### Momentum Supply Constraints on Regional Wind Power Production

Recent work has shown that global momentum flux constrains the ultimate wind power resource to be less than what would be estimated from a simple climatology of existing wind at turbine hub-height (Miller et al., 2011) and that increasing surface roughness in a defined region with linear scale on the order of 1000 km has little impact on the total dissipation of kinetic energy in that region (Barrie and Kirk-Davidoff, 2010). The latter invariance presumably arises from the down-scale nature of the turbulent energy cascade. The convergence of the eddy flux of momentum depends largely on the large scale circulation, so that increasing roughness at the surface results in a reduction of wind speed such that dissipation always balances an approximately fixed momentum flux convergence from larger scales of motion. However, the details and elasticity of this constraint have not been adequately addressed. Does the elasticity of the momentum supply depend strongly on the size of the region that is roughened? Does it depend on the height of the turbines or the details of the way turbine drag is imposed? Is the elasticity different on land and at sea? In this work we will use the Weather Research and Forecasting model (WRF) to address these questions, and in particular to evaluate the hypothesis that the climatological momentum dissipation (approximately 1 W/m^2 in the global average) is a good rule-of-thumb estimate of the ultimately extractable wind power resource for any finite region.