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Geophysical limits to global wind power

Kate Marvel, Ben Kravitz, and Ken Caldeira · Nature Climate Change 3, 118-121 · 2013

Key finding. Adding drag to a global climate model shows that wind turbines at the Earth's surface could extract kinetic energy at a rate of at least 428 terawatts and turbines distributed through the whole atmosphere at least 1,873 terawatts — more than 20 and more than 100 times the roughly 18 terawatts of present global primary power demand.

Two stacked line plots against latitude from 90 degrees south to 90 degrees north, each with a red line for drag added near the surface, extracting 428 terawatts, and a blue line for drag added throughout the atmosphere, extracting 429 terawatts. The upper panel shows the change in zonal mean temperature in kelvin: the red line is mostly positive, around plus half a kelvin through the tropics, while the blue line is mostly around minus one kelvin, and both plunge to about minus three at the North Pole. The lower panel shows the percentage change in zonal mean precipitation, with both lines oscillating between roughly plus 17 and minus 21 per cent and mostly below zero.
At extraction rates more than twenty times global energy demand, the two ways of taking the energy have opposite temperature effects — surface drag warms, whole-atmosphere drag cools — while both dry the planet. Scaled down to the roughly 18 terawatts civilization actually uses, these become changes of about a tenth of a kelvin and about 1 per cent. Figure 2 from Marvel, Kravitz, and Caldeira (2013), Nature Climate Change 3, 118-121. Reproduced under author reuse rights. Extracted from the published PDF and resized for web display.

What question did this research address?

Extracting energy from the wind slows the wind. Enough turbines would therefore extract less, not more — in the limit of infinite drag the atmosphere stops moving and there is nothing left to take. Somewhere between those extremes lies a maximum rate of extraction set by the atmosphere itself.

This paper asked where that geophysical maximum lies, both for turbines at the surface and for high-altitude wind power throughout the depth of the atmosphere, and what the climate would look like at extraction rates approaching it.

What did we find?

Drag was added to the CAM3.5 climate model, either in the near-surface layers alone or uniformly through the whole atmosphere, and the rate of kinetic energy transferred to those added momentum sinks was tracked as the drag was increased.

Extraction rises with added drag and then must turn over. The simulations approach but do not reach the turnover, so the reported figures — 428 terawatts near the surface, 1,873 terawatts through the whole atmosphere — are lower bounds on the geophysical limit rather than the limit itself.

Extraction is not free of consequence for the atmosphere's energetics. Each additional watt extracted near the surface lowers total atmospheric kinetic energy by 80 kilojoules; each watt extracted through the whole atmosphere lowers it by 400 kilojoules.

Whole-atmosphere extraction largely pays for itself out of increased production. Total atmospheric kinetic energy production rises by about 0.8 watts per watt extracted, sustained by increased conversion of available potential energy — up to about 1,600 terawatts, beyond which production and poleward heat transport both decline.

That breakdown marks a regime shift in the circulation. In the most extreme whole-atmosphere case the Hadley cells extend all the way to the poles, each hemisphere transporting heat with a single overturning cell, and mass-weighted mean wind speed falls from 18.5 to 3.1 metres per second.

At extraction rates near 428 terawatts, zonal mean temperature changes by about 1 kelvin and zonal mean precipitation by about 10 per cent. Scaling those effects down to the roughly 18 terawatts of global energy demand gives zonal mean changes of about 0.1 kelvin and about 1 per cent.

The sign of the global mean temperature effect depends on where the energy is taken. At the level of global demand, uniformly distributed near-surface turbines warm the Earth by 0.03 kelvin while turbines distributed through the atmosphere cool it by 0.007 kelvin; global mean precipitation falls in both cases.

Why does it matter?

It answers the resource question and closes it. There is far more power in the winds than civilization uses, by a factor of at least twenty even confining turbines to the surface, so the case against wind power cannot be that the atmosphere does not contain enough energy.

It also disposes of the objection that using wind at scale would itself change the climate. The climatic effects are large only at extraction rates twenty times global demand; at the scale civilization actually needs, uniformly distributed turbines shift zonal mean temperature by about a tenth of a kelvin.

What limits wind power is therefore economics, siting, and local environmental considerations — not a global geophysical ceiling. The binding constraints on wind lie elsewhere, in where the resource is and when it arrives.

Citation

Kate Marvel, Ben Kravitz, and Ken Caldeira (2013). Geophysical limits to global wind power. Nature Climate Change 3, 118-121.

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