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 of the Food Chain

A model of water flow within the potable water supply chain

Compost modelling

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This model implements a very simple proxy for vertical dispersion of heat in a lake based on the equation:

dT/dt = 1/A d(EA)/dz (dT/dz)

where: T: temperature (oC); t: time (days); z: depth (m); A: cross-sectional area (m2); E: vertical dispersion coefficient (m2 d-1)

If we consider that E is constant (it is in this model), then the equation becomes dT/dt = (EA/A)(d^2T/dz^2) = E(d^2T/dz^2), the classic diffusion equation

The model is simplified by exchanging temperature as a state variable, rather than executing  the full heat balance. This would require a computation of fluxes of atmospheric longwave and shortwave radiation, water longwave radiation, water conduction and convection, and water evaporation and condensation.

The vertical dispersion coefficients are adjusted artificially so that mixing increases at lower temperatures, thus quickly homogenizing the water column in colder months of the year.

For school

This stock and flow diagram provides a broad description of the key nutrient pathways (N and P) that exist in a dune-lake system subject to external loadings emanating from intensive agriculture.

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.

Two households with PV systems and Electric Vehicles, sharing a battery and connected to the grid. What are the advantages?

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

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)

This model provides a dynamic simulation of the Sverdrup (1953) paper on the vernal blooming of phytoplankton.

The model simulates the dynamics of the mixed layer over the year, and illustrates how it's depth variation leads to conditions that trigger the spring bloom. In order for the bloom to occur, production of algae in the water column must exceed respiration.

This can only occur if vertical mixing cannot transport algae into deeper, darker water, for long periods, where they are unable to grow.

Sverdrup, H.U., 1953. On conditions for the vernal blooming of phytoplankton. J. Cons. Perm. Int. Exp. Mer, 18: 287-295

Simple energy balance model of a planet with albedo, ocean, and atmosphere.

Our final beer game!

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

This diagram provides an accessible description of the key processes that guide the water quality within a lake.

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

A simple phosphorus model for a generic lake.