The dynamics of ice sheets is defined by the advection of mass and temperature. Reduced mass influx makes advection timescale to become longer, which is equivalent to a longer system’s memory of its initial conditions. In this case the Milankovitch theory becomes an initial value problem. The dependence of the similarity parameter that governs initial-values sensitivity on poorly defined mass balance makes ice ages to be hardly predictable and disambiguation of paleo-records to be challenging.

Are phenomenological dynamical paleoclimate models physically similar to Nature? We demonstrated that though they may be very accurate in reproducing empirical time series, this is not sufficient to claim physical similarity with Nature until similarity parameters are considered. We suggest that the diagnostics of physical similarity should become a standard procedure before a phenomenological model can be utilized for interpretations of historical records or future predictions.

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 a phenomenological dynamical paleoclimate model with a more physically explicit dynamical model.

Reconstruction and explanation of past climate evolution using proxy records is the essence of paleoclimatology. In this study, we use dimensional analysis of a dynamical model on orbital timescales to recognize theoretical limits of such forensic inquiries. Specifically, we demonstrate that major past events could have been produced by physically dissimilar processes making the task of paleo-record attribution to a particular phenomenon fundamentally difficult if not impossible.

In this study, we highlight a component of global warming variability, a scaling law that is based purely on fundamental physical properties of the climate system.