Analysis of a Precambrian resonance-stabilized day length

During the Precambrian era, Earth's decelerating rotation would have passed a 21-hour period that would have been resonant with the semidiurnal atmospheric thermal tide. Near this point, the atmospheric torque would have been maximized, being comparable in magnitude but opposite in direction to the lunar torque, halting Earth's rotational deceleration, maintaining a constant day length, as detailed by Zahnle and Walker (1987). We develop a computational model to determine necessary conditions for formation and breakage of this resonant effect. Our simulations show the resonance to be resilient to atmospheric thermal noise but suggest a sudden atmospheric temperature increase like the deglaciation period following a possible "snowball Earth" near the end of the Precambrian would break this resonance; the Marinoan and Sturtian glaciations seem the most likely candidates for this event. Our model provides a simulated day length over time that resembles existing paleorotational data, though further data is needed to verify this hypothesis.