*The 100 kyr Glacial Cycle of the Late Quaternary Ice Age Glaciation Histories Constrained by Global Models of the Physical Process of Glacial Isostatic Adjustment .*

**W Richard Peltier, ***Dept. of Physics, University of Toronto,*

*Web Lecture on February 18, 2021 at 3:00 PM (Paris Time)*

The physical basis of the modern theory of the glacial isostatic adjustment process is embodied in a Fredholm integral equation of the second kind. The kernel of this integral equation consists of the difference between Green functions for the impulse response of the approximately spherical viscoelastic planet for radial displacement (Peltier, 1974) and for the perturbation to the gravitational potential field (Peltier and Andrews, 1976). The inversion of this integral equation for a given history of surface mass loading is a prediction of the space and time dependence of the level of the sea with respect to the continuously deforming surface of the solid Earth. The theory is gravitationally self–consistent in the sense that sea level is constrained to evolve such that the surface of the global ocean remains a surface of constant gravitational potential on which the potential is a slowly varying function of time. When its height is measured with respect to the centre of mass of the Earth, this surface is the (time dependent) geoid of classical geodesy. Because the rotational state of the planet is significantly influenced by the exchange of mass between the oceans an land-based ice sheets during the glacial cycle the integral equation must be modified to include the feedback of this changing rotation state upon sea level itself resulting in a theoretical structure that must be applied iteratively in order to ensure that this feedback is accurately represented (eg see the reviews by Peltier, 1998 and 2015 for detailed discussion).

Given relative sea level histories constrained by the radio-Carbon or Uranium-Thorium dating of samples known to have been located at sea level at the time in the past determined by their age , the Fredholm integral equation poses an inverse problem for both the internal viscoelastic structure of the planet and for the history of surface mass loading to which it has been subjected over the period of time over which such data are available, generally the interval of time since Last Glacial Maximum, now understood to have occurred at approximately 26,000 years before present (BP) in calendar years. In order to infer the history surface mass loading of the planet by glacial ice, one requires an adequately accurate model of the internal viscoelastic structure of the planet. Because errors in the fit to relative sea level data are correlated to errors in the viscoelastic structure employed to make the RSL predictions. To make progress requires that it is possible by an appropriate choice of data to reduce this correlation error sufficiently that an iterative approach to the inversion for both the history of surface mass loading and the internal viscoelastic structure is convergent. Recent analyses of this issue by Roy and Peltier (2015, 2017) suggest that this methodology is in fact convergent.

The characteristics of the most recent and adequately converged model are embodied in that referred to in the literature as ICE-6G_C_D (VM5a) of Peltier et al. (2015, 2018). This model remains unique internationally, as were its predecessors in the ICE-NG (VMX) series from the University of Toronto in that they are truly global (G) models that consist of a single representation of surface mass loading of all of the continents and a single depth dependent radial viscoelastic structure, the elastic component of which is assumed to constrained by body wave and free oscillation seismology, leaving the viscous component, represented by an effective (assumed Newtonian) viscosity the simultaneous operation of both components being represented by a linear viscoelastic Maxwell rheology. Recent analyses of the robustness of this model against the impact of the influence of lateral heterogeneity of viscosity has been established by the analysis of Li et al. (2020). In this presentation I will focus primarily upon the inferred surface loading of the planet over the most recent 100 kyr cycle of the ice-age. However, I will also discuss the constraints that may be brought to bear in order to extend this loading history to of order a million years as such extension is in fact required if adequately accurate predictions of the rotational response to the ice-age cycle are of interest.

R**eferences**

Peltier, W.R., ”The impulse response of a Maxwell earth”, *Rev. Geophys. Space Phys.*, **12**, 649669, 1974.

Peltier, W.R., and J.T. Andrews, “Glacial isostatic adjustment I: the forward problem”, *Geophys. J. Roy astr. Soc.*, **46**, 605-646, 1976.

Peltier, W.R., “Glacial isostatic adjustment II: the inverse problem”, *Geophys. J. Roy. astr.*, *Soc.*, **46**, 669-706, 1976.

Peltier, W.R., “Postglacial variations in the level of the sea: Implications for climate dynamics and solid-Earth geophysics”, invited paper, *Reviews of Geophysics*, **36**, 603-689, 1998

Peltier, W.R. “The history of the Earth’s rotation: Impacts of deep Earth physics and surface climate variability”, In: Gerald Schubert (editor-in-chief) Treatise on Geophysics, 2nd edition, Vol. 9., Oxford:Elsevier, p. 221-279, 2015.

Peltier, W.R., Argus, D.F. and Drummond, R., “Space geodesy constrains ice-age terminal deglaciation: the global ICE-6G_C (VM5a) model”, *J. Geophys. Res. – Solid Earth*, **120(1),** 450-487, doi:10.1002/2014JB011176, 2015.

Peltier, W.R., Argus, D.F. and Drummond, R., Comment on the paper “An Assessment of the ICE-6G_C(VM5a) glacial isostatic adjustment model”, by Purcell et al., *J. Geophys. Res.-Solid Earth*, 123(2), 2019-2028, doi:10.1002/2016JB013844, 2018.

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