Do phenomenological dynamical paleoclimate models have physical similarity with Nature? Seemingly, not all of them do

Abstract

Phenomenological models may be impressive in reproducing empirical time series, but this is not sufficient to claim physical similarity with Nature until comparison of similarity parameters is performed. We illustrated such a process of diagnostics of physical similarity by comparing the phenomenological dynamical paleoclimate model of Ganopolski (2023), the van der Pol model (as used by Crucifix, 2013), and the model of Leloup and Paillard (2022) with the physically explicit Verbitsky et al. (2018) model that played a role of a reference dynamical system. We concluded that phenomenological models of Ganopolski (2023) and of Leloup and Paillard (2022) may be considered to be physically similar to the proxy parent dynamical system in some range of parameters, or in other words they may be derived from basic laws of physics under some reasonable physical assumptions. We have not been able to arrive at the same conclusion regarding the van der Pol model. Though developments of better proxies for the parent dynamical system should be encouraged, we nevertheless believe that the diagnostics of physical similarity, as we describe it here, should become a standard procedure to delineate a model that is merely a statistical description of the data from a model that can be claimed to have a link with known physical assumptions. The similarity parameters we advance here as the key dimensionless quantities are the ratio of the astronomical forcing amplitude to the terrestrial ice sheet mass influx and the so-called V number that is the ratio of the amplitudes of time-dependent positive and negative feedbacks. We propose using available physical models to discover additional similarity parameters that may play central roles in ice age rhythmicity. Finding values for these similarity parameters should become a central objective of future research into glacial–interglacial dynamics.