This study is conducted to fill this critical gap, systematically investigating the occurrence of solar radiation “anomalies” and the underlying mechanisms. Decade-long measurements of total irradiance, direct irradiance, diffuse irradiance, and cloud types (1998 to 2014) collected at the U. S. DOE ARM Southern Great Plains (SGP) site are used in the analysis. Occurrence frequencies of positive dtot under eight cloudy conditions (shallow cumulus, other low clouds expect shallow cumulus clouds, deep convection; altocumulus; altostratus; cirrostratus/anvil; cirrus; congestus) are presented. We also try to find the linkages between positive dtot and the other radiation components (e.g., direct and diffuse irradiances), and cloud properties (e.g., cloud structure). Comparison with the normal cases (dtot<0) is also made to facilitate detecting the unique characteristics of the “anomalies” and cloudy conditions. It is expected that the findings will not only deepen our understanding of cloud-radiation interactions but also improve the forecasting of solar energy under cloudy conditions.