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.

风电场等效粗糙度高度的准确参数化对于中尺度气候模拟以及风力涡轮机的功率预测至关重要。现有模型的一个明显不足之处是结果敏感地取决于$s_X/s_{ÿ}$， 在哪里 $s_X$ 其他 $s_{ÿ}$是涡轮的无量纲的沿流向和跨向的间距。为了理解这一问题，我们对三种类型的中等，大型和小型准无限风电场进行了大涡模拟（LESs）$s_X/s_{ÿ}$。我们发现，转子处的风速与轮毂高度处的水平平均风速不同，这对于风力发电场较小的风场尤其如此。$s_X/s_{ÿ}$。轮毂高度处的这种流动不均匀性在确定风电场的等效粗糙度高度中起着重要作用，但在现有模型中通常被忽略。考虑到轮毂高度处的流动不均匀性，我们针对风电场的等效粗糙度高度提出了一种新的自上而下/自下而上的耦合模型。我们将模型与现有模型和LES进行了比较。结果表明，所提出的模型能够预测所有类型风电场的等效粗糙度高度，而与$s_X/s_{ÿ}$的价值。