Closing the sea level budget at the Last Glacial Maximum

Establishing the volume of excess ice contained in the global ice sheets during the Last Glacial Maximum (LGM; ∼26,000–19,000 y ago) remains a longstanding problem in Ice Age climate dynamics. Expressed as the equivalent lowering of global mean sea level (GMSL), estimates of this value have varied from 105 (1) to 163 m (2), with many estimates suggesting ∼120 m (3). This wide range introduces substantial uncertainties in LGM global boundary conditions (ice sheet height and extent and continental shelf exposure) that strongly influence climate through their impacts on atmospheric and ocean circulation and global temperature. More recently, this uncertainty has influenced our understanding of present sea level change, whereby the ongoing glacial isostatic adjustment (GIA) of the solid Earth to the redistribution of mass since the LGM must be accounted for in satellite measurements of sea level and of current mass changes from shrinkage of glaciers and ice sheets. In PNAS, Lambeck et al. (4) present a comprehensive analysis of nearly 1,000 paleo-sea level markers to reconstruct GMSL change over the last 35,000 y, with their estimate for the LGM GMSL of 134–140 m being significantly larger than most published estimates but similar to a recent reassessment of the Barbados sea level record (130 m) that had been the basis for many estimates of ∼120 m (5). If it stands, this reconstruction will reduce uncertainties in our understanding of Ice Age climate and modern sea level change. At the same time, however, it raises a significant challenge: is it possible to explain this total sea level change from our best estimates of the contributions from individual LGM glaciers and ice sheets?

There are two common approaches to deriving information on LGM sea level. One is to use ice sheet models to reconstruct LGM glaciers and ice sheets, but thus far, there has been only one systematic effort at reconstructing all LGM ice sheets and glaciers in this way (2). Most glaciological models to date, however, ignore far-field relative sea level (RSL) records that best represent GMSL changes. Therefore, there is no guarantee that a sum of individual ice sheet reconstructions will match far-field inferences. The other approach, taken by Lambeck et al. (4), is to invert far-field RSL records to infer GMSL changes and then distribute the equivalent mass among the various ice sheets. If the sum of the individual reconstructions from ice sheet models equals the GMSL change derived from far-field sites, the sea level budget is closed. If the budget is not closed, then the individual ice sheet reconstructions or the geophysical analysis and far-field data used to reconstruct GMSL must be reassessed.

Lambeck et al. (4) use a standard iterative approach to reconstruct GMSL from far-field sites that involves estimating an initial global ice volume from those sites, distributing that mass among the different global ice sheets using geological and glaciological constraints, inverting the far-field records for information that improves the estimate of global ice volume, and assessing the ice sheet reconstructions from near-field sea level data and redistributing the mass as needed. This iterative approach is repeated until convergence is reached. There is one important caveat to their particular implementation, however, whereby the difference between the far-field–derived global value and the sum of the glaciers and Northern Hemisphere ice sheets is simply distributed within the Antarctic ice sheet and is not assessed with any near-field data.

A necessary outcome of this approach is that it derives the earth rheology parameters (lithosphere thickness and mantle viscosity) that determine the GIA response. Despite there being a long history of inverting RSLs for GIA from the last Ice Age for this purpose (6), the parameters continue to be debated, particularly for the lower mantle viscosity (7, 8). Interestingly, Lambeck et al. (4) find two equally possible solutions for this parameter, reflecting a low-viscosity (LM_lv) vs. a high-viscosity (LM_hv) lower mantle, that bracket the debated values, which leads to the reported range of LGM GMSL. Lambeck et al. (4) remain largely neutral on this result, other than to favor the LM_hv value because it results in an Antarctic Ice Sheet (AIS) volume that is more similar to (but still greater than) other reconstructions.

Insofar as the iterative approach taken by Lambeck et al. (4) requires that the sea level budget be closed, we can compare the volumes of their individual LGM ice sheets to other published studies to assess where there is good agreement and where the largest uncertainties exist (Fig. 1A). Lambeck et al. (4) do not report the volumes for the Northern Hemisphere ice sheets, but we assume they are similar to those previously published by their group. Moreover, they have not previously published an estimate for the North American Ice Sheet Complex (NAIS), but we can infer it by subtracting the sum of their other estimates from the total GMSL. Finally, we follow Lambeck et al.’s (4) preference and only address the solution for the LM_hv (134 m) (this only affects their estimate for the AIS). Recognizing that, with these caveats, these estimates may differ from any new values derived by Lambeck et al. (4), we infer the contributions in their analysis to be 21 m for the Eurasian Ice Sheet (EIS) (9), 3.1 m for the Greenland Ice Sheet (GrIS) (10), 6 m for glaciers (2), and 23 m for the AIS for the LM_hv solution, leaving 80.9 m for the NAIS.

