This model describes phosphorus cycling in a dune-lake system in the Northland region of New Zealand. It is based on stock and flow diagrams where each orange oval represents an input, while each blue box represents a stock. Each arrow represents a flow. Flows involve a loss from the stock at which they start and add to the stock at which they end.

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.

Interplay between wolves eating sheep and farmers killing wolves.

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

We incorporate logistic growth into the moose dynamics, and we replace the death flow of the moose with a kill rate modeled from the kill rate data found on the Isle Royale website.

I start with these parameters:
Wolf Death Rate = 0.15
Wolf Birth Rate = 0.0187963
Moose Birth Rate = 0.4
Carrying Capacity = 2000
Initial Moose: 563
Initial Wolves: 20

I used RK-4 with step-size 0.1, from 1959 for 60 years.

The moose birth flow is logistic, MBR*M*(1-M/K)
Moose death flow is Kill Rate (in Moose/Year)
Wolf birth flow is WBR*Kill Rate (in Wolves/Year)
Wolf death flow is WDR*W

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.

Eastern oyster growth model calibrated for Long Island Sound

This is a one box model for an idealized farm with one million oysters seeded (one hectare @ a stocking density of 100 oysters per square meter)

1. Run WinShell individual growth model for one year with Long Island Sound growth drivers;

2. Determine the scope for growth (in dry tissue weight per day) for oysters centered on the five weight classes)
 
3. Apply a classic population dynamics equation:

dn(s,t)/dt = -d[n(s,t)g(s,t)]/ds - u(s)n(s,t)

s: Weight (g)
t: Time
n: Number of individuals of weight s
g: Scope for growth (g day-1)
u: Mortality rate (day-1)

4. Set mortality at 30% per year, slider allows scenarios from 30% to 80% per year

5. Determine harvestable biomass, i.e. weight class 5, 40-50 g (roughly three inches length)

Primitives for Watershed modeling project. Click Clone Insight at the top right to make a copy that you can edit.

The converter in this file contains precipitation for Phoenix only.

A simulation illustrating simple predator prey dynamics. You have two populations.

•Average (Status Quo) Case

Combining electromobility and renewable energies since 2014.

http://www.amsterdamvehicle2grid.nl/

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 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.

Very simple model demonstrating growth of phytoplankton using Steele's equation for potential production and Michaelis-Menten equation for nutrient limitation.

Both light and nutrients (e.g. nitrogen) are modelled as forcing functions, and the model is "over-calibrated" for stability.

The phytoplankton model approximately reproduces the spring-summer diatom bloom and the (smaller) late summer dinoflagellate bloom.
 
Oyster growth is modelled only as a throughput from algae. Further developments would include filtration as a function of oyster biomass, oyster mortality, and other adjustments.

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.

Compost modelling

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 version adds diagenesis, using an extra state variable (phosphorus in the sediment) and incorporates desorption processes that release phosphorus trapped in the sediment back to the water column.

The temporal dynamics of the model simulate the typical development of pollution in time.

1. Low loading, low P concentration in lake
2. High loading, increasing P concentration in lake
3. Desorption rate is low, P in sediment increases
4. Measures implemented for source control, loading reduces
5. P in lake gradually decreases, but below a certain point, desorption increases, and lake P concentration does not improve
6. Recovery only occurs when the secondary load in the sediment is strongly reduced.

Bathtub SFD

Directly inspired from Meadows (Systems Thinking)

Westley, F. R., O. Tjornbo, L. Schultz, P. Olsson, C. Folke, B. Crona and Ö. Bodin. 2013. A theory of transformative agency in linked social-ecological systems. Ecology and Society 18(3): 27. link

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale.

Experiment with adjusting the moose birth-rate to simulate Over-shoot followed by environmental recovery