It is not often that a new perspective is proposed in climate science, however, a set of two 2011 papers have done that (h/t to John Droz Jr!).
These papers are
Miller, L. M., Gans, F., and Kleidon, A.: Estimating maximum global land surface wind power extractability and associated climatic consequences, Earth Syst. Dynam., 2, 1-12, doi:10.5194/esd-2-1-2011
with the abstract
“The availability of wind power for renewable energy extraction is ultimately limited by how much kinetic energy is generated by natural processes within the Earth system and by fundamental limits of how much of the wind power can be extracted. Here we use these considerations to provide a maximum estimate of wind power availability over land. We use several different methods. First, we outline the processes associated with wind power generation and extraction with a simple power transfer hierarchy based on the assumption that available wind power will not geographically vary with increased extraction for an estimate of 68 TW. Second, we set up a simple momentum balance model to estimate maximum extractability which we then apply to reanalysis climate data, yielding an estimate of 21 TW. Third, we perform general circulation model simulations in which we extract different amounts of momentum from the atmospheric boundary layer to obtain a maximum estimate of how much power can be extracted, yielding 18–34 TW. These three methods consistently yield maximum estimates in the range of 18–68 TW and are notably less than recent estimates that claim abundant wind power availability. Furthermore, we show with the general circulation model simulations that some climatic effects at maximum wind power extraction are similar in magnitude to those associated with a doubling of atmospheric CO2. We conclude that in order to understand fundamental limits to renewable energy resources, as well as the impacts of their utilization, it is imperative to use a “top-down” thermodynamic Earth system perspective, rather than the more common “bottom-up” engineering approach.”
Kleidon, Axel, 2011: How does the earth system generate and maintain thermodynamic disequilibrium and what does it imply for the future of the planet? Article submitted to Royal Society. arXiv:1103.2014v1 [nlin.AO] 10 Mar 2011
with the abstract
“More than forty years ago, James Lovelock noted that the chemical composition of the earths atmosphere far from chemical equilibrium is unique in our solar system and attributed this to the presence of widespread life on the planet. Here I show how this rather fundamental perspective on what represents a habitable environment can be quantified using non-equilibrium thermodynamics. Generating disequilibrium in a thermodynamic variable requires the extraction of power from another thermodynamic gradient, and the second law of thermodynamics imposes fundamental limits on how much power can be extracted. When applied to complex earth system processes, where several irreversible processes compete to deplete the same gradients, it is easily shown that the maximum thermodynamic efficiency is much less than the classic Carnot limit, so that the ability of the earth system to generate power and disequilibrium is limited. This approach is used to quantify how much free energy is generated by various earth system processes to generate chemical disequilibrium. It is shown that surface life generates orders of magnitude more chemical free energy than any abiotic surface process, therefore being the primary driving force for shaping the geochemical environment at the planetary scale. To apply this perspective to the possible future of the planet, we first note that the free energy consumption by human activity is a considerable term in the free energy budget of the planet, and that global changes are closely related to this consumption of free energy. Since human activity and associated demands for free energy is anticipated to increase substantially in the future, the central question in the context of future global change is then how human free energy demands can increase sustainably without negatively impacting the ability of the earth system to generate free energy. I illustrate the implications of this thermodynamic perspective by discussing the forms of renewable energy and planetary engineering that would enhance overall free energy generation and thereby ”empower” the future of the planet.”
In response to the first paper, I contacted Axel Kleidon with the following e-mail on April 4 2011
I have one question so far. The winds are created by spatial gradients in heating and cooling. The westerlies, for example, result since it is colder through the troposphere at higher latitudes than equatorward. Sea breezes occur due to a warmer lower troposphere over land adjacent to cooler, stably stratified ocean water.
While I can see how vast areas of wind turbines could alter the pattern of heating and cooling (and thus alter the wind patterns to an extent) - both due to their waste heat and alteration of surface fluxes of heat, moisture and momentum, I do not see how the kinetic energy is lost as it is just redistributed. The waste heat, for example, still would be spatially heterogeneous and would generate wind flow.
One would need to show that the gradients of warm and cool regions are reduced as a result of the wind turbines to show a global average reduction in “free energy”.
Let me know how this issue is handled. Meanwhile, I will keep studying your paper! :-)
He responded with the reply on April 11 2011
Thanks for your question.
One critical aspect is that the strength of the atmospheric circulation is thermodynamically limited and that it already operates near maximum strength (i.e. maximum power, or equivalently, maximum generation of kinetic energy, or maximum dissipation or maximum entropy production — they all yield about the same). This can be shown relatively easily by quantifying how much power can be drawn out of the hemispheric gradient in solar irradiation. The derivation essentially follows the Carnot limit, except that the Carnot limit makes two critical assumptions that do not apply for the atmosphere:
* First, the Carnot limit assumes that there are no other irreversible processes within the system that compete for the same gradient. In the atmosphere, emission of radiation depletes the same hemispheric insolation gradient, so that kinetic energy generation competes with emission of terrestrial radiation. This reduces the maximum efficiency by a factor of 2.
* Second, the generation of kinetic energy and the associated heat transport depletes the temperature gradient that drives the generation. This reduces the maximum efficiency by another factor of 2.
The resulting maximum thermodynamic efficiency is about 2%, or 900 TW, which is very close to what is estimated from observations. In other words, the large-scale atmospheric circulation is approx. as strong as possible. In essence, this is the same as the maximum power principle in electrical engineering. This derivation is shown in section 4.3 and 4.4 of the attached.
