Gaussian-based multicolumn spatial distribution method for wind farm parameterizations

Wind farm parameterizations are crucial for quantifying the wind-farm atmosphere interaction, where wind turbines are typically modeled as elevated momentum sinks and sources of turbulence kinetic energy (TKE). These quantities must be properly distributed to the mesoscale grid. Existing parameterizations use the single-column method. However, this method can easily lead to the errors of the spatial distribution of the sink and source, thereby impacting the accuracy of mesoscale flow simulations. To this end, we propose a multi-column spatial distribution method based on the Gaussian function. This method distributes the sink and source to multiple vertical grid columns based on the grid weights, which are analytically determined by integrating the two-dimensional Gaussian function over the mesoscale grid. We have applied this method to the classic Fitch model, proposed the improved Fitch-Gaussian model, and integrated it into the mesoscale Weather Research and Forecasting model. Using high-fidelity large eddy simulation as a benchmark, we compared the performance of the proposed method with the single-column method. The results show that the proposed method captures the spatial distribution of the sink and source more accurately, with a higher correlation coefficient and lower normalized root mean square error. Furthermore, the Fitch-Gaussian model better captures the overall spatial distribution patterns of velocity deficit and added TKE. Therefore, the proposed method is recommended for future mesoscale wind farm simulations, especially when the influence of the wind turbine rotor spans multiple mesoscale grid columns.