Waterplane and the GM are all part of the ship’s susceptibility to parametric rolling.
Longitudinal waves (head and following) cause the most change in stability and, therefore, create maximum parametric excitation. Parametric roll resonance develops when the frequency of stability change is nearly twice that of natural roll frequency or when the frequency of encounter is nearly twice that of natural roll frequency. The value of natural roll frequency mostly depends on GM value (transversal distribution of weight also may have an influence). Therefore, whether parametric roll resonance may occur in following or head seas depends mostly on current GM value. Wave length also has an influence because it is related to the wave frequency on which the frequency of encounter is dependent. While the physical basis of parametric roll resonance in following and head seas is essentially identical, head seas parametric roll is more likely coupled with, or at least influenced by, the heave and pitch motion of the ship, as these motions are typically more pronounced in head seas.
A ship that is sailing in longitudinal seas experiences a time-varying transverse stability characterized by increased stability when the ship has a wave trough amidships and decreased stability in the wave crest. If such a ship experiences a small arbitrary roll disturbance, then that disturbance can grow provided that the stability fluctuations occur at a frequency approximately twice the natural frequency of roll and provided that the roll damping is less than some threshold value. This rolling motion, under certain circumstances, can grow to quite large amplitudes and is referred to as “autoparametrically excited roll” or simply “parametric roll”.