On the origin of late Holocene sea-level highstands within equatorial ocean basins

Abstract

Late Holocene sea-level highstands of amplitude $\text{∼3}\text{m}$ are endemic to equatorial ocean basins. These highstands imply an ongoing and moderate, sub-mm/yr, sea-level fall in the far field of the Late Pleistocene ice cover that has long been linked to the process of glacial isostatic adjustment (GIA; Clark et al., 1978). Mitrovica and Peltier (1991) coined the term ‘equatorial ocean syphoning’ to describe the GIA-induced sea-level fall and they provided the first physical explanation for the process. They argued that water migrated away from far-field equatorial ocean basins in order to fill space vacated by collapsing forebulges at the periphery of previously glaciated regions. We provide a complete physical explanation for the origin of equatorial ocean syphoning, and the associated development of sea-level highstands, using numerical solutions of the equation that governs meltwater redistribution on spherical, viscoelastic Earth models. In particular, we separate the total predicted sea-level change into contributions associated with ice and meltwater loading effects, and, by doing so, isolate a second mechanism that contributes significantly to the ocean syphoning process. Ocean loading at continental margins induces a ‘levering’ of continents and a subsidence of offshore regions that has also long been recognized within the GIA literature (Walcott, 1972). We show that the influx of water into the volume created by this subsidence produces a sea-level fall at locations distant from these margins—indeed over the major ocean basins—that is comparable in amplitude to the syphoning mechanism isolated by Mitrovica and Peltier (1991).

Introduction

The prediction of gravitationally self-consistent sea-level variations driven by ice mass loads is a problem in geophysics that can be traced back over at least a century (e.g. Woodward, 1888; Daly, 1925; Walcott, 1972; Farrell and Clark, 1976; Clark et al., 1978). Woodward (1888) for example, considered a rigid Earth and he predicted that sea-level would fall within 17° of a melting point mass. Daly (1925) extended Woodward's theory to incorporate elastic deformations of the planetary model. These and other efforts culminated in the derivation, by Farrell and Clark (1976), of the so-called ‘sea-level equation’ for both elastic and viscoelastic global Earth models.

The Farrell and Clark (1976) sea-level theory is valid for a non-rotating Earth with a fixed continental shoreline, and it has played a seminal role in the modern development of the field of glacial isostatic adjustment (henceforth GIA). Indeed, the first applications of the theory considered sea-level variations driven by the Late Pleistocene glacial cycles (e.g. Clark et al., 1978; Peltier et al., 1978; Wu and Peltier, 1983). These applications were based on a somewhat cumbersome numerical formalism in which the ocean geometry (and surface mass load) was discretized into a set of circular disks. More recently, spectral forms of the Farrell and Clark (1976) sea-level equation have been derived (e.g., Nakada and Lambeck, 1989; Mitrovica and Peltier, 1991) and an efficient pseudo-spectral algorithm has been developed for their solution (Mitrovica and Peltier, 1991). The pseudo-spectral approach is now the standard algorithm for sea-level predictions within the GIA literature.

Since the early 1990s various limitations of the Farrell and Clark (1976) sea-level theory have been addressed. For example, the influence on sea level of: GIA-induced perturbations in the Earth's rotation vector (Han and Wahr, 1989; Bills and James, 1996; Milne and Mitrovica 1996, Milne and Mitrovica 1998a; Peltier, 1998a); time-dependent shoreline geometry (Lambeck and Nakada, 1990; Johnston, 1993; Peltier, 1994; Milne and Mitrovica, 1998b) and retreating marine-based ice margins (Lambeck et al., 1998; Milne, 1998; Peltier, 1998b; Milne et al., 1999), have all been treated, albeit with widely diverging accuracies (see Mitrovica and Milne (2002) for a detailed comparison of the approaches used in these studies). Revised sea-level equations that accurately incorporate all of these extensions are described in Milne (1998), Milne et al. (1999), Lambeck et al. (2002) and Mitrovica and Milne (2002).

Numerical solutions of the sea-level equation have revealed a remarkable geographic variation in postglacial sea-level trends (Clark et al., 1978; Tushingham and Peltier, 1992). Indeed, Clark et al. (1978) used a global solution to identify six zones which they argued would be characterized by broadly similar postglacial sea-level histories. For the purposes of this paper, four of their zones are particularly relevant. These are: (I) a monotonic sea-level fall associated with previously glaciated (and rebounding) regions; (II) a sea-level rise at the periphery of these areas due to the collapsing forebulge (and a transition between I and II); (V) a far-field region of low-amplitude late Holocene sea-level fall occurring subsequent to the cessation of deglaciation and leading to a sea-level highstand; and (VI) a late Holocene highstand of varying amplitude at far-field continental shorelines.

