Correction of the Solar Azimuth Discontinuity at Sunrise and Sunset

Solar azimuth may become indefinite at sunrise and sunset. This discrepancy is corrected in the present work. The correction concerns application of Fourier–series analysis to the solar paths over a site during days when the problem arises. The result is the derivation of a new curve that is fitted with great accuracy to the daily solar azimuth values, thus bridging the gap of the discontinuity. A demonstration for the solar azimuth correction is given for 3 sites around the world (Athens, Stockholm, and Sydney). The correction can be applied to any solar geometry code; in this work the algorithm of the XRONOS code is selected without (XRONOS.bas, a BASIC programme) and with (XRONOS.m, a MATLAB code) the correction proposed. A corrected expression for the atmospheric refractive index at various altitudes is given in Appendix A as the refraction of solar right is treated in XRONOS.