A reconciled solution of Meltwater Pulse 1A sources using sea-level fingerprinting

The most rapid global sea-level rise event of the last deglaciation, Meltwater Pulse 1A (MWP-1A), occurred ∼14,650 years ago. Considerable uncertainty regarding the sources of meltwater limits understanding of the relationship between MWP-1A and the concurrent fast-changing climate. Here we present a data-driven inversion approach, using a glacio-isostatic adjustment model to invert for the sources of MWP-1A via sea-level constraints from six geographically distributed sites. The results suggest contributions from Antarctica, 1.3 m (0–5.9 m; 95% probability), Scandinavia, 4.6 m (3.2–6.4 m) and North America, 12.0 m (5.6–15.4 m), giving a global mean sea-level rise of 17.9 m (15.7–20.2 m) in 500 years. Only a North American dominant scenario successfully predicts the observed sea-level change across our six sites and an Antarctic dominant scenario is firmly refuted by Scottish isolation basin records. Our sea-level based results therefore reconcile with field-based ice-sheet reconstructions.


Sea-level dataset
Supplementary Fig. 1: Flow chart of the iterative inversion procedure adopted in this study. Green boxes denote steps where GIA modelling is used to isolate the fingerprint signal, blue boxes represent steps in the data-driven statistical inversion, and purple boxes are conditional statements.  Supplementary Fig. 6: Estimated local MWP-1A sea-level rise trend at six selected sites using our uniform scenario. Same as Fig.  2 in main text but using the uniform distribution scenario for coral sea-level indicators.

Supplementary Note 1 Local GIA Signal in Northwest Scotland
The effects of the local GIA signal caused by variations of the British-Irish Ice Sheet (BIIS) are shown in Supplementary Fig.  7. We computed the likely range of the local GIA signal by combining three BIIS ice history models with 120 Earth models (Supplementary Fig. 7d-f). By subtracting the mean of the GIA ensemble from the original RSL reconstructions (blue error bars), the non-local ice-sheet induced sea-level rise signal in Northwest Scotland can be obtained (black error bars). These corrected RSL reconstructions are input into the Monte Carlo linear regression and used to estimate the local MWP-1A magnitude ( Supplementary Fig. 7g-i). There are clear differences between the GIA signals associated with the three BIIS models (up to 15 m) due to differences in local ice thickness and timing of deglaciation (see original publications 1-5 for details). However, these differences do not impact on our estimate of the local MWP-1A magnitude because this only depends on the gradient of the local GIA signal between the initiation and termination of MWP-1A, which is similar for all three ice models. Consequently, the three ice models result in similar values for the local MWP-1A magnitude ( Supplementary Fig. 7g-i).

Supplementary Note 2 Jackknife Resampling -Robustness of Results
The degree to which our inversion results depend on the choice of RSL sites is assessed by jackknife resampling, which also reveal each site's contribution to the final inversion result. The inversion is repeated six times, each time removing one site from the six-site database. The results (shown in Supplementary Fig. 8) are generally consistent, pointing to a dominant NAIS contribution, except for the result obtained by excluding Barbados (third panel in Supplementary Fig. 8). When Barbados is excluded, Northwest Scotland becomes the only site that is sensitive to the source of meltwater (all other far-field sites are insensitive; see main text Fig.  1). Under this circumstance, due to the proximity of Northwest Scotland to the SIS, the Northwest Scotland MWP-1A magnitude predominantly determines the SIS inversion with the contributions from the NAIS and AIS essentially unconstrained, resulting in large uncertainty ranges (third panel in Supplementary Fig. 8). Another important feature is that excluding Northwest Scotland causes the melt contribution from the NAIS to become very large and the contribution from the SIS to become very small. The reason for this is similar, excluding Northwest Scotland leaves Barbados as the only site that is sensitive to the source of meltwater.
Since Barbados is mainly sensitive to sources from the NAIS and AIS (main text Fig. 1), it is possible to partition the contribution from the NAIS and AIS, but not from the SIS. These two features are also reflected in the feasible distributions of our final inversion results shown in Supplementary Fig. 9 (same distribution as shown in main text Fig. 5 but different data representation). It is clear that the NAIS and AIS contributions to MWP-1A are strongly negatively correlated (R = -0.96), reflecting the Barbados sensitivity to the contributions from these two ice sheets. In contrast, the SIS contribution shows a weak correlation to the NAIS and AIS contributions (R = -0.30 and 0.28), indicating that the inverted SIS contribution is primarily dependent on the isolation basin stratigraphy evidence from Northwest Scotland.
We seek to resolve the ambiguities indicated by the above jackknifing process by re-running the jackknife method but excluding the SIS fingerprint, to allow us to just identify the partitioning of the NAIS and AIS contributions, which were mostly debated to be the dominant source of MWP-1A 7-12 . The results of this test are shown in Table 1, which indicates a stable solution with a dominant NAIS source (∼15.5 m) and a small Antarctic contribution (∼2 m). This result provides robust evidence for a NAIS dominant scenario rather than an AIS dominant scenario. However, to obtain a similarly stable jackknife result when inverting sources from three ice sheets, at least one more sea-level data site at a location that is sensitive to the MWP-1A sources is needed.
Sea-level index points from the Argentine Shelf could provide a powerful constraint since local RSL variation will be sensitive to melt from the nearby AIS. However, although shell sediment records from the Argentine Shelf have been dated through the MWP-1A interval 13 , the indicative meaning of shell sea-level indicators remains problematic (see Guilderson et al. 13 ). Additionally, RSL change on the Argentine Shelf will be influenced by variations in the adjacent Patagonian Ice Sheet, the deglaciation history of which, though improved by a recent glacial geomorphology data compilation of Davies et al. 14 , has not yet been calibrated with sea-level data. Sea-level index points from locations such as Bonaparte Gulf 15,16 and Echigo Plain, Japan 17 are also dated to across MWP-1A, but due to the lack of temporal resolution and their insensitivity to the sources of MWP-1A, they are not particularly useful for our fingerprinting technique. Lastly, using the local GIA correction method introduced in this study, it would be possible to use other near-field sea-level constraints for MWP-1A source inversion (e.g., records from southwest Norway 18 ). However, estimating the local GIA signal requires a well-studied local deglaciation history and sufficient temporal resolution during MWP-1A, which currently is only achieved in Northwest Scotland.

