Physical limits of wind energy within the atmosphere and its use as renewable energy: From the theoretical basis to practical implications

Abstract

How much wind energy does the atmosphere generate, and how much of it can at best be used as renewable energy? This review aims to give first-order estimates and sensitivities to answer these questions that are consistent with those obtained from numerical simulation models. The first part describes how thermodynamics determines how much wind energy the atmosphere is physically capable of generating at large scales from the solar radiative forcing. The work done to generate and maintain large-scale atmospheric motion can be seen as the consequence of an atmospheric heat engine, which is driven by the difference in solar radiative heating between the tropics and the poles. The resulting motion transports heat, which depletes this differential solar heating and the associated, large-scale temperature difference. This interaction between the thermodynamic driver and the resulting dynamics leads to a maximum in the global mean kinetic energy generation rate of about 1.7 W m$^{-2}$, which matches rates inferred from observations of about 2.1 - 2.5 W m$^{-2}$ very well. The second part focuses on the limits of converting the kinetic energy of the atmosphere into renewable energy. The momentum balance of the lower atmosphere shows that at large-scales, only a fraction of about 26% of the kinetic energy can at most be converted to renewable energy, yielding a typical resource potential of about 0.5 W m$^{-2}$ per surface area. The apparent discrepancy with much higher yields of small wind farms can be explained by the spatial scale of about 100 km at which kinetic energy near the surface is being dissipated and replenished. I close with a discussion of how these insights are compatible to established meteorological concepts, inform practical applications, and can set the basis for doing climate science in a simple, analytical, and transparent way.