Abstract. With the current expansion of wind power as a renewable energy source, wind turbines increasingly extract kinetic energy from the atmosphere, thus impacting its energy resource. Here, we present a simple, physics-based model (the Kinetic Energy Budget of the Atmosphere; KEBA) to estimate wind energy resource potentials that explicitly account for this removal effect. The model is based on the regional kinetic energy budget of the atmospheric boundary layer that encloses the wind farms of a region. This budget is shaped by horizontal and vertical influx of kinetic energy from upwind regions and the free atmosphere above, as well as the energy removal by the turbines, dissipative losses due to surface friction and wakes, and downwind outflux. These terms can be formulated in a simple yet physical way, yielding analytic expressions for how wind speeds and energy yields are reduced with increasing deployment of wind turbines within a region. We show that KEBA estimates compare very well to the modelling results of a previously published study in which wind farms of different sizes and in different regions were simulated interactively with the Weather Research and Forecasting (WRF) atmospheric model. Compared to a reference case without the effect of reduced wind speeds, yields can drop by more than 50 % at scales greater than 100 km, depending on turbine spacing and the wind conditions of the region. KEBA is able to reproduce these reductions in energy yield compared to the simulated climatological means in WRF (n=36 simulations; r2=0.82). The kinetic energy flux diagnostics of KEBA show that this reduction occurs because the total yield of the simulated wind farms approaches a similar magnitude as the influx of kinetic energy. Additionally, KEBA estimates the slowing of the region's wind speeds, the associated reduction in electricity yields, and how both are due to the depletion of the horizontal influx of kinetic energy by the wind farms. This limits typical large-scale wind energy potentials to less than 1 W m−2 of surface area for wind farms with downwind lengths of more than 100 km, although this limit may be higher in windy regions. This reduction with downwind length makes these yields consistent with climate-model-based idealized simulations of large-scale wind energy resource potentials. We conclude that KEBA is a transparent and informative modelling approach to advance the scientific understanding of wind energy limits and can be used to estimate regional wind energy resource potentials that account for the depletion of wind speeds.
Parsing the Kinetic Energy Budget of the Ocean Surface Mixed Layer