Description: In this study, we propose a statistical method to validate sea-level reconstructions using geological records known as sea-level indicators (SLIs). SLIs are often the only available data to retrace late-glacial relative sea level (RSL). Determining the RSL from SLI height is not straight forward, the elevation at which an SLI was found usually does not represent the past RSL. In contrast, it has to be related to past RSL by investigating sample’s type, habitat and deposition conditions. For instance, water distribution at which a specific specimen is found today can be related to the indicator's depositional height range. Furthermore, the precision of dating varies between geological samples, and, in case of radiocarbon dating, the age has to be calibrated using a non-linear calibration curve. To avoid an a-priori assumption like normal-distributed uncertainties, we define likelihood functions which take into account the indicative meaning’s available error information and calibration statistics represented by joint probabilities. For this conceptional study, we restrict ourselves to one type of indicators, shallow-water shells, which are usually considered as low-grade samples giving only a lower limit of former sea level, as the depth range in which they live spreads over several tens of meters, and does not follow a normal distribution. The presented method is aimed to serve as a strategy for glacial isostatic adjustment reconstructions, in this case for the German Paleo-Climate Modelling Initiative PalMod (https://www.palmod.de/en) and by extending it to other SLI types.

Description: We present a data assimilation algorithm for the time-domain spectral-finite element code VILMA. We consider a 1D earth structure and a prescribed glaciation history ICE5G for the external mass load forcing. We use the Parallel Data Assimilation Framework (PDAF) to assimilate sea level data into the model in order to obtain better estimates of the viscosity structure of mantle and lithosphere. For this purpose, we apply a particle filter in which an ensemble of models is propagated in time, starting shortly before the last glacial maximum. At epochs when observations are available, each particle's performance is estimated and they are resampled based on their performance to form a new ensemble that better resembles the true viscosity distribution. In a proof of concept we show that with this method it is possible to reconstruct a synthetic viscosity distribution from which synthetic data were constructed. In a second step, paleo sea level data are used to infer an optimised 1D viscosity distribution.

Description: Glacial isostatic adjustment is dominated by Earth rheology resulting in a variability of relative sea-level (RSL) predictions of more than 100 meters during the last glacial cycle. Seismic tomography models reveal significant lateral variations in seismic wavespeed, most likely corresponding to variations in temperature and hence viscosity. Therefore, the replacement of 1D Earth structures by a 3D Earth structure is an essential part of recent research to reveal the impact of lateral viscosity contrasts and to achieve a more consistent view on solid-Earth dynamics. Here, we apply the VIscoelastic Lithosphere and MAntle model VILMA to predict RSL during the last deglaciation. We create an ensemble of geodynamically constrained 3D Earth structures which is based on seismic tomography models while considering a range of conversion factors to transfer seismic velocity variations into viscosity variations. For a number of globally distributed sites, we discuss the resulting variability in RSL predictions, compare this with regionally optimized 1D Earth structures, and validate the model results with relative sea-level data (sea-level indicators). This study is part of the German Climate Modeling initiative PalMod aiming the modeling of the last glacial cycle under consideration of a coupled Earth system model, i.e. including feedbacks between ice-sheets and the solid Earth.

Description: Gravitationally consistent solutions of the Sea Level Equation from leakage‐corrected monthly‐mean GFZ RL06 Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On (GRACE‐FO) Stokes coefficients reveal that barystatic sea level averaged over the whole global ocean was rising by 1.72 mm a−1 during the period April 2002 until August 2016. This rate refers to a truely global ocean averaging domain that includes all polar and semienclosed seas. The result corresponds to 2.02 mm a−1 mean barystatic sea level rise in the open ocean with a 1,000 km coastal buffer zone as obtained from a direct spatial integration of monthly GRACE data. The bias of +0.3 mm a−1 is caused by below‐average barystatic sea level rise in close proximity to coastal mass losses induced by the smaller gravitational attraction of the remaining continental ice and water masses. Alternative spherical harmonics solutions from CSR, JPL, and TU Graz reveal open‐ocean rates between 1.94 and 2.08 mm a−1, thereby demonstrating that systematic differences among the processing centers are much reduced in the latest release. We introduce in this paper a new method to approximate spatial leakage from the differences of two differently filtered global gravity fields. A globally constant and time‐invariant scale factor required to obtain full leakage from those filter differences is found to be 3.9 for GFZ RL06 when filtered with DDK3, and lies between 3.9 and 4.4 for other processing centers. Spatial leakage is estimated for every month in terms of global grids, thereby providing also valuable information of intrabasin leakage that is potentially relevant for hydrologic and hydrometeorological applications.

