Steady States: From a Party to Earth’s Surface Heat

Imagine a social get-together in a reception hall. For about an hour after the start of the alcohol-free cocktails, new guests keep arriving. Feeling a little crowded inside, some guests decide to leave the hall to step outside for a stroll through the property. At a certain point it works out, as a result of their reflexes, that the number of people walking into the hall is the same as those walking out. Since the number of guests inside the hall is constant, we have what’s called a steady state. As long as the input of new guests equals the output of existing guests, steady state is maintained. A more sombre but far more important steady state involving humans would be achieved if we could stabilize world population by lowering birth rates to match declining death rates. (Long extraterrestrial journeys won’t be economically or technologically feasible in the foreseeable future and won’t serve as output rates.)

Many essential and approximate steady states occur at the molecular level. They involve  compounds and elements that are part of natural cycles. For instance, the amount of phosphorus in both land and sea would approximately be at steady state if humans recycled it. Phosphorus is an essential element and is found in nucleic acids such as DNA and RNA but also in molecules involved in cellular energetics such as ADP and ATP. The key is the polyatomic ion phosphate (PO43-). In the soil, microorganisms break down plant debris and animal waste to release the ion. Some phosphate from rocks is also added to soil. But the soil’s input rate is balanced by the output rate when plants uptake the essential ion and runoff removes some phosphate before plants can absorb them. When phosphate is added to land on an industrial scale without  corresponding recycling practices, then the output rate into rivers and oceans is accentuated. Snce the 1950s, the environmental flow of phosphorus has quadrupled; steady state has been thrown off, impairing marine freshwater and marine ecosystems.

Schematic-view-of-the-coupled-biogeochemical-cycles-of-carbon-nitrogen-and-phosphorusAlthough natural cycles are often introduced as separate phenomena in textbooks, in reality they are integrated. For example the phosphorus and carbon cycles are tightly coupled. There is evidence that between 23 and 150 million years ago, spanning the late Jurassic , Cretaceous, and Paleogene periods, the phosphorus cycle has not always been at steady state. It seems to have been affected by episodes of global warming.

steadyState
If the outflow rate around the loose plug equals the rate of water pouring out of the faucet, the amount of water in the sink is in steady state.

On that note, can there be a steady state involving heat? Although heat and temperature are not the same concept, since the number of air molecules in the atmosphere is approximately constant, when one is fairly steady, so is the other. Imagine the amount of heat at the earth’s surface represented as the amount of water in a sink. Above the sink we have a faucet gently turned on, but we also have a loose plug over the drain. If the inflow rate from the faucet is equal to the the amount of water that seeps around the loose plug and goes down the drain, the amount of water in the sink will be constant.

Now imagine tightening the plug ever so slightly.  The water in the sink starts to rise, but eventually the extra pressure from the extra water’s weight above the drain helps establish a new steady state. The difference between the current and prior  states is that we now a higher, albeit constant, level of water in the sink.

Getting back to the analogy we started: if water represents heat, then the plug is represented by water vapour and carbon dioxide in the atmosphere. Since the concentration of water vapour is far less affected by human activity than CO2, it’s the addition of the latter to the atmosphere that tightens the plug. If we can stabilize carbon emissions, then although we will have a higher average global temperature than pre-industrial levels, we won’t be entrapping more heat.

Can there be a natural corrective action like the effect of gravity in our analogy? After all, the geologic record reveals that the earth has repeatedly experienced changes  in CO2 concentrations. Before answering the question, we have to be careful and point out an important characteristic of real-world steady states. Natural systems involve many factors and create complex, cyclical steady states, not flat lines. The graph below reveals that for over half a million years, the CO2 concentration has oscillated from about 180 ppm to under 300 ppm. (Even if we had never burnt fossil fuels, in merely one year, due to seasonal variations, carbon dioxide peaks and ebbs—with a much lower amplitude of course.) But the current, human induced 410+ ppm-spike in CO2 has been unprecedented in over half a million years. Given that it has taken an average of 100 000 years to get a drop of only 120 ppm,

waiting for a natural correction would bring about too many negative consequences for too many species, including our own.

Achieving approximate steady states involving ions, gases and heat is what our living earth does in the long stages between catastrophes.  It’s time for our politics, technology and lifestyles to be in tune with the time-tested cycles of geology, biology and climate.

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