To illustrate these patterns we show, in Fig. 1A, a global numerical prediction of the present-day rate of change of sea level due to GIA. A detailed description of the calculation used to generate Fig. 1 will be provided in the next section. The prediction assumed that the deglaciation event completely ceased at $\text{5}\text{kyr}$ BP, and thus the patterns reflect ongoing sea-level adjustments during a time in which no meltwater is being added into the oceans. These patterns remain relatively unaltered over the last $\text{5}\text{kyr}$, although the amplitudes decrease with time. The colour scale in the figure is chosen to highlight sea-level trends in the far field of the Late Pleistocene ice sheets; however, both zones I and II of Clark et al. (1978) are evident in the saturated red and blue regions, respectively, in the near field of these ice sheets. For this numerical calculation, the ongoing rebound of previously glaciated regions leads to a present-day sea-level fall that is in excess of $\text{1}\text{cm/yr}$ in zone I, and a peripheral subsidence leading to submergence at rates as high as $\text{5}\text{mm/yr}$ in zone II.

The Clark et al. (1978) zone V is evident in the broad swath of sea-level fall within equatorial ocean basins. The amplitude of this fall reaches $\text{∼0.5}\text{mm/yr}$. Mitrovica and Peltier (1991) coined the term ‘equatorial ocean syphoning’ to describe the flux of water away from the far-field regions. They argued that the process was due to the migration of meltwater from the far-field into the near-field regions vacated by the collapsing peripheral forebulges (that is, migration from zones V to II).

Zone VI described by Clark et al. (1978) is also evident in Fig. 1A as the thin band of anomalous offshore sea-level rise and onshore sea-level fall along far-field coastlines. Walcott (1972) was the first to provide an explanation for this pattern, which is commonly known as ‘continental levering’. Subsequent to the onset of deglaciation, the oceanic regions are subject to a water load but the continental regions are not. As a consequence, the continents are flexed upward at their margin and downward offshore, giving rise to the pattern evident in Fig. 1A. Jagged coastlines are superimposed on this relatively smooth pattern and hence sites located toward the continental interior will show elevated rates of sea-level fall (and progressively higher amplitude sea-level highstands), while those located toward the ocean will exhibit lower rates of sea-level fall and even, in some cases, submergence. Nakada and Lambeck (1989) have explored this geometry in detail as part of their analysis of far-field sea-level highstands within the Australian region.

If one extrapolates the rates evident in Fig. 1A back to the cessation of the model deglaciation ($\text{5}\text{kyr}$ BP), then one obtains sea-level highstands within equatorial ocean basins (zone V) of order 3 m. The recognition that GIA provides a mechanism for the development of such highstands has advanced several diverse disciplines. For example, ‘$\text{3}\text{m}$ beaches’ and exposed coral reef terraces are endemic to equatorial regions and they play a prominent role in the literature of Quaternary geology (e.g., Pirazzoli and Montaggioni, 1986; Pirazzoli, 1993). Furthermore, the analysis of highstand amplitudes (in both zones V and VI) has placed important bounds on both remnant late Holocene melting of polar ice complexes and mantle viscosity (e.g. Montaggioni and Pirazzoli, 1984; Nakada and Lambeck, 1989).

Despite a quarter century of global numerical predictions our understanding of the physical cause of GIA-induced late Holocene far-field sea-level trends remains incomplete. For example, is the syphoning mechanism described by Mitrovica and Peltier (1991) the only contributor to the development of $\text{3}\text{m}$ beaches in equatorial ocean basins, or are there other effects that contribute significantly? Furthermore, what is the relative importance of the Mitrovica and Peltier (1991) mechanism and continental levering to the observed sea-level trends near continental shorelines? In this paper, we revisit these general issues using a detailed decomposition of the signals embedded in the governing sea-level equation.

Far-field sea-level change during glaciation and deglaciation phases will be dominated by the flux of water between ice reservoirs and the ocean basins. Although we focus here on the late Holocene interglacial, we emphasize that the syphoning and levering mechanisms described below will nevertheless be active during the entire glacial cycle. Indeed, these mechanisms contribute significantly to the complex relationship between site-specific sea-level trends and the eustatic sea-level curve since the last glacial maximum (LGM). However, this relationship also involves a suite of other signals, including the direct gravitational effect of diminishing ice reservoirs, and water influx into regions vacated by retreating marine-based ice (e.g. Milne et al., 1999). The interested reader is referred to our companion article, Milne et al. (2002), and also to Lambeck et al. (2001), for a discussion of far-field sea-level change since LGM.