Fig. 1.

(A) Published reconstructions of the ice equivalent sea level in ice sheets and glaciers at the LGM. In each case, the red squares are the values inferred from Lambeck et al. The horizontal red bar at 134–140 m is the value of GMSL lowering at the LGM derived by Lambeck et al. (4). GL, glaciers. (B) Reconstructions of the ice equivalent sea level in the AIS published since 1994. The red squares are the two solutions derived by Lambeck et al. (4). Glaciological reconstructions generally do not account for changing ocean area in their stated equivalent sea level contributions, thus inducing slightly smaller values than those given by most GIA-based reconstructions.

Fig. 1A compares the Lambeck (Lm) ice sheet reconstructions (red squares) with a selection of other reconstructions published over the last 20 y. Of the various ice sheets, the Lm reconstructions of the GrIS and EIS are comparable to the most recent reconstructions (differences of ∼2–4 m), with the good agreement suggesting that these values are now reasonably established. The various NAIS reconstructions have the largest spread (27 m). The Lm NAIS reconstruction is near the high end of the other reconstructions, but we note that the low-end NAIS reconstructions (<65 m) are from versions of the ICE-4G model, which have since been revised to a higher value in the ICE-5G model that is similar to the Lm reconstruction. One recent NAIS reconstruction that, for the first time, used a Bayesian approach to constrain a glaciological model against geological, geodetic, and RSL data estimated an intermediate value of ∼70 ± 2 m for the NAIS (11). Given that the Lm reconstructions for the other Northern Hemisphere ice sheets are likely correct, one implication is that any substantial reduction in the Lm NAIS volume must be largely accommodated by an increase in the Lm AIS volume to balance the LGM sea level budget.

The spread of the AIS reconstructions is 17.3 m when excluding the LM_lv solution (Fig. 1A), with a range from 5.7 m to the 23-m estimate from the LM_hv solution (the LM_lv solution increases the range by another 7 m). Why is there such a range? In Fig. 1B, we show published AIS reconstructions over the last 20 y that have been derived from a number of different approaches. Although the Lm LM_hv reconstruction is the largest, it is within 1–5 m of a number of reconstructions that were published before 2012, whereas it is 14–17 m larger than a number of reconstructions published in the last 2 y.

Given the uncertainties in climate, basal parameters, ocean temperatures, and other factors, ice sheet models can generate a wide range of LGM contributions (12). Each of the reconstructions published before 2012 was subject to one or more of these uncertainties, yet all similarly simulate AIS LGM excess ice volumes >14 m. None of these earlier reconstructions, however, were subject to a significant set of paleo-constraints. In contrast, all but one of the recent reconstructions adopt various paleo constraints on LGM ice extent and elevation (marine records, ice cores, near-field sea level and geodetic data, and cosmogenic ages on glacial erratics sampled from mountains projecting through the ice sheet). One model has demonstrated the sensitivity to these constraints, whereby it reconstructed 6.7 m when using all possible constraints (13) and 14.5 m when excluding cosmogenic ages (14). Based on a large ensemble of runs that explores a range of parameters, another model found contributions up to 15 m using paleo and present day constraints and up to 40 m when model misfits with these data are ignored (12).

Even when the AIS reconstructions that are <10 m are excluded, there is still a significant gap between the Lm LM_hv reconstruction and those published since 2002 (Fig. 1B). If the Lm AIS reconstruction is correct, it will thus require a reevaluation of the data constraints, climate forcings, and glaciological assumptions that have been used in all recent reconstructions. Indeed, a recent assessment of the data constraints suggests that there are a number of inherent issues with many of them that may bias the result toward more restricted AIS margins or less ice surface elevation change (15).

We consider three other possible solutions to the case of missing LGM ice. First, it is becoming increasingly clear that the effective radial profile of the Earth's viscosity structure has lateral dependence that needs to be quantified (5). Deglacial reconstructions for North America and Eurasia that rely on GIA constraints have to date ignored the lateral variation in viscosity under each continent. Second, the interpretation of many paleo-sea level proxies relies on observed living depth ranges. These ranges, however, are likely sensitive to ocean conditions (acidity, nutrient levels, temperature, and transmissivity of solar insolation) that could have changed significantly under glacial conditions, requiring a careful reevaluation of potential uncertainties of the living ranges of sea level proxies. Finally, newly discovered records from the Arctic Ocean suggest that an ice sheet may have grounded on the East Siberian margin (16). These features are inferred to be pre-LGM, but age constraints on them are poor. Modeling, reconsideration of existing data, and some targeted field studies are needed to fully rule out the possibility of previously unaccounted for grounded ice in the Northern Hemisphere.