“Simpson's Law” and the Spectral Cancellation of Climate Feedbacks

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 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.