The relationship between the clearness index and the time averaged sunshine number is studied over short time intervals such as one hour. Several non-linear statistical models have been used. Meteorological and radiometric data from various weather stations of Romania (South-Eastern Europe) are analyzed. Nonlinearity of the relationship is only apparent near the boundary for relative sunshine sigma of 0 or 1 and manifests itself in clearness index jumps mainly at sigma = 0 rather than sigma = 1. The negative clearness index jump at sigma = 0 decreases while the slope of the relationship increases when the sunshine number is averaged over longer time periods. (C) 2016 Elsevier Ltd. All rights reserved.