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 CRH exceeds a critical value near 75\%. We show that the ACRE can be estimated from CRH, 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 time scales in six regions of the tropics. We propose that the exponential dependence of precipitation on CRH is a result of cloud-longwave feedbacks, which facilitate a shift from convective to stratiform conditions.