Refraction near the horizon-an empirical approach. Part 1: terrestrial refraction of the dip

This study aims at providing improved closed-form refraction estimates for observations near the horizon. In this first part, over 1800 previously published direct measurements of the horizon's depression (dip) over the sea are reanalyzed using a nonconventional robust procedure for coping with numerous real, large, and asymmetric outliers from abnormal dips. The derived 1-parameter function agrees with those proposed in modern almanacs and for land surveying. It is found that the dips of warmer and colder sea surfaces vs. air are best described with two different functions. The two proposed 3-parameter functions, also using temperature difference between air and sea and wind speed, reduce the estimated error of the 1-parameter function by ∼⅓ and the number of outliers by ∼⅔.