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Submitted to Proceedings of the National Academy of Sciences of the United States of America

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In a solid and detailed paper, Lu, McElroy and Kiviluoma computed the potential for wind-generated electricity[1]. We believe such estimates are both interesting and important. However, the estimate seems too high, essentially because the wind turbines have direct access to only a small vertical fraction of the atmosphere.

The average amount of solar radiation at the top of the atmosphere is 340 W/m². Assuming that 1 % of this is in the kinetic energy of the atmosphere[1] and since 1 % of the atmospheric mass is in the bottom 100 m layer of air, we arrive at $P_{<100}=$0.034 W/m², which is roughly the total kinetic energy of the atmosphere per area in this layer. We chose the layer relevant to the 100 m diameter turbines at low altitudes considered in the paper. Compare this to the wind farm numbers used in the work; 2.5 MW turbines with an interturbine aerial spacing of 0.28 km² (onshore)[1] corresponds to 1.8 W/m² at 20 % capacity factor, which is the minimum capacity factor used in the work. This is 53 $\times P_{<100}$. Let us also look at the final result in Table 1 in [1]: Taking the example of Germany (onshore, area:$3.6\times 10^{11}$ m²), the overall average for the wind energy potential corresponds to 1.0 W/m${}^{2}=29\times P_{<100}$. This is lower than the above value and consistent with it, since the authors were carefully selective of the regions for deployment, with due reason.

The estimates of [1] are higher than $P_{<100}$ by much more than an order of magnitude, as explained above. We believe that for such an amount of energy to be extracted, large back reaction to change the air circulation would at least need to occur, which is a crucial aspect not considered there. Our calculations are rough: For instance, we did not subtract for albedo nor account for the higher wind velocities at higher altitudes taking a larger fraction of the atmospheric kinetic energy, so that the discrepancy could quite well be larger. We believe it is important to understand the mechanism behind such a large discrepancy to clarify whether it is possible to extract such an amount of energy from wind.