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This ap p end ix gives the d efinitions of the basics sand w ave charact eristics. These are firstly the sand w ave crest, trou gh, height and length, w hich are show n in Figu re A 1. Su bsequ ently the d efinitions of m igration and asym m etrical m ovem ent are visu alized in resp . Figu re A 2 and Figu re A 3.