NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: David Iwancio
Date: 2022 Aug 1, 18:57 -0700
For taking individual practice sights this seems reasonable (or it might be interesting to work "backwards" to determine the distance to land), but for a round of sights to get a celestial fix you'll end up with a (probably insignificant) bias towards the nearer shore.
One question is how this error compares to how much dip varies in non-standard conditions. One paper I found at https://journals.lib.unb.ca/index.php/ihr/article/view/27073 suggests that it can vary by as much as ~1.0' for a 2 °C difference between air and water temperature.
On a side note, for Bowditch tables 12 & 14 the β0 term appears to be (1 - Re/Rr) where Re is the radius of the earth and Rr is the radius of curvature of a refracted ray of light. I came to this conclusion from looking at https://www.mathscinotes.com/2013/08/distance-to-the-horizon-assuming-refraction/