A new coupled model for the equivalent roughness heights of wind farms

Accurate parameterization of wind farms’ equivalent roughness heights is critical to meso-scale climate simulations as well as power predictions of wind turbines. A notable inadequacy of the existing models is that the results sensitively depend on s_x/s_y, where s_x and s_y are the dimensionless streamwise and spanwise spacing of the turbines. To understand the issue, we conduct large-eddy simulations (LESs) for three types of quasi-infinite wind farms with moderate, large, and small s_x/s_y. We find that the wind speed at the rotor is different from the horizontally averaged wind speed at the hub height, and this is particularly true for wind farms with small s_x/s_y. This flow inhomogeneity at the hub height plays an important role in determining wind farms’ equivalent roughness height but is often neglected in the existing models. Accounting for the flow inhomogeneity at the hub height, we propose a new coupled top-down/bottom-up model for the equivalent roughness heights of wind farms. Our model is compared with the existing models and our LESs. The results show that the proposed model is able to predict the equivalent roughness height of all types of wind farms irrespective of s_x/s_y’s value.