Wave Height and Horizon Dip

Abstract

A mariner who takes the height of the sun or a star to find his position at sea, must correct his observation for horizon dip. Throughout history, dip values have been tabulated based on the idealized assumption of a perfectly flat sea. Literature on wave height correction for dip is scarce, especially in the Western part of the world and suggested procedures are often conflicting or incorrect. We investigate the effect of wave height on the apparent horizon for realistic wave height distributions by optical ray tracing methods and show that there are two eye height corrections: one representing the apparent rise of the horizon itself and the second when sights are selectively taken from wave crests. Tables and formulas for dip and horizon distance taking wave height into account are presented. Copyright © 2015 Institute of Navigation.

La discussion par Kummer d’une quadrature sur la réfraction astronomique : commentaire historique

“…Or nous sommes persuadez qu'on ne doit presque rien négliger dans une semblable matiere : car quelque soin & quelque peine qu'on se donne, il arrive qu'on se trompe encore souvent d'une quantité trop sensible. » [45, p. 70-71] Les marins corrigent E en lui retranchant la moitié de la hauteur des vagues estimée à l'horizon [46], ou une fraction plus savante [47]. Ils savent aussi qu'en présence d'un mirage inférieur δ > 2E /r S car 〈κ〉 < 0 (voir le sous-paragraphe 7.2.3 de [5]) : « Les observations faites par MM.…”

Did Monge really explain inferior mirages?

“…So the total width of this image depends on the height of the tallest irregularities on the surface: rocks and bushes on dry land, or the largest waves on water. The importance of the dip of the sea horizon for celestial navigation has produced a huge literature on this subject; e.g., [67][68][69][70][71], some of which has been incorporated in the literature of refraction [72] and mirages [73,74].…”