Guest Post by Willis Eschenbach (@WEschenbach at X, my own blog is here.)
I’d like to take a moment to discuss some implications of my peer-reviewed paper about my implementation of a Constructal climate model. The paper is available here. I’ll steal some images from the paper for this discussion
To understand the model, it’s necessary to understand the Constructal Law. The Constructal Law is the most recently discovered fundamental law of thermodynamics. It applies to flow systems far from equilibrium, which is much of what we see in the world around us.
The Constructal Law was discovered by Adrian Bejan in 1996. His statement of it is as follows:
“For a flow system to persist in time it must evolve in such a way that it provides easier access to its currents.”
In terms of the Earth’s climate as a whole, what this means is that the climate system is always working to maximize the flow of power from the tropics to the poles and from there out to space.
This is the missing link in the current generation of climate models. They view the climate as a passive, linear system where if, say, the albedo increases by some amount X, then some other variable will perforce change by an amount Y. But that’s not the case.
Instead, the climate is dynamic. It responds to changing conditions, not randomly, but always following the Constructal Law by evolving in the direction of increasing the throughput of power from the tropics to the poles.
Now, Bejan and Reis applied the Constructal Law to the Earth’s climate and derived the equations governing the situation.
Fig. 1. Conceptual Constructal model. Earth’s surface is divided into a hot equatorial zone (area AH, temperature TH) and the cold polar zones (total area AL, temperature TL). Heat flow q is transported from hot to cold zones by atmospheric and oceanic circulation.
Clearly, that is an extremely simplified model. There’s no ocean, no mountains, just a simple sphere with some unspecified means of transporting the heat from the tropics to the poles.
The model calculates four different variables—the average temperatures TH and TL of the hot and cold zones, the area AH of the hot zone, and the power flow “q”.
The model calculates the temperature using two observable climate variables—the albedo (how much solar energy is reflected back to space) and the “greenhouse factor” (how much upwelling surface radiation is absorbed by the atmosphere). The short version is that the albedo regulates how quickly the power from the sun enters the system, and the greenhouse factor regulates how quickly that power leaves the system. Obviously, the temperature of the system will depend on the ratio of the two—if more power is entering than leaving the system will warm, and vice versa.
But as I said above, this is not a simple linear relationship. What happens is that the climate system is constantly evolving, subject to the constraints of power in and power out, to maximize the power throughput.
However, what Bejan and Reis didn’t do was to actually implement that model on a computer and test it against the actual Earth’s climate. So I set out to do that, and succeeded far beyond my expectations.
Here’s what the system looks like on the real Earth. Just as in the model, there is a clear hot zone and two cold zones, and the boundary between them is roughly linear and symmetrical north/south.
Fig. 2. Actual Earth hot equatorial zone (area AH, temperature TH) and cold polar zones (total area AL, temperature TL). Note that unlike the oceans that follow the theoretical boundaries shown in Fig. 1, the desert areas are in the cold zone.
And despite the model not having deserts and mountains and oceans and all the rest, here’s how well the model is able to emulate the actual average temperatures of the hot and cold zones.
Fig. 3. Annual mean temperatures from CERES observations (blue/cyan) and Constructal model (red/orange). Top: hot zone temperature TH. Bottom: cold zone temperature TL. Note that the model is NOT tuned to reproduce these temperatures, it is only tuned to reproduce the interzonal temperature difference.
Other than a slight variation around 2010, the computed and actual temperatures are so close that they overlap each other almost exactly.
And here are the annual changes in the anomalies of the actual and modeled power flow “q” from the tropics to the poles.
Fig. 4. Anomalies (about data mean) of the CERES satellite data (blue) and modeled Constructal results (red) for the amount of power flowing from the Equator to the Poles.
This graph is clear evidence that the model is actually capturing how the climate works. It does indeed follow the Constructal Law, maximizing the power flowing from the tropics to the poles just as the Constructal Law predicts.
Finally, here’s how well the model calculates the area of the hot zone “AH”.
Figure 5. As in Figure 1, but overlaid with what the model calculates as the boundaries between the hot and cold zones.
As I said, I was quite surprised by this. I didn’t expect the model to emulate the Earth anywhere near as well as it did.
Finally, I used the model to see what the climate sensitivity would be if the greenhouse factor were increased by, say, a doubling of CO2. I got an answer of an increase of 1.1°C from a doubling of CO2. This is at the lower end of the other previous estimates of this sensitivity, but it is not the lowest.
Figure 6. The climate sensitivity estimated from doubling the CO2 in the Constructal climate model.
However, this does not include any changes in the albedo or any effect of the warming on the prevalence or timing of thunderstorms and cumulus fields, so it is likely an upper bound on the climate sensitivity.
Let me close this section by noting that, as shown in Figure 6 above, despite hundreds of thousands of hours of computer time and human study, the uncertainty and spread of the estimates of the constant called the “climate sensitivity” have increased over time. I view this as evidence that the underlying theory is incorrect. That theory says that the changes in temperature are a simple linear function of the downwelling radiation times the constant climate sensitivity. The Constructal Law says that this is not the case, and the model demonstrates that.
Conclusions and Implications
1) The model shows that the Earth’s climate system is indeed ruled by the Constructal Law, in that it maximizes tropical-polar power flow. Any model that does not include this active evolution of the system is an incorrect representation of reality.
2) Two variables alone, the albedo and the greenhouse factor, are sufficient to explain the changes in the surface temperature, as well as the variations in the equatorial-polar energy flow and the area of the hot zone. So while the model clearly shows that the greenhouse effect is real and important … the model also shows that it’s only half the story.
3) The climate sensitivity, which is how much the temperature will rise from a doubling of CO2, is likely to be quite small. So it looks like Thermageddon™ is cancelled, sorry, no refunds of the billions spent on meaningless climate gestures.
4) While it is at least somewhat possible to provide some direction and bounds on the future evolution of the greenhouse factor, that’s only half of the equation. The other half is the albedo. The variations in albedo are mostly ruled by the clouds, which everyone agrees are the part of the climate that is least understood and hardest to model, measure, or predict. As a result, the state of our current knowledge of clouds makes any long-term projections of future climate states … well … let me call them wildly hubrimistic and leave it at that.
Late night here, the redwood forest is wrapped in fog. The fog channels sound and makes it carry, so I can hear the currently high Pacific Ocean surf grumbling and gnawing on the coast six miles (10 km) to the west. Ah, dear friends, what an amazing, entrancing, awesome world it is our privilege to inhabit.
I can only wish the best of life for all of you,
w.
PS—Yes, you’ve heard it before: when you comment, please QUOTE the exact words you are discussing. It helps greatly to avoid the misunderstandings that are the bane of the intarwebs.
PPS:
hubrimistic
adjective
hu·bri·mis·ticˌˈhyü-brə-ˈmi-stik
: of, relating to, or characterized by feeling or showing unwarranted hope for the future, with just a soupçon of hubris thrown in for good measure
