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 and integrated into the governing equations. Existing parameterizations use a single-column method solely based on the relationship between the coordinates of the rotor center and the mesoscale grid. However, this method fails to account for the effects of different wind turbine positions within the grid, particularly neglecting the contributions of other turbines located in close proximity to grid boundaries. This can easily lead to errors of the spatial distribution of the sink and source, thereby impacting the accuracy of mesoscale flow simulations. To this end, we propose a multicolumn 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 approach to the classic Fitch model, proposed as the improved Fitch-Gaussian model, and integrated it into the mesoscale Weather Research and Forecasting model. The validation results demonstrate that when turbines are situated near grid boundaries, the proposed method captures the spatial distribution of the sink and source terms more accurately, exhibiting a higher correlation coefficient and a lower normalized root–mean–square error. For turbines located near the grid center, the performance of the proposed method is virtually identical to that of the single–column approach. However, due to the inherent limitations of the Fitch model, the Fitch-Gaussian model still faces challenges in accurately predicting the magnitude and streamwise evolution of the momentum sink, velocity deficit, and added TKE in wind farm wakes. Nevertheless, the Fitch-Gaussian model better captures their overall spatial distribution patterns. Therefore, the proposed Gaussian-based multicolumn spatial distribution method is recommended for future mesoscale wind farm simulations, especially in cases where the influence of the wind turbine rotor spans multiple mesoscale grid columns.

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• Atmospheric fluid dynamics
• Wind energy