth blows the system!
(governments are trying to push growth on already unstable systems !)

The existing global capitalistic growth paradigm is totally flawed

The chaotic turbulence is the result of the concept and flawed strategy of infinite bigness this has been the destructive influence on all empires and now shown up by Feigenbaum numbers and Dunbar numbers for neural netwoirks

See Guy Lakeman Bubble Theory for more details on keeping systems within finite limited size working capacity containers (villages communities)

The time-variable solution to a step-function change in inflow concentration for an ideal, completely mixed lake.

This model describes the flow of energy from generation to consumption for neighborhoods in the metro Atlanta area. It also calculates the cost of energy production and the number of years it will take to recover that cost.

DRAFT conceptual model of climate change connections in Yamuna river project.

HANDY Model of Societal Collapse from Ecological Economics Paper