Work in recent decades has demonstrated a robust relationship between tropical precipitation and the column relative humidity (CRH). This study identifies a similar relationship between CRH and the atmospheric cloud radiative effect (ACRE) calculated from satellite observations. Like precipitation, the ACRE begins to increase rapidly when the CRH exceeds a critical value near 75%. We show that the tight relationship between CRH and ACRE allows the ACRE to be estimated from the CRH calculated from reanalysis fields, similar to the way that CRH has been used to estimate precipitation. Our method reproduces the annual mean spatial structure of ACRE in the tropics, and skillfully estimates the mean ACRE on monthly and daily timescales in six regions of the tropics. We speculate that this link between ACRE and CRH is important to longwave cloud feedbacks which have recently been identified as important to many processes.