Guest Post by Willis Eschenbach

Figure 1. The Experimental Setup

I keep reading statements in various places about how it is indisputable “simple physics” that if we increase the amount of atmospheric CO2, it will inevitably warm the planet. Here’s a typical example:

In the hyperbolic language that has infested the debate, researchers have been accused of everything from ditching the scientific method to participating in a vast conspiracy. But the basic concepts of the greenhouse effect is a matter of simple physics and chemistry, and have been part of the scientific dialog for roughly a century.

Here’s another:

The important thing is that we know how greenhouse gases affect climate. It has even been predicted hundred years ago by Arrhenius. It is simple physics.

Unfortunately, while the physics is simple, the climate is far from simple. It is one of the more complex systems that we have ever studied. The climate is a tera-watt scale planetary sized heat engine. It is driven by both terrestrial and extra-terrestrial forcings, a number of which are unknown, and many of which are poorly understood and/or difficult to measure. It is inherently chaotic and turbulent, two conditions for which we have few mathematical tools.

The climate is composed of five major subsystems — atmosphere, ocean, cryosphere, lithosphere, and biosphere. All of these subsystems are imperfectly understood. Each of these subsystems has its own known and unknown internal and external forcings, feedbacks, resonances, and cyclical variations. In addition, each subsystem affects all of the other subsystems through a variety of known and unknown forcings and feedbacks.

Then there is the problem of scale. Climate has crucially important processes at physical scales from the molecular to the planetary, and at temporal scales from milliseconds to millennia.

As a result of this almost unimaginable complexity, simple physics is simply inadequate to predict the effect of a change in one of the hundreds and hundreds of things that affect the climate. I will give two examples of why “simple physics” doesn’t work with the climate — a river, and a block of steel. I’ll start with a thought experiment with the block of steel.

Suppose that I want to find out about how temperature affects solids. I take a 75 kg block of steel, and I put the bottom end of it in a bucket of hot water. I duct tape a thermometer to the top end in the best experimental fashion, and I start recording how the temperature change with time. At first, nothing happens. So I wait. And soon, the temperature of the other end of the block of steel starts rising. Hey, simple physics, right?

To verify my results, I try the experiment with a block of copper. I get the same result, the end of the block that’s not in the hot water soon begins to warm up. I try it with a block of glass, same thing. My tentative conclusion is that simple physics says that if you heat one end of a solid, the other end will eventually heat up as well.

So I look around for a final test. Not seeing anything obvious, I have a flash of insight. I weigh about 75 kg. So I sit with my feet in the bucket of hot water, put the thermometer in my mouth, and wait for my head to heat up. This experimental setup is shown in Figure 1 above.

After all, simple physics is my guideline, I know what’s going to happen, I just have to wait.

And wait … and wait …

As our thought experiment shows, simple physics may simply not work when applied to a complex system. The problem is that there are feedback mechanisms that negate the effect of the hot water on my cold toes. My body has a preferential temperature which is not set by the external forcings.

For a more nuanced view of what is happening, let’s consider the second example, a river. Again, a thought experiment.

I take a sheet of plywood, and I cover it with some earth. I tilt it up so it slopes from one edge to the other. For our thought experiment, we’ll imagine that this is a hill that goes down to the ocean.

I place a steel ball at the top edge of the earth-covered plywood, and I watch what happens. It rolls, as simple physics predicts, straight down to the lower edge. I try it with a wooden ball, and get the same result. I figure maybe it’s because of the shape of the object.

So I make a small wooden sled, and put it on the plywood. Again, it slides straight down to the ocean. I try it with a miniature steel shed, same result. It goes directly downhill to the ocean as well. Simple physics, understood by Isaac Newton.

As a final test, I take a hose and I start running some water down from the top edge of my hill to make a model river. To my surprise, although the model river starts straight down the hill, it soon starts to wander. Before long, it has formed a meandering stream, which changes its course with time. Sections of the river form long loops, the channel changes, loops are cut off, new channels form, and after while we get something like this:

Figure 2. Meanders, oxbow bends, and oxbow lakes in a river system. Note the old channels where the river used to run.

The most amazing part is that the process never stops. No matter how long we run the river experiment, the channel continues to change. What’s going on here?

Well, the first thing that we can conclude is that, just as in our experiment with the steel block, simple physics simply doesn’t work in this situation. Simple physics says that things roll straight downhill, and clearly, that ain’t happening here … it is obvious we need better tools to analyze the flow of the river.

Are there mathematical tools that we can use to understand this system? Yes, but they are not simple. The breakthrough came in the 1990’s, with the discovery by Adrian Bejan of the Constructal Law. The Constructal Law applies to all flow systems which are far from equilibrium, like a river or the climate.

It turns out that these types of flow systems are not passive systems which can take up any configuration. Instead, they actively strive to maximize some aspect of the system. For the river, as for the climate, the system strives to maximize the sum of the energy moved and the energy lost through turbulence. See the discussion of these principles here, here, here, and here. There is also a website devoted to various applications of the Constructal Law here.

There are several conclusions that we can make from the application of the Constructal Law to flow systems:

1. Any flow system far from equilibrium is not free to take up any form as the climate models assume. Instead, it has a preferential state which it works actively to achieve.

2. This preferential state, however, is never achieved. Instead, the system constantly overshoots and undershoots that state, and does not settle down to one final form. The system never stops modifying its internal aspects to move towards the preferential state.

3. The results of changes in such a flow system are often counterintuitive. For example, suppose we want to shorten the river. Simple physics says it should be easy. So we cut through an oxbow bend, and it makes the river shorter … but only for a little while. Soon the river readjusts, and some other part of the river becomes longer. The length of the river is actively maintained by the system. Contrary to our simplistic assumptions, the length of the river is not changed by our actions.

So that’s the problem with “simple physics” and the climate. For example, simple physics predicts a simple linear relationship between the climate forcings and the temperature. People seriously believe that a change of X in the forcings will lead inevitably to a chance of A * X in the temperature. This is called the “climate sensitivity”, and is a fundamental assumption in the climate models. The IPCC says that if CO2 doubles, we will get a rise of around 3C in the global temperature. However, there is absolutely no evidence to support that claim, only computer models. But the models assume this relationship, so they cannot be used to establish the relationship.

However, as rivers clearly show, there is no such simple relationship in a flow system far from equilibrium. We can’t cut through an oxbow to shorten the river, it just lengthens elsewhere to maintain the same total length. Instead of being affected by a change in the forcings, the system sets its own preferential operating conditions (e.g. length, temperature, etc.) based on the natural constraints and flow possibilities and other parameters of the system.

Final conclusion? Because climate is a flow system far from equilibrium, it is ruled by the Constructal Law. As a result, there is no physics-based reason to assume that increasing CO2 will make any difference to the global temperature, and the Constructal Law gives us reason to think that it may make no difference at all. In any case, regardless of Arrhenius, the “simple physics” relationship between CO2 and global temperature is something that we cannot simply assume to be true.

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