Several common practices are tested for assessing the effective solar zenith angle that can be associated to each measurement in time-series of in situ or satellite-derived measurements of hourly irradiation on horizontal surface. High quality 1 min measurements of direct irradiation collected by the BSRN stations in Carpentras in France and Payerne in Switzerland, are aggregated to yield time series of hourly direct irradiation on both horizontal and normal planes. Time series of hourly direct horizontal irradiation are reconstructed from those of hourly direct normal irradiation and estimates of the effective solar zenith angle by one of the six practices. Differences between estimated and actual time series of the direct horizontal irradiation indicate the performances of six practices. Several of them yield satisfactory estimates of the effective solar angles. The most accurate results are obtained if the effective angle is computed by two time series of the direct horizontal and normal irradiations that should be observed if the sky were cloud-free. If not possible, then the most accurate results are obtained from using irradiation at the top of atmosphere. Performances show a tendency to decrease during sunrise and sunset hours. The effective solar azimuth angle is computed from the effective solar zenith angle.