As offshore wind farms grow in size, the blockage effect associated with the atmospheric gravity waves they trigger is expected to become more important. To model this, recent research has produced an Atmospheric Perturbation Model (APM), which simulates the mesoscale flow in the atmospheric boundary layer at a low computational cost compared to traditional methods. However, as a simplified reduced-order model, it can not resolve individual turbine wakes, and has to be coupled to an engineering wake model to predict farm power output. Over the years, three coupling methods have been developed, and been combined into the open-source framework WAYVE. This paper compares them, discussing both their theoretical validity and their performance. For the latter, we validate the velocities and power outputs predicted by WAYVE against 27 LES simulations. We find that the velocity matching (VM) and the pressure-based (PB) methods perform the best. Of these two, the VM method is more consistent with the APM output, while the PB method has a significantly lower computational cost.