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 with 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 to the same conclusion regarding the van der Pol model. Though developments of better proxies of 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.