Deep convective clouds (DCCs) are crucial in the Earth's energy budget. Although the abundant DCC-generated ice-phase anvil and cirrus theoretically have a warming effect, the reported observations of their cloud radiative effect (CRE) by previous studies are unexpectedly negative. Here, we find that the apparent contradiction between theory and observations resulted from neglecting the radiative contribution of background underlying clouds based on the five-years active and passive satellite observations in global. The probability of underlying clouds below the anvils is up to 2/3. They can contribute up to 70 % of the observed total shortwave cooling effect when they fully overlap with anvils. After excluding the effect of underlying clouds, most of the anvil CRE changes sign from negative to positive, increasing by over +25 W/m2, especially over land. This revelation suggests a substantially underestimated warming effect of DCC anvils and cirrus in previous observations. Also, it may imply an underestimated aerosol-driven positive radiative forcing on DCC, which has been estimated as neutral previously.
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