Description: Viscoelastic deformations of an earth structure in response to a time-varying surface load are analyzed in glacial isostatic adjustment (GIA). When solving this problem, aspects like flexure of the lithosphere and retarded response of mantle material become evident. Quantified are these by flexural rigidity and relaxation times. The concepts partly lose their relevance when changing from a 1D earth structure (only radial variations) to a 2D or a 3D earth structure (lateral variations). In regions like Fennoscandia and Laurentide, which are affected by GIA, lateral variations of the lithosphere and mantle structure are moderate and, so, the application of a 1D earth structure is widely accepted. But, also for these two regions one has to keep in mind that the respective 1D earth structures differ and that such an approximation mainly holds in the central part of the respective region. In contrast, lateral variations or a local structure of different viscosity have to be considered in areas like Patagonia, Antarctica or Alaska which is located above tectonic activity or covers a region with significant lateral changes in earth structure. But, already for the two former examples one has to keep in mind that the respective 1D earth structures inferred from GIA modelling differ between the two regions. Focusing on the relaxation behavior and the mantle-material transport, we discuss the effect of lateral variations on the deformation process. We will assess to which extent a 1D earth structure can represent lateral variability in structural features, and, at which point a 3D earth structure has to be considered. Such questions are of concern, when discussing GIA for geodetic applications as well as in earth system modeling as this study contributes to the climate modeling initiative Palmod.

Description: Based on the latest GFZ release 06 of monthly gravity fields from GRACE satellite mission, area-averaged barystatic sea-level is found to rise by 2.02 mm/a during the period April 2002 until August 2016 in the open ocean with a 1000 km coastal buffer zone when low degree coefficients are properly augmented with information from satellite laser ranging. Alternative spherical harmonics solutions from CSR, JPL and TU Graz reveal rates between 1.94 and 2.08 mm/a, thereby demonstrating that systematic differences among the centers are much reduced in the latest release. The results from the direct integration in the open ocean can be aligned to associated solutions of the sea-level equation when fractional leakage derived from two differently filtered global gravity fields is explicitly considered, leading to a global mean sea-level rise of 1.72 mm/a. This result implies that estimates obtained from a 1000 km coastal buffer zone are biased 0.3 mm/a high due the systematic omission of regions with below-average barystatic sea-level rise in regions close to substantial coastal mass losses induced by the reduced gravitational attraction of the remaining continental ice and water masses.

Description: We present a compilation and analysis of ~ 1000 Holocene relative shore-level (RSL)indicators located around the Baltic Sea including relative sea-level data points as well as data points from the Ancylus Lake and the following transitional phase. The spatial distribution covers the Baltic Sea and near-coastal areas fairly well, but some gaps remain mainly in Sweden. RSL data follow the standardized HOLSEA format and, thus, are ready for spatially comprehensive applications in, e.g., glacial isostatic adjustment (GIA) modelling. We apply a SQL database system to store the nationally provided data sets in their individual form and to map the different input into the HOLSEA format as the information content of the individual data sets from the Baltic Sea area differs (https://doi.org/10.5880/GFZ.1.3.2020.003). The majority of the RSL data is related to the last marine stage in Baltic Sea history after 8.5 ka BP (thousand years before present). These samples were grouped according to their dominant RSL tendencies into three clusters: regions with negative, positive and complex (transitional) RSL tendencies. Overall, regions with isostatic uplift driven negative tendencies dominate and show regression in the Baltic Sea basin during the last marine stage. Shifts from positive to negative tendencies in RSL data from transitional regions show a mid-Holocene highstand around 7.5-6.5 ka BP which is consistent with the end of the final melting of the Laurentide Ice Sheet. Comparisons of RSL data with GIA predictions including global ICE-5G and ICE-6G_C ice histories show good fit with RSL data from the regions with negative tendencies, whereas in the transitional areas in the eastern Baltic, predictions for the mid-Holocene clearly overestimate the RSL and fail to recover the the region where a mid-Holocene RSL highstand derived from the proxy reconstructions should appear. These results motivate improvements of ice-sheet and Earth-structure models and show the potential and benefits of the new compilation for future studies.