Supplementary Note 3 Isolation Basin Evidence
This section provides detailed interpretations of Scottish isolation basin stratigraphy to support the definition of the sea-level oscillation limit used in the main text.
In addition to providing sea-level index points, the isolation basin records from Northwest Scotland provide a unique insight into the magnitude and sources of MWP-1A due to their near-field location and the wealth of information contained within the sedimentation staircase 19 . Prior to MWP-1A, the dominant signal recorded by Northwest Scotland sea-level index points is uplift-induced sea-level fall triggered by local ice loss. With this continuous sea-level fall, some basins that were originally connected with the ocean would become isolated. This process is represented by a sediment phase transition from a marine phase (silt/clay) to a freshwater phase (organic mud and peat, Supplementary Fig. 10a). During MWP-1A, if the rate of sea-level rise due to melt from the NAIS, AIS and SIS outpaced the local rate of land uplift, it would case isolation basins in the right height window to reconnect to the ocean, resulting in two isolation events (i.e., marine-freshwater-marine-freshwater, so-called sea-level oscillation), which should be recorded by sediment stratigraphy (Supplementary Fig. 10b). However, for all isolation basins at four sites across Northwest Scotland (Applecross, Arisaig, Kentra and Kintyre; main text Fig. 4g) that were isolated shortly before or during MWP-1A, there is no sea-level oscillation recorded (see isolation basin stratigraphic reconstructions in Shennan et al. [20][21][22][23]. These records therefore provide strong evidence that during MWP-1A the rate of sea-level rise in Northwest Scotland due to far-field ice melt cannot have significantly outpaced the local land uplift rate (i.e., there was no or only a very minor RSL oscillation 19,[22][23][24][25] ).
This condition is met by our MWP-1A source partition, the RSL predictions generated by the ANU_MWP ice model (Supplementary fig. 11a-d) show a monotonic sea-level fall across MWP-1A and provide good fit to SLIPs at different periods for Arisaig, Kentra and Kintyre. The only minor sea-level oscillation occurs at Applecross where local RSL is underestimated, indicating the adopted ice thickness in this region is too thin in the ANU_MWP ice model.
We place an upper bound on the rate of land uplift (i.e., sea level oscillation limit) at Arisaig during MWP-1A by identifying the largest rate predicted by combining the ANU and BRITICE-CHRONO ice models with 120 Earth models that closely reflect mantle properties beneath the British Isles 26 . The maximum rate produces 9.8 m uplift in 500 years obtained by combining the ANU model with the weakest upper and lower mantle model of 4/100 × 10 20 Pa s, respectively. The PATTON2017 model may produce a larger land uplift rate, but it has not been calibrated to any sea-level records across Scotland and therefore the resulting land uplift rate is less meaningful as a constraint for MWP-1A magnitude.
Several previous studies have used isolation basin evidence to constrain the MWP-1A magnitude and sources 6,21,23,27 . When a regional BIIS model is combined with a global ice model (e.g., a revised version of the model of Bassett et al. 9 ) with a dominant AIS contribution to MWP-1A 28,29 , this results in a strong sea-level oscillation across Scotland during MWP-1A (see Fig. 10 of Shennan et al. 6 ). Because the idea of a substantial SIS contribution has only recently been proposed, previous studies inferred a lower global MWP-1A magnitude to avoid this RSL oscillation, but this is inconsistent with our estimations 20 m sea-level rise in the far field. One way to improve this inconsistency is to estimate MWP-1A magnitude and sources using far-field and near-field data together. Liu 27 provides a novel method that combines isolation basin evidence with far-field sea-level records from Tahiti, Barbados and Sunda Shelf to infer the MWP-1A sources from the NAIS and AIS. However, the method adopted to remove the local GIA signal for Scotland in that study results in significant uncertainty, which makes the sea-level index points from Scotland less useful for inverting the MWP-1A sources. Liu 27 therefore was not able to exclusively rule out either a small or large Antarctic contribution.   Supplementary References