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CO2 absorbs and emits radiation, which allows it to act both as radiative forcing and feedback. Recent work has shown CO2's feedback effect becomes dominant in hothouse climates, giving rise to a non‐monotonic climate sensitivity around 310 K. However, CO2's feedback effect in colder climates is less clear. We use a line‐by‐line model to explore the CO2‐dependence of the longwave clear‐sky feedback and identify a dividing temperature. Above 290 K, feedback increases with CO2 concentration; below 290 K, feedback decreases with CO2 concentration. We explain this dependence in terms of spectral competition under CO2 increases. In hot climates, CO2's moderate feedback replaces near‐zero feedback from the H2O bands; in cold climates, CO2's moderate feedback replaces the large feedback from the surface. Given that global mean temperature is currently close to 290 K, our results suggest that feedback CO2‐dependence is weak at present but can be important in past and future climates. Plain Language Summary: CO2 traps heat, causing warming. But CO2 also emits heat to space, acting as radiative feedback. Recent work has shown CO2's feedback effect crucially helps to stabilize very hot climates, but how does it affect present‐day Earth? We show that in hot climates, more CO2 increases Earth's feedback, while in cold climates, more CO2 decreases it. To understand why, we explain that the surface is an effective emitter, CO2 is a moderate emitter, while H2O is a poor emitter. At high temperatures, adding CO2 to the atmosphere thus replaces feedback that would have otherwise come from H2O, increasing the overall feedback; at low temperatures, adding CO2 replaces feedback that would have otherwise come from the surface, decreasing the overall feedback. Currently, Earth's global‐mean temperature falls between these two temperature regimes, where CO2's effect on feedback is nearly zero. Our results explain why CO2's impact on feedback is small now but can be significant in past or future climates. Key Points: An increase in CO2 concentration strengthens Earth's feedback in hot climates, ∂λ/∂CO2 > 0, but weakens it in colder climates, ∂λ/∂CO2 < 0Whether feedback CO2‐dependence, ∂λ/∂CO2, is positive or negative primarily depends on the extent of the H2O windowFeedback CO2‐dependence and forcing temperature‐dependence, ∂λ/∂CO2 = −∂F2x/∂Ts, can be important for past or future climates [ABSTRACT FROM AUTHOR]

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. Plain Language Summary: When the Earth is warmer, it loses more heat to space. The simplest formula describing this relationship is a line with an upwards slope, where the slope determines how much Earth warms from added greenhouse gases. Here, we report that the relationship between local temperature and rate of heat loss to space can be more complicated on seasonal time scales, often taking the form of loops or other curved shapes. We come up with a way to measure how big these loops are, and explain why they happen. Our results underline that Earth's response to seasonal changes is generally different from Earth's response to global warming. Key Points: Monthly outgoing longwave radiation (OLR) is a multivalued function of local surface temperature, exhibiting loops and other complex shapesOLR loops occur both in clear‐sky and all‐sky data, so the behavior is robust to cloudsOLR loops arise because humidity lags surface temperature in the tropics, and lapse rates lead to surface temperature in the extratropics [ABSTRACT FROM AUTHOR]

We spectrally resolve the conventional clear‐sky temperature and water vapor feedbacks in an idealized single‐column framework, and show that the well‐known partial compensation of these feedbacks is actually due to an almost perfect cancellation of the spectral feedbacks at wavenumbers where H2O is optically thick. This cancellation is a natural consequence of "Simpson's Law", which says that H2O emission temperatures do not change with surface warming if relative humidity (RH) is fixed. We provide an explicit formulation and validation of Simpson's Law, and furthermore show that this spectral cancellation of feedbacks is naturally incorporated in the alternative RH‐based framework proposed by Held and Shell (2012, https://doi.org/10.1175/jcli-d-11-00721.1) and Ingram (2012, https://doi.org/10.1029/2011jd017221, 2013b, https://doi.org/10.1007/s00382-012-1294-3), thus bolstering the case for switching from conventional to RH‐based feedbacks. We also find a negligible RH‐based clear‐sky lapse rate feedback, suggesting that the impact of changing lapse rates depends crucially on whether relative or specific humidity is held fixed. Plain Language Summary: Feedback analyses aim to isolate processes in the climate system which may amplify or diminish its response to an external forcing. In calculating feedbacks due to the warming of the atmosphere, however, a choice must be made as to whether the absolute or relative humidity (RH) is to be held fixed as the impact of warming is assessed. Here we examine these impacts frequency‐by‐frequency in the infrared spectrum, and find that fixing the RH leads to a much simpler picture than fixing absolute humidity. Key Points: Conventional feedbacks exhibit strong spectral cancellationThis cancellation follows from "Simpson's Law" for water vapor thermal emissionRelative humidity‐based feedbacks naturally incorporate this cancellation, and more naturally manifest Simpson's Law [ABSTRACT FROM AUTHOR]