A linear wave according to method (ii) requires a/H¼0.5 and a solitary wave a/H¼1. The Ursell parameter U in method (iii) is herein defined with the wave height H in analogy to Le Me´haute´ (1976), Huber (1980), or Panizzo et al. (2005), and not in the classical way with the wave amplitude a. For a linear wave it tends to U-0. According to Ursell (1953) his parameter is a more appropriate criterion to identify linear waves than simply a/H¼0.5 since a linear wave requires not only identical crest and trough amplitudes (Fig. 11(a)) but also small ratios of H/h and H/L.