A detailed analysis of the effect of clouds on irradiance yields insights into the interaction between clouds and radiation and the precise forecasting of short-term solar radiation. Existing research has mainly focused on the impact of the cloud fraction (CF), i.e., the area distribution of clouds, on radiation. However, three-dimensional cloud information, such as the cloud thickness, also significantly affects solar radiation. This study proposes an innovative index based on the luminance of clouds in all-sky images (ASIs) to characterize the three-dimensional information of clouds, namely, CT, which is usually omitted in the binarization of ASIs. By using two-year synchronous ground irradiance and ASI observation data, the relationship between CT and the cloud radiative effect (CRE) is studied for different types of clouds under two situations, the sun being obscured and unobscured by clouds. The comparison with the commonly used CF indicates that CT has the same or higher negative correlation with the CRE of global horizontal irradiance. Moreover, the correlation between CT and CF with the CREs of direct normal irradiance (DNI) and diffuse irradiance (DFI) is explored in detail. The results indicate that CT has a more negative correlation with the CRE of DNI than that of CF when the sun is obscured, particularly for altocumulus clouds. A detailed discussion indicates that cloud radiative enhancement effects mainly occur under cumulus clouds with a minimum distance between the clouds and the sun (CSMD) of less than three solar radii, but cirrus clouds and altocumulus clouds can also induce cloud radiative enhancement effects.