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.

SO4^2- is in M

H2S is in M

CH4 is in M

CO2 is in M

------------------------------------------

AOM is a rate (mol Ed * L^-1 * y^-1), Ed = electron donor, here CH4)

AOM = fT*vmax*FK*FT

--------------------------------------------------------

fT is the temperature contribution. Dimension less.

f(T) = Q10^((T-Ref. T)/10)

--------------------------------------------------------

vmax is the maximum turnover rate of SO4^2- and CH4. The unit is mmol Ed * L^-1 * y^-1.

vmax = µ*B/Y*ϕ , at 5 deg C

µ: Max. specific growth rate pr year. Average from Dale et al 2006 (tab. 4).

B: The steady-state biomass conc. (mol C biomass L^-1). Calculated from Kallmayer et al 2012 and cell abundance data from M5. 

Y: Yield (mol C biomass produced per mol E(D) consumed). Calculated from Dale et al 2006 (tab. 4).

ϕ: Porosity av. of the SMTZ from M5 data.

-----------------------------------------------------

FK is the kinetic contribution and is unitless. 

FK = ([Ed]/KEd + [Ed]) ([Ea]/KEa+[Ea])

[Ed]: Conc. of e- donor. 

KEd: half-saturation constant of e- donor.  

[Ea]: Conc. of e- acceptor.

KEa: half-saturation constant of e- acceptor. 

All in M.

------------------------------------------------------

FT is the thermodynamic contribution and is unitless. 

FT = 1 - exp (ΔGNET/chi*R*T)

ΔGNET is the net Gibbs energy change from the reaction. 

ΔGNET = ΔGINSITU + ΔGBQ

ΔGINSITU = -16.9+8.3145*[T]*Ln([HS^-]*[HCO3^-]/[SO4^2-]*[CH4])

 ΔGBQ = 1.75 avraged from Dale et al 2008. 

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.

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.

Thanks to Jacob Englert for the model if-then-else structure.

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

My AP Environmental Homework for the Cats Over Borneo Assignment

The beginning of a systems dynamics model for teaching NRM 320.

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 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.

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.

With Our-Green-Spine we have discovered new insights how trees / forest / green structures are part of the managing system of controlling the temperature of our Earth via their cooling capacity by using water and influencing the water cycle. We want to translate our insights in a climate model. People who to join us please send an email to marcel.planb@gmail.com.
Thanks, Marcel de Berg

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)

Here is an average representation of Earth today. Enjoy!

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.

Simple Model of the Food Chain

From Schluter et al 2017 article A framework for mapping and comparing behavioural theories in models of social-ecological systems COMSeS2017 video. See also Balke and Gilbert 2014 JASSS article How do agents make decisions? (recommended by Kurt Kreuger U of S)

Bathtub SFD

The fishing sector (artisanal and industrial) considered as a renewable resource is a sector with a strong potential to create employment and new resources necessary for the population. It is also an important source of foreign exchange due to the export of sea products and represent a potential for the development of entrepreneurship.

Indeed, Benin, a West African country with a population of about twelve million inhabitants, has a 125 km long coastline. Benin's fisheries sector contributes only 3% of the GDP, forms a very small part of exports, while Beninese fisheries products are in increasing demand in Europe.

However, the widespread use of non-regulatory fishing methods and gear, the uncontrolled increase in fishing effort, the degradation of ecosystems, and the pollution of water bodies by household and industrial waste mean that national production of fishery is stagnating at an average of 39,500 tons per year.

The increase in commercial fisheries production is therefore becoming an imperative in order to continue to guarantee the fishing industry and to safeguard its sustainability and to increase its contributions to the GDP. Simulation models can be used to help making durable decisions.

In the proposed model, we assumed that the largest population of fishermen harvesting the most important species of fish in the large sea of Benin, the shrimp.

The complete the fishery system consists of the coupled dynamic systems of the Fish population and the one hand and the Fishing boat (fishing industry) on the other, that have been represented by the Stocks.

Earnings of the fishermen are used to maintain, buy new fishing boats or to replace old boats that go out of commission, but also, to take care of families.

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.

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.