When kinetic energy is extracted from the boundary layer, then it is obviously limited to what is generated within the atmosphere. Actually, it is a lot less, again because of thermodynamic limits (you cannot bring the atmosphere to a standstill). Furthermore, much of the areas are not accessible: 1/2 of the KE is dissipated in the free atmosphere, and of the remaining, 3/4 are dissipated over oceans. That alone leaves only 112.5 TW, of which, as said before, not all can be extracted. The GCM simulations that we did support the line of reasoning as well as the orders of magnitude.
The waste, dissipative heat plays practically no role since it is very small compared to the forcing in solar irradiation.
Hope these explanations help, otherwise I’d be happy to explain more.
I asked a follow up question on April 14, 2011
I plan to post sometime next week. However, I have another question. As you are aware, terrain extracts kinetic energy from the atmosphere even in the absence of any surface frictional effects (e.g. see pages 459 to 462 in the 2002 version of my modeling book).
What would be an equivalent terrain feature and impinging wind and stability that would result in the same limit from the wind extraction due to wind turbines? This would help in scaling the issue and providing another perspective.
Axel promptly replied
I think the best case (but still vague) are waves and sand dunes.
Waves generate roughness and should thereby extract more momentum from the atmosphere. The power involved in wave generation is about 63 TW (from the MIT people, Ferrari and Wunsch I think) and this power is taken from the kinetic energy of the atmospheric boundary layer. Now, we could ask if this is maximized. A rough estimate would be like this: 450 TW of dissipation within the boundary layer, 3/4 of which over the ocean, and if we take 1/3 of being extractable, we get about 110 TW, which is not too far off. And, after all, waves are not as high as wind turbines, so we should expect a lot less.
Another example would be the effect of dunes in sand transport, for which it has been proposed that dune formation maximizes sand transport. From an atmospheric point of view, this would mean maximum extraction of kinetic energy to drive the sand transport.
An issue with models (as far as I know how models handle this issue), by the way, is that they dissipate this transferred free energy by turbulence rather than transferring it to the ocean or to the sand. Oceans are usually driven by wind drag, but the resulting power input has already been dissipated by the model’s drag parameterization in the atmospheric boundary layer. So this should be quite an inconsistency in the coupling of models, with effects on the turbulent fluxes. I really think this points out that models do not handle interactions correctly at system boundaries with respect to free energy transfer.
Hope these thoughts help clarify some of the issues.
My follow up on April 14 2011 was
Thank you for the quick feedback.
There is still the issue of “form drag” that I wrote on in my e-mail. This is related to pressure forces, not the friction. Even small obstacles have this. For a 2-D hill (or mountain), as I show on page 462 of my book, it is given by
wave drag = the integral in x of the pressure as a function of x along the terrain slope times the x-gradient of the terrain.
This will occur in inviscid flow, but also in turbulent flow. Wind turbines would have this effect in addition to turbulent dissipation of the wind.
Large scale models do have parameterizations for this wave drag effect from terrain but not from other surface features that I am aware of. They use a aerodynamic roughness based formulation (i.e. frictional drag), but this is not the way it should be done with respect to form drag. In terms of your GCM runs with wind turbines, I assume you handled this just with frictional drag (page 4 of your paper). I assume one could interpret form drag as be part of C(sub ext),of course, but it might be useful to break into the two forms of drag.
I agree with you on the way models mishandle sand transport (and sea water spray also) as we discuss in our paper
Pielke, R.A. and T.J. Lee, 1991: Influence of sea spray and rainfall on the surface wind profile during conditions of strong winds. Bound.-Layer Meteor., 55, 305-308.
We wrote in our abstract that
“Janin and Cermak (1988) have: determined that airborne sediment in a wind tunnel substantially alters the low-level wind profile. This material apparently causes a reduction in wind speed since the pressure gradient force must accelerate both the air and the sediment, against the force of surface shearing stress.”
and then applied this concept to sea spray, where we wrote
“In this brief paper, we explore whether atmospheric wind profiles would be expected to be modified during periods of high winds as a result of heavy rainfall or sea spray. Although there has been controversy regarding the effect of sediment load on pressure drop (e.g., Rangaraju, 1988), our assumption that the wind profile rem~ins logarithmic is based on the physical modeling of Janin and Cermak (1988) in which even with sand loading in the atmosphere, the square root of the total kinetic energy profile remains logarithmic. This means that a given pressure gradient force can accelerate either air, or a combination of air and a suspended material but when suspended material is present, the actual air velocity will be less.”
I am really intrigued by your ideas, and appreciate the opportunity to discuss with you.
Axel replied on April 27 2011
[S]orry for the delay, I was on vacation and my internet connection collapsed when my iPad asked for a factory restore that required an internet connection…
Yes, I agree regarding your comment about form drag, which we did not consider. We originally added extra roughness to the frictional drag, but then separated this into the extra term C_ext. In principle, one should be able to add a separate form drag to this, although this would likely depend on the turbine characteristics and the wind park layout and makes this more complicated. I guess the effect of considering the form drag would lead to an even lower efficiency of what can be extracted from the wind and converted into useful power. Any extra “complication” seems to degrade thermodynamic efficiencies…
Thanks very much for sending the link to your paper! Yes, it is basically what I am talking about regarding the misrepresentation, with the addition that a maximum of power transfer from air flow to sand flow could help to quantify/constrain the interaction between air and sand flow.
Likewise, I enjoy this discussion with you very much as well.
I look forward to hearing more on Axel’s research on this topic!