Solar irradiance clustering can enhance solar power capacity planning and help improve forecasting models by identifying similar irradiance patterns influenced by seasonal and weather changes. In this study, we adopt an efficient two-level clustering approach to automatically identify seasons using the clear sky irradiance in first level and subsequently to identify daily cloud level as clear, cloudy and partly cloudy within each season in second level. In the second level of clustering, three methods are compared, namely, Daily Irradiance Index (DII or $β$), Euclidean Distance (ED), and Dynamic Time Warping (DTW) distance. The DII is computed as the ratio of time integral of measured irradiance to time integral of the clear sky irradiance. The identified clusters were compared quantitatively using established clustering metrics and qualitatively by comparing the mean irradiance profiles. The results clearly establish the superiority of the $β$-based clustering approach as the leader, setting a new benchmark for solar irradiance clustering studies. Moreover, $β$-based clustering remains effective even for annual data unlike the time-series methods which suffer significant performance degradation. Interestingly, contrary to expectations, ED-based clustering outperforms the more compute-intensive DTW distance-based clustering. The method has been rigorously validated using data from two distinct US locations, demonstrating robust scalability for larger datasets and potential applicability for other locations.