| Summary: | The relationship between outgoing longwave radiation (OLR) and the surface temperature has a major influence on Earth's climate sensitivity. Studies often assume that this relationship is approximately linear, but it is unclear whether the approximation always holds. Here we show that, on seasonal timescales, clear-sky OLR is a multivalued function of local surface temperature. In many places, the OLR-temperature relationship is better approximated by a loop than a line and we quantify the resulting "OLR loopiness", that is, how much clear-sky OLR varies between different seasons with the same surface temperature. Based on offline radiative calculations, in the tropics OLR loops are mainly caused by seasonal variations in relative humidity that are out of phase with surface temperature; in the extratropics, OLR loops are mainly due to variations in lapse rates. Our work provides a mechanism through which Earth's climate feedback can differ between seasonal and long-term time scales.
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