WIP Stock Flow representation of Panarchy Adaptive Cycles

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

Z212 from System Zoo 1 p142-148

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 prototypes the working of an Smart Grid with Electric Vehicles

The objective is testing the theoretical advantages of batteries (also batteries in Electric Vehicles) in combination with renewable energies. The model considers two houses, that store energy both in Electric Vehicles (Vehicle to Grid), and in a communal battery.

Except when specified otherwise, the units of all variables are expressed in W/h.

Press "Story" in the lower bar for a guided tour over the model. Better seen at 50% zoom.

by Carlos Varela (cvarela@gmx.at)

Simple model of the global economy, the global carbon cycle, and planetary energy balance.

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.

This model implements the equations proposed by Ketchum in 1954. The rationale behind the concept is that only phytoplankton that grows above a certain rate will not be flushed out of an estuary.

For biological processes:

Pt  =  Po exp(kt)

Where Pt is the phytoplankton biomass at time t, Po is the initial biomass, and k is the growth rate.

For physical processes:

Pm  =  Po (1-r)^m

Where Pm is the phytoplankton biomass after m tidal cycles, and r is the exchange ratio (proportion of estuary water which does not return each tidal cycle).

By substitution, and replacing t by m in the first equation, we get:

Pm = Poexp(km).(1-r)^m

For phytoplankton to exist in an estuary, Pm = Po (at least), i.e. 1 / (1-r)^m = exp(km)
ln(1) - m.ln(1-r) = km
-m.ln(1-r) = km
k = -ln(1-r)

Ketchum (1954) Relation between circulation and planktonic populations in estuaries. Ecology 35: 191-200.

In 2005, Ferreira and co-workers showed that this balance has direct implications on biodiversity of estuarine phytoplankton, and discussed how this could be relevant for water management, in particular for the EU Water Framework Directive 60/2000/EC (Ecological Modelling, 187(4) 513-523).

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 modern carbon cycle model for use in virtual education modules.

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)

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.

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.

all pictures sourced from google images

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.

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.

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.

This is to support a discussion on money flows and growth. Money as a lubricant for the flow of embodied energy in human systems.
See also A Prosperous Way Down website

HANDY Model of Societal Collapse from Ecological Economics Paper 

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.