Simple Model of the Food Chain

Forcings and feedbacks based on Tom Fiddaman, James Hansen and other feedback and cycle diagrams

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.

As initially proposed by Pr. William M White of Cornell University:

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.

Thinking about biodiversity policy in the United States, specifically relating to the Endangered Species Act of 1973. I have focused on the impacts that governmental policy will have on the environment, rather than contributions from both the government and the private sector. I have also chosen to focus on the financial aspect of policy, keeping all other factors equal.

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.

all pictures sourced from google images

Similar layout to CEU insight based on 2016 Land Use Science article on Causal Analysis by Patrick Meyfroidt This is focussed on causal chains

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.

ENP 65000 assignment

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 Tucson only. Tucson watersheds are Arroyo Chico, Canada Agua, and Lower Canada del Oro.

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.

サンプル

Harvested fishery with stepwise changes in fleet size. Ch 9 p337-339 John Morecroft (2007) Strategic Modelling and Business Dynamics

Model of how different features impact water supply and how water access disparity can influence conflict.

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 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 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.

Concepts are designed for Universatility and local variables without forcing a one size fits all model. 

Measurements in the course are designed to maintain a system perspective in all planning and measurement systems.