This model uses simple functions (converters, cosine) to simulate the water balance inside a reservoir.

Harvested fishery with endogenous investment and ship deployment policy. Ch 9 p345-360 John Morecroft (2007) Strategic Modelling and Business Dynamics. See simpler models at IM-2990 and IM-2991

Examining the ecosystem of the sea turtle and how that influences its population as an endangered species.

This diagram provides a stylised description of important feedbacks within a shallow-lake system.

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 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.

This is step 2 in making a climate model based on our insights of how trees actively contribute to the cooling capcacity of the Earth.​

In this step we divide the incoming energy from the sun to the land and to the oceaan.

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 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.

Interplay between wolves eating sheep and farmers killing wolves who kill deer that eat crops that feed sheep.

Marine plastic is rapidly increasing due to increasing production and use of plastic in all economic activities, short use times and long life times of plastic, and large mismanagement of plastic waste. With this, the threat plastic poses to the marine biosphere is also increasing and will continue to increase over a long time into the future. Risk knowledge is limited and risk perception and awareness are not resulting in significant mitigation efforts. The case study will aim at modeling the use and life cycles of plastic and the transport paths that lead to plastic entering the ocean. The models will be used to simulate possible futures based on a scenario approach. The results of these efforts will be visualized with the goal to increase risk awareness.

This model illustrates predator prey interactions using real-life data of wolf and moose populations on the Isle Royale. It was "cloned" from a model that InsightMaker provides to its users, at
https://insightmaker.com/insight/2068/Isle-Royale-Predator-Prey-Interactions
Thanks Scott Fortmann-Roe.

I've created a Mathematica file that replicates the model, at
http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/Moose-n-Wolf-InsightMaker.nb

It allows one to experiment with adjusting the initial number of moose and wolves on the island.

I used steepest descent in Mathematica to optimize the parameters, with my objective data being the ratio of wolves to moose. You can try my (admittedly) kludgy code, at
http://www.nku.edu/~longa/classes/2018spring/mat375/mathematica/Moose-n-Wolf-InsightMaker-BestFit.nb

{WolfBirthRateFactorStart,
WolfDeathRateStart,
MooseBirthRateStart,
MooseDeathRateFactorStart,
moStart,
woStart} =
{0.000267409,
0.239821,
0.269755,
0.0113679,
591,
23.};

Our final beer game!

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 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 slider to turn off dispersion (set to zero), and see that if the tidal wave did not mix with the estuary water due to turbulence, the estuary would quickly become a freshwater system.

The World3 model is a detailed simulation of human population growth from 1900 into the future. It includes many environmental and demographic factors.

Use the sliders to experiment with the initial amount of non-renewable resources to see how these affect the simulation. Does increasing the amount of non-renewable resources (which could occur through the development of better exploration technologies) improve our future? Also, experiment with the start date of a low birth-rate, environmentally focused policy.

Simple Model of the Food Chain

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 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.