Using a digital terrain model to calculate visual sunrise and sunset times

Since its advent the Digital Terrain Model (DTM) has been employed widely i n the sciences for the solution of problems requiring a digital model of la ndforms. In this paper we describe a new use of the DTM in the calculation of highly accurate visual sunrise and sunset times that are required by the observant population in Israel. We have employed ray tracing to determine the effect of atmospheric refraction through a simplified layered atmospher e. A general analytic expression for the atmospheric refraction was determi ned from these calculations as a function of the observer's height for two model atmospheres known as the subtropical summer and winter atmospheres. T hese expressions determine the general magnitude of the refraction as a fun ction of apparent view angle of the observer. We also determined a simplifi ed analytic expression for the effect of atmospheric refraction on the vert ical angular profile of the mountainous horizon as calculated from the DTM (atmospheric refraction magnifies the mountainous features of the horizon). These expressions are then used in calculating the apparent vertical angul ar position of the Sun as a function of time. The time when the upper limb of the Sun first (last) appears to rise (set) over the horizon adjusted for the effect of refraction determines the time of the visible sunrise (sunse t). Comparison with observations have shown that the visible sunrise and su nset times can be typically determined to better than 15 s using the 25 m D TM of Israel and eastern Jordan. (C) 2000 Elsevier Science Ltd. All rights reserved.