Description: Highlights: • A first standardized and publicly available Holocene relative sea-level database for the Baltic Sea is presented. • The database holds 1099 revised data points with an estimation of vertical and chronological uncertainties. • Negative RSL tendencies prevail over the positive and complex tendencies in the Baltic Sea Basin. • Mid-Holocene RSL highstand occurred around 7.5–6.5 ka BP being consistent with the end of the final melting of the LIS. • The contribution of ice loading in the eastern Baltic Sea Basin is likely overestimated in the ICE-5G and ICE-6G_C models. Abstract: We present a compilation and analysis of 1099 Holocene relative shore-level (RSL) indicators located around the Baltic Sea including 867 relative sea-level data points and 232 data points from the Ancylus Lake and the following transitional phase. The spatial distribution covers the Baltic Sea and near-coastal areas fairly well, but some gaps remain mainly in Sweden. RSL data follow the standardized HOLSEA format and, thus, are ready for spatially comprehensive applications in, e.g., glacial isostatic adjustment (GIA) modelling. We apply a SQL database system to store the nationally provided data sets in their individual form and to map the different input into the HOLSEA format as the information content of the individual data sets from the Baltic Sea area differs. About 80% of the RSL data is related to the last marine stage in Baltic Sea history after 8.5 ka BP (thousand years before present). These samples are grouped according to their dominant RSL tendencies into three clusters: regions with negative, positive and complex (transitional) RSL tendencies. Overall, regions with isostatic uplift driven negative tendencies dominate and show regression in the Baltic Sea basin during the last marine stage. Shifts from positive to negative tendencies in RSL data from transitional regions show a mid-Holocene highstand around 7.5–6.5 ka BP which is consistent with the end of the final melting of the Laurentide Ice Sheet. Comparisons of RSL data with GIA predictions including global ICE-5G and ICE-6G_C ice histories show good fit with RSL data from the regions with negative tendencies, whereas in the transitional areas in the eastern Baltic, predictions for the mid-Holocene clearly overestimate the RSL and fail to recover the mid-Holocene RSL highstand derived from the proxy reconstructions. These results motivate improvements of ice-sheet and Earth-structure models and show the potential and benefits of the new compilation for future studies.

Description: Understanding the future fate of the Greenland Ice Sheet (GIS) in the context of anthropogenic CO2 emissions is crucial to predict sea level rise. With the fully coupled Earth system model of intermediate complexity CLIMBER-X, we study the stability of the GIS and its transient response to CO2 emissions over the next 10 Kyr. Bifurcation points exist at global temperature anomalies of 0.6 and 1.6 K relative to pre-industrial. For system states in the vicinity of the equilibrium ice volumes corresponding to these temperature anomalies, mass loss rate and sensitivity of mass loss to cumulative CO2 emission peak. These critical ice volumes are crossed for cumulative emissions of 1,000 and 2,500 GtC, which would cause long-term sea level rise by 1.8 and 6.9 m respectively. In summary, we find tipping of the GIS within the range of the temperature limits of the Paris agreement. Key Points Bifurcation points exist at global mean temperature anomalies of 0.6 and 1.6 K relative to pre-industrial Mass loss rate and sensitivity to cumulative CO2 emission peak near the equilibrium ice volumes belonging to these temperature anomalies Substantial long-term mass loss of the Greenland ice sheet for cumulative emissions larger than 1,000 Gt carbon