Empirical studies indicate that the rate of energy transfer to the magnetosphere increases as solar wind coupling parameters increase, up to a certain limit, and then the rate remains constant. The split separator line merging model undergoes the same behavior. When the model interplanetary magnetic field (IMF) magnitude exceeds a critical value, the field configuration in the Chapman-Ferraro current plane ceases to expose closed field lines to the solar wind. The critical value depends upon IMF orientation, stagnation pressure, and earth's dipole tilt angle. The absence of exposed closed field lines prevents closed-to-open flux transfer and, consequently, energy transfer. Further, the limit on energy transfer governed by the model dipole tilt angle affords the first explanation of both the semiannual and UT variations of geomagnetic activity completely in terms of merging.