A generalized top down model for Equivalent Roughness of Fully Developed Wind Farm*

In mesoscale numerical simulations, wind farms are often parameterized as surface roughness using the top-down model. The top-down model (Phys. Fluids 22 (1), 46--56) works well for fully developed wind farms with moderate turbine spacing but its performance deteriorates for farms with large streamwise or spanwise turbine spacing. In the present study, we propose a parameterization to characterize flow non-uniformity at the hub height. This parameterization is subsequently incorporated in the top-down model, and solved by coupling the Jensen model and the wake layer model to match the mean flow from the two models at the hub-height. Predictions of our model are compared with other models and a suite of large-eddy simulation (LES) data. We find that the new model is able to predict the equivalent roughness height of fully developed wind farms more accurately than the conventional top-down model.