Near-resonance tidal evolution of the Earth-Moon system influenced by orbital-scale climate change

We build a conceptual coupled model of the climate and tidal evolution of the Earth-Moon system to find the influence of the former on the latter. An energy balance model is applied to calculate steady-state temperature field from the mean annual insolation as a function of varying astronomical parameters. A harmonic oscillator model is applied to integrate the lunar orbit and Earth's rotation with the tidal torque dependent on the dominant natural frequency of ocean. An ocean geometry acts as a bridge between temperature and oceanic frequency. On assumptions of a fixed hemispherical continent and an equatorial circular lunar orbit, considering only the 41 kyr periodicity of Earth's obliquity $\varepsilon$ and the $M_2$ tide, simulations are performed near tidal resonance for $10^6$ yr. It is verified that the climate can influence the tidal evolution via ocean. Compared with the tidal evolution with constant $\varepsilon$, that with varying $\varepsilon$ is slowed down; the Earth-Moon distance oscillates in phase with $\varepsilon$ before the resonance maximum but exactly out of phase after that; the displacement of the oscillation is in positive correlation with the difference between oceanic frequency and tidal frequency.