Dependence of the resonant rotational period on the mean surface temperature. By virtue of Eq. (24), the LOD at which the Lamb resonance occurs scales as the inverse square root of the mean surface temperature (solid curve). In Appendix I, we show that the same dependence holds if one considers a moist adiabatic profile. The shaded area of temperature variations highlights 95% confidence intervals for the past temperature evolution according to the carbon cycle model of Krissansen-Totton et al. (2018). The identified geological eras correspond to the LOD evolution model of Farhat et al. (2022). The overlap between the modeled temperature evolution and the black curve places the resonance occurrence in the late Paleozoic/early Mesozoic.