Nature: There is enough power in Earth’s winds to be a primary source of near-zero-emission electric power as the global economy continues to grow through the twenty-first century. Historically, wind turbines are placed on Earth’s surface, but high-altitude winds are usually steadier and faster than near-surface winds, resulting in higher average power densities1. Here, we use a climate model to estimate the amount of power that can be extracted from both surface and high-altitude winds, considering only geophysical limits.
We find wind turbines placed on Earth’s surface could extract kinetic energy at a rate of at least 400 TW, whereas high-altitude wind power could extract more than 1,800 TW. At these high rates of extraction, there are pronounced climatic consequences. However, we find that at the level of present global primary power demand (~ 18 TW; ref. 2), uniformly distributed wind turbines are unlikely to substantially affect the Earth’s climate. It is likely that wind power growth will be limited by economic or environmental factors, not global geophysical limits.
Here, we quantify geophysical limits to wind power by applying additional drag forces that remove momentum from the atmosphere in a global climate model. We perform simulations in which drag is applied to either the near-surface environment or the entire atmosphere, and analyse consequences for the atmospheric kinetic energy budget and climate. When small amounts of additional drag are added to the atmosphere, the rate of kinetic energy extraction (KEE) increases. However, in the limit of infinite drag, the atmosphere is motionless and there is no kinetic energy to extract. This suggests that there must be some amount of added drag that maximizes KEE. We refer to this maximum KEE as the geophysical limit to global wind power. Here, we consider only geophysical limitations, not technical or economic constraints on wind power.
Main
The large-scale climate impacts of increased surface drag have been considered in previous studies. In an idealized global climate model, surface friction was uniformly increased across the globe, and this was found to decrease atmospheric kinetic energy and shift eddy-driven mid-latitude jets polewards3. In a general circulation model with specified sea surface temperatures, altered surface drag and modified surface roughness height over selected regions, caused slight increases in global surface temperatures4. This effect was also observed when land-surface roughness was increased in a climate model incorporating a mixed-layer ocean5. Other studies have investigated the wind anomaly patterns produced by isolated regions of increased surface roughness6; and estimated wind resource potential over land that was not ice-covered7.
However, these studies focused solely on increased surface drag. The effects of increased drag in the interior of the atmosphere have been studied8 where a drag term was added to regions of the atmosphere where wind speeds exceeded a cutoff velocity. Unfortunately, aspects of that work make their results difficult to interpret. For example, they include wake turbulence in a term that involves momentum transfer to the turbine blades despite the fact that there is no such momentum transfer in the wake and introduce a frictional parameter with units that are difficult to reconcile with their equations.
Results
Limits on wind power availability.
We differentiate among three types of kinetic energy loss represented in the CAM3.5 model9:
- Viscous dissipation refers to the rate at which work is done by viscosity of air in converting mean and turbulent kinetic energy to internal energy through heat.
- Roughness dissipation refers to the rate at which pre-existing surface momentum sinks such as the land or ocean surface dissipate kinetic energy.
- KEE refers to the removal of kinetic energy caused by momentum loss to the added momentum sinks. In the case of wind turbines, the kinetic energy would be converted to mechanical or electrical energy, most of which would ultimately be dissipated as heat. In our simulations, this heat is dissipated locally. Drag added to the atmosphere has important secondary consequences: the velocity change and associated velocity gradients may affect both roughness and viscous dissipation. Here, KEE refers only to the rate of transfer of kinetic energy to added momentum sinks.
The parameter we introduce to vary additional drag is ρArea: the effective extraction area per unit volume, discussed in Methods and Supplementary Section SA.1. Figure 1a shows KEE as a function of ρArea for cases where drag has been added to the near-surface layers (cases labelled SL(n)) and whole atmosphere (cases labelled WA(n)). (See also Supplementary Fig. SA.1a for the results on logarithmic scales.) As expected for low values of added drag, increasing extraction area increases KEE, that is, (d(KEE)/dρArea)>0. At the geophysical limit to global wind power, (d(KEE)/dρArea) = 0. As shown in Fig. 1b, for both the near-surface and whole-atmosphere cases we approach but do not reach this limit. Therefore, the geophysical limits exceed the maximum KEE values found in our study for both cases.
