"Simpson's Law" and the Spectral Cancellation of Climate Feedbacks. Issue 14 (22nd July 2021) - Jeevanjee, Nadir; Koll, Daniel D. B.; Lutsko, Nicholas
Abstract: 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 H2 O is optically thick. This cancellation is a natural consequence of "Simpson's Law", which says that H2 O 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 cancellation This cancellation follows from "Simpson's Law" for water vapor thermal emission Relative humidity‐based feedbacks naturally incorporate this cancellation, and more naturally manifest Simpson's Law