Long‐Term Earth‐Moon Evolution With High‐Level Orbit and Ocean Tide Models

Abstract

Tides and Earth-Moon system evolution are coupled over geological time. Tidal energy dissipation on Earth slows  Earth Es rotation rate, increases obliquity, lunar orbit semi-major axis and eccentricity, and decreases lunar inclination. Tidal and core-mantle boundary dissipation within the Moon decrease inclination, eccentricity and semi-major axis. Here we integrate the Earth-Moon system backwards for 4.5 Ga with orbital dynamics and explicit ocean tide models that are "high-level" (i.e., not idealized). To account for uncertain plate tectonic histories, we employ Monte Carlo simulations, with tidal energy dissipation rates (normalized relative to astronomical forcing parameters) randomly selected from ocean tide simulations with modern ocean basin geometry and with 55, 116, and 252 Ma reconstructed basin paleogeometries. The normalized dissipation rates depend upon basin geometry and  Earth E s rotation rate. Faster Earth rotation generally yields lower normalized dissipation rates. The Monte Carlo results provide a spread of possible early values for the Earth-Moon system parameters. Of consequence for ocean circulation and climate, absolute (un-normalized) ocean tidal energy dissipation rates on the early Earth may have exceeded  today E s rate due to a closer Moon. Prior to  E 3 Ga, evolution of inclination and eccentricity is dominated by tidal and core-mantle boundary dissipation within the Moon, which yield high lunar orbit inclinations in the early Earth-Moon system. A drawback for our results is that the semi-major axis does not collapse to near-zero values at 4.5 Ga, as indicated by most lunar formation models. Additional processes, missing from our current efforts, are discussed as topics for future investigation. Plain Language Summary Tidal dissipation ins oceans and solid body cause the distance to the Moon and the length of day to increase over time. Tides also change the eccentricity and tilt of the lunar orbit, and  Earth E s obliquity (the tilt between the equator plane and the ecliptic plane of our orbit around the Sun). This paper attempts to calculate the evolution of the Earth-Moon system over the whole of  Earth E s history using sophisticated ocean tide and orbit models. Over long time scales, the rate at which tidal energy is being dissipated is affected by the geometrical configuration of the continents, the length of day, and mean sea level, which is affected by plate tectonic forces and the presence or absence of large ice caps. The faster rotating Earth of the past was less efficient at dissipating energy and the present placement of the continents enhances some tides due to resonances. In addition, tidal dissipation in the Moon slows the orbit evolution by absorbing energy from the orbit and there was a time in the distant past when the  Moon s E tidal dissipation was large. The evolution of the Earth-Moon system is complex and uncertain, but it can be addressed with advanced models.

The thermal–orbital evolution of the Earth–Moon system with a subsurface magma ocean and fossil figure

“…Second, Tian, Wisdom and Elkins-Tanton (2017) focused on whether the evection resonance could extract excess angular momentum from an early fast-spinning Earth. Third, Daher, Arbic, Williams, Ansong, Boggs, Müller, Schindelegger, Austermann, Cornuelle, Crawford et al (2021) developed a sophisticated framework for tides in Earth's oceans to evolve the lunar orbit, but they do not include the effects of the lunar magma ocean or a fossil figure on the evolution of the Earth-Moon system.…”

Tidal dynamics in palaeo‐seas in response to changes in physiography, tidal forcing and bed shear stress

“…There is no shortage of tidal evidence in the ancient rock record (Eriksson, 1977; Kvale & Archer, 1991; Räsänen et al ., 1995; Kvale, 2006; Raaf & Boersma, 2007; James et al ., 2010; Davis et al ., 2012; Longhitano et al ., 2012; Gugliotta et al ., 2015; Rossi et al ., 2016; Fritzen et al ., 2019; Collins et al ., 2020; Phillips et al ., 2020), although some of the concepts developed from the study of ancient tidally‐influenced sedimentary strata can be inconsistent with phenomena recognized in modern tidal environments (see discussion in Gugliotta & Saito, 2019; Cosma et al ., 2020; Finotello et al ., 2020). Numerical modelling of ancient basins (Wells et al ., 2010; Hill et al ., 2011; Mitchell et al ., 2011; Collins et al ., 2018; Dean et al ., 2019; Green et al ., 2020; Collins et al ., 2021; Daher et al ., 2021) can help to test hypotheses formulated from the study of the rock record, reduce discrepancies between interpreted ancient and modern tides and tidal deposits, and improve the calibration of ancient tidal signals to astronomical parameters. Complementarily, the rock record can help to constrain model inputs and interpret results (Ward et al ., 2015; Dean et al ., 2019; Byrne et al ., 2020; Green et al ., 2020; Haigh et al ., 2020; Collins et al ., 2021; Daher et al ., 2021) and exclude anomalous ‘numerically‐viable’ simulations (Ward et al ., 2020).…”

“…Numerical modelling of ancient basins (Wells et al ., 2010; Hill et al ., 2011; Mitchell et al ., 2011; Collins et al ., 2018; Dean et al ., 2019; Green et al ., 2020; Collins et al ., 2021; Daher et al ., 2021) can help to test hypotheses formulated from the study of the rock record, reduce discrepancies between interpreted ancient and modern tides and tidal deposits, and improve the calibration of ancient tidal signals to astronomical parameters. Complementarily, the rock record can help to constrain model inputs and interpret results (Ward et al ., 2015; Dean et al ., 2019; Byrne et al ., 2020; Green et al ., 2020; Haigh et al ., 2020; Collins et al ., 2021; Daher et al ., 2021) and exclude anomalous ‘numerically‐viable’ simulations (Ward et al ., 2020). The integration of field data and numerical modelling also helps to test, quantify and visualize the spatio‐temporal changes in tidal processes resulting from changes in basin configuration (Collins et al ., 2021).…”

“…Specific objectives are to: (i) simulate the propagation of tides in the Jurassic Sundance and Curtis seas in present day Utah, USA (Fig. 1) using a range of potential palaeophysiographies, initial open‐ocean tidal forcing inputs, and bed shear stress values to assess their impact on tidal processes; (ii) compare sediment distribution proxies derived from simulated flow speed and bed shear stress values (Ward et al ., 2015, 2020) to deposits of the Upper Jurassic Curtis Formation of the innermost Curtis Sea, using the rocks to inform the models (in a similar fashion as Byrne et al ., 2020; Green et al ., 2020; and Daher et al ., 2021); and (iii) analyse the implications of these simulation results on basin history and sequence stratigraphy of similar systems.…”

North Atlantic Drift Sediments Constrain Eocene Tidal Dissipation and the Evolution of the Earth-Moon System

“…The current rate at which rotational energy dissipates is, however, a poor guide for the past: Present-day tidal dissipation would imply zero Earth-Moon distance at ~1.5 Ga, whereas the Moon is ~4.5 Myr old (Hansen, 1982;Waltham, 2015;Green et al, 2017). While it is generally accepted that tidal dissipation must have been lower throughout Earth history, uncertainties on its temporal evolution remain (Daher et al, 2021). This ambiguity also holds for geologic Epochs as recent as the Eocene: Color reflectance (a*) data from Walvis Ridge ODP Site 1262 has been used both by Meyers and Malinverno (2018) and Zeebe and Lourens (2022) to reconstruct tidal dissipation around 55 Ma.…”