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.

My model is on global population and its impact on the availability of natural resources. The stocks in my system include food availability, soil resources and water resource availability. One question I believe my model can address is, what are the connections between food availability, soil resources and water resource availability; or in other words, are these stocks influenced equally by variables?  I hope to show a direct correlation between all three of these stocks. Food availability as stated in The Impact of Population Growth on Food Supplies and the Environment stated that, “The continued production of an adequate food supply is directly dependent on ample fertile land, fresh water, energy, plus the maintenance of biodiversity.” As population continues to grow so will the inputs to natural resources including water, fertilizer, and the need to have more available land.  What is more astonishing is that if these natural resources are never completely tapped dry, on a per capita perspective availability these resources will decline on astronomical levels since it has to be split amongst people (Pimental et al, 1996).

The flows in my system include food production,drought, water pollution, and greenhouse gases. I picked drought as a flow since it directly impacts the level of water available. Take for instance in California, the five year drought has caused scarcity and triggered state-wide executive orders to conserve water (California Department of Water Resources, 2017). Drought and water pollution can be affected by the number of people living in a country, which is why I picked these elements as flows. Furthermore food production, water pollution and greenhouse gases have strong influences on the availability of natural resources.

I picked mortality rates, birth rates, water scarcity, and industrial development as my variables. Since birth rates and mortality rates vary depending on the country I picked these as variables on my system since population growth is influenced by these variables.   Impact of Population Growth describes how the U. S. is already being affected by population growth, as stated here, “In populous industrial nations such as the United States, most economies of scale are already being exploited; we are on the diminishing returns part of most of the important curves.”

I have decided to change “developed countries” and undeveloped countries” as stocks to variables since these factors actually act more like variables. One question I hope to address with my model is how developed countries can  reduce their impact on resources? Furthermore, Population growth rate does depend on whether a country is developed versus undeveloped, so a country's level of economic development is more of a variable. I have decided to change food production from a stock to a flow, since it seems to be more of a flow that might affect the level of a stock of available food. I have also changed water scarcity from a stock to a variable because it actually affects the flow of water into an overall stock of fresh drinking water

this is the Australian food web of the water buffalo

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.

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.

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

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

Clone of: 

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.

A model of an infectious disease and control

Simple model of the global economy, the global carbon cycle, and planetary energy balance.

Dissolved oxygen mass balance in a tide pool, forced by tides and light.

Economic growth cannot go on forever, although politicians and most economist seem to think so. The activity involved in economic growth necessarily  generates entropy (disorder and environmental degradation). Entorpy in turn generates powerful negative feedback loops which will, as a response from nature, ensure that economic activity will eventually grind to a complete halt.  In these circumstances organised society cannot persist and will collapse. The negative feedback loops shown in this graph have already started to operate. The longer economic growth continues unabated, the more powerful these negative feedback loops will become. How long can economic growth continue before it is overwhelmed? It may not be very far in the future.

This a simple and "totally accurate" model of the exponential human population.

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

This incomplete model represents a building that is heated by conduction from the hot outside air, solar gain through the windows, and internal heat from the people and machines inside. To complete the model, define the flow that represents the heat removed by mechanical cooling.

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.

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

Clone of IM-1954 to tidy up layout. 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.

The primary goal is matching the discharge and flows from the Edwards Aquifer with the recharge into the groundwater system.