Using a ray tracing program to calculate sunrise times over a digital terrain model based visible horizon using a simplified atmospheric model, part II

In a previous paper we compared observations to calculated values of the sunrise times for one place in Jeru-salem. It was shown that the sunrise over the actual physical horizon could be modeled to an accuracy of about & PLUSMN;15 s for most of the year. Success of those calculations suggested that terrain modeling was the most important factor in obtaining this result. To investigate this point, we repeated our calculations using the ray tracing method and simplified atmosphere developed by Siebren Van der Werf, whose atmospheric model is easily applied to other places in the world. Our results show that the new calculation method maintained our requirement of & PLUSMN;15 s accuracy (required for publication of sunrise time tables, critical for daily Jewish obser-vances worldwide). Standard formulas for atmospheric refraction produce approximately the same results even for near horizon zenith angles. For portions of the year where low altitude inversions are especially important, e. g., during those days associated with maximum radiative cooling, these additional atmospheric effects can be effectively modeled in a very simple way.