On post-glacial sea level - II. Numerical formulation and comparative results on spherically symmetric models

Abstract

S U M M A R YTheoretical approaches to computing gravitationally self-consistent sea-level changes in consequence of ice growth and ablation are comprised of two parts. The first is a mapping between variations in global sea level and changes in ocean height (required to define the surface load), and the second is a method for computing global sea-level change arising from an arbitrary surface loading. In Mitrovica & Milne (2003) (Paper I) we described a new, generalized mapping between sea-level change and ocean height that takes exact account of the evolution of shorelines associated with both transgression and regression cycles and time-dependent marine-based ice margins. The theory is valid for any earth model. In this paper we extend our previous work in three ways. First, we derive an efficient, iterative numerical algorithm for solving the generalized sea-level equation. Secondly, we consider a special case of the new sea-level theory involving spherically symmetric earth models. Specifically, we combine our iterative numerical formulation with viscoelastic Love number theory to derive an extended pseudo-spectral algorithm for solving the new sea-level equation. This algorithm represents an extension of earlier methods developed for the fixed-shoreline case to precisely incorporate shoreline migration processes. Finally, using this special case, we quantitatively assess errors incurred in previous efforts to extend the traditional (fixed shoreline) sea-level equation of Farrell & Clark (1976) to treat time-dependent shorelines. We find that the approximations adopted by Johnston (1993) and Milne (1998) to treat transgression and regression at shorelines introduce negligible (∼1 per cent) error into predictions of post-glacial relative sea-level histories. In contrast, the errors associated with the Peltier (1994) sea-level equation are an order of magnitude larger, and comparable to the error incurred using the traditional sea-level theory. Furthermore, our numerical tests verify the high accuracy of the Milne (1998) approximation for treating the influence of grounded, marine-based ice.Predicting gravitationally self-consistent sea-level changes driven by the melting of ice sheets on a deformable earth is a complex undertaking. Under the assumption of an equilibrium, or hydrostatic, theory (e.g. Dahlen 1976), the sea-level redistribution will be governed by the gravitational field of the planet, since the sea surface is constrained to remain on an equipotential. However, this field is, in turn, perturbed by the redistribution of ocean mass, both through the direct attraction of the total (ice plus ocean) surface mass load and by solid earth deformations driven by this mass loading. As a further complexity, load-induced perturbations to the rotation vector of the planet will also have an impact on sea level, both through the re-orientation of the rotational potential and the deformation that results from this re-orientation. In addition, the ocean loading is defined by the local geometry of the shorelines,...

Differences between the last two glacial maxima and implications for ice-sheet, δ18O, and sea-level reconstructions

“…4e7; Table 5). We solve the sea-level equation using the Kendall et al (2005) method, which is adapted to account for feedback from Earth's rotational vector . The model takes into account self-gravitational feedbacks, moving shorelines, and marine-terminating ice sheets, and the sea-level equation is solved in an iterative, pseudo-spectral manner Tamisiea, 2011;Williams, 2016) that incorporates a spherically symmetric Earth representation.…”

Simulation of the Greenland Ice Sheet over two glacial–interglacial cycles: investigating a sub-ice- shelf melt parameterization and relative sea level forcing in an ice-sheet–ice-shelf model

“…This model has three key input components: a reconstruction of Late Pleistocene ice-sheet history (Peltier, 2004), an earth model that simulates the solid earth deformation due to changes in the surface mass redistribution between the oceans and ice sheets (Peltier, 1974), and a model of sea level change (Farrell and Clark, 1976). The sea level model included perturbations to the rotation vector (Milne and Mitrovica, 1998;Mitrovica et al, 2001Mitrovica et al, , 2005, time-dependent shoreline migration, and an accurate treatment of sea level change in areas characterized by ablating marine-based ice (Kendall et al, 2005;Mitrovica and Milne, 2003).…”

The effect of sediment loading in Fennoscandia and the Barents Sea during the last glacial cycle on glacial isostatic adjustment observations

“…The effect of sediments can also be included in the sea level equation, as shown by Dalca et al (2013). Here, we follow Dalca et al (2013), Kendall et al (2005) and references therein. Only the key elements will be repeated here, and some small differences will be pointed out.…”

“…Second, ocean-continent margins change with time to account for ice sheets replacing sea and vice versa, as well as accounting for the change in coastline as sea level rises next to a sloped coastline (see Kendall et al, 2005, and references therein). The change in ocean-continent margins depends on the topography, which depends on the sea level change.…”