Environmental Systems Calculus*

When we talk about the human habitation of Earth today, we want quantitative understandings of the planet’s carrying capacity. Materials and energy balances are key tools in achieving a quantitative understanding of the behavior of environmental systems.  They serve as a method of accounting for the flow of energy and materials into and out of a system.  Mass balances provide us with a tool for modeling the production, transport, and fate of things like pollutants or resources in an environment… examples of mass balances include prediction of rainwater runoff, oxygen balance in a stream, the temperature change in a river from the discharge of cooling water from a power plant, or the temperature rise due to global warming.

In its simplest form a materials or mass balance may be viewed as an accounting balance. For an environmental process the equation would be

Accumulation = input – output.

There are both known and unknown inputs, outputs, and accumulations in system modeling, but the mass balance should account for and solve the amount of unknown inputs and outputs.

Time is also a factor: For many environmental problems time is an important factor in establishing the degree of severity of the problem or in designing a solution. Another simple equation from environmental engineering:

Mass rate of accumulation = mass rate of input – mass rate of output

In plug-flow systems, a calculus equation can tell you how many km of pipe is needed to decontaminate a certain amount of polluted water as it flows through the pipe with a catalyst inserted. This kind of rate-of-flow-and-conversion is another calculation we need in order to understand our carrying capacity as a planet.

So, our situation is this. As human civilization has grown and continues to, we are increasing the inputs of some things in the system at a rate that outpaces the output. At the same time, we have a hard time calculating the availability and sustainability of some of the key resources – estimates have been wrong time and again. Likewise, we don’t know the tipping point of some processes, since we’ve never been to this spot before. More on what this means for our future as humans on this planet, and how theology affects our calculations, next time.

* Intro to Environmental Engineering Fourth edition (Davis & Cornwell). My family includes an environmental engineer.

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