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During the glacial cycles of the past 800 000 years, Eurasia and North America were periodically covered by large ice sheets, causing up to 100 m of sea-level change. While Late Pleistocene glacial cycles typically lasted 80 000–120 000 years, the termination phases were completed in only 10 000 years. During these glacial terminations, the North American and Eurasian ice sheets retreated, which created large proglacial lakes in front of the ice-sheet margin. Proglacial lakes accelerate deglaciation as they facilitate the formation of ice shelves at the southern margins of the North American and Eurasian ice sheets. These ice shelves are characterized by basal melting, low surface elevations, and negligible friction at the base. Here, we use an ice-sheet model to quantify the (combined) effects of proglacial lakes on Late Pleistocene glacial terminations by examining their interplay with glacial isostatic adjustment (GIA) and basal sliding. We find that proglacial lakes accelerate the deglaciation of ice sheets mainly because there is an absence of basal friction underneath ice shelves. If friction underneath grounded ice is applied to floating ice, full deglaciation is postponed by a few millennia, resulting in more ice remaining during interglacial periods and no extensive ice shelves forming. Additionally, the large uncertainty in melt rates underneath lacustrine ice shelves translates to an uncertainty in the timing of the termination of up to a millennium. Proglacial lakes are created by depressions in the landscape that remain after an ice sheet has retreated. The depth, size, and timing of proglacial lakes depend on the rate of bedrock rebound. We find that if bedrock rebounds within a few centuries (rather than a few millennia), the mass loss rate of the ice sheet is substantially reduced. This is because fast bedrock rebound prevents the formation of extensive proglacial lakes. Additionally, a decrease in ice thickness is partly compensated for by faster bedrock rebound, resulting in a higher surface elevation; lower temperatures; and a higher surface mass balance, which delays deglaciation. We find that a very long bedrock relaxation time does not substantially affect terminations, but it may lead to a delayed onset of the next glacial period. This is because inception regions, such as northwestern Canada, remain below sea level throughout the preceding interglacial period.

Introduction: Limited data inform about the optimal dosing and duration of suppressive antimicrobial therapy (SAT) for orthopedic implant infection (OII). We aimed to compare the effectiveness of low-dosage with standard-dosage SAT and evaluate the safety of stopping SAT. Methods: All patients with OII treated with SAT from 2011 to 2022 were retrospectively included. Data were extracted from electronic patient files. Low-dosage SAT was defined as antimicrobial therapy dosed lower than the standard dosage recommended for OII. The association of dosing strategy and other factors with failure-free survival were assessed by Kaplan–Meier and Cox proportional hazard models. Results: One-hundred-and-eight patients were included. The median follow-up time after SAT initiation was 21 months (interquartile range (IQR) 10–42 months). SAT was successful in 74 patients (69 %). Low-dosage SAT (n=82) was not associated with failure in univariate (hazard ratio (HR) 1.23, 95 % confidence interval (CI) 0.53–2.83) and multivariate analyses (HR 1.24, 95 % CI 0.54–2.90). In 25 patients (23 %), SAT was stopped after a median treatment duration of 26 months. In this group, one patient (4 %) developed a relapse. Conclusions: In this study, low-dosage SAT was as effective as standard dosage SAT. Moreover, stopping SAT after 2 to 3 years may be justified in patients with a good clinical course. These findings warrant further research on optimal dosing and duration of SAT and on the durability of in vivo biofilms.

Glacial isostatic adjustment (GIA) has a stabilizing effect on the evolution of the Antarctic ice sheet by reducing the grounding line migration following ice melt. The timescale and strength of this feedback depends on the spatially varying viscosity of the Earth's mantle. Most studies assume a relatively long and laterally homogenous response time of the bedrock. However, the mantle viscosity is spatially variable, with a high mantle viscosity beneath East Antarctica and a low mantle viscosity beneath West Antarctica. For this study, we have developed a new method to couple a 3D GIA model and an ice sheet model to study the interaction between the solid Earth and the Antarctic ice sheet during the last glacial cycle. With this method, the ice sheet model and GIA model exchange ice thickness and bedrock elevation during a fully coupled transient experiment. The feedback effect is taken into account with a high temporal resolution, where the coupling time steps between the ice sheet and GIA model are 5000 years over the glaciation phase and vary between 500 and 1000 years over the deglaciation phase of the last glacial cycle. During each coupling time step, the bedrock elevation is adjusted at every ice sheet model time step, and the deformation is computed for a linearly changing ice load. We applied the method using the ice sheet model ANICE and a 3D GIA finite element model. We used results from a regional seismic model for Antarctica embedded in the global seismic model SMEAN2 to determine the patterns in the mantle viscosity. The results of simulations over the last glacial cycle show that differences in mantle viscosity of an order of magnitude can lead to differences in the grounding line position up to 700 km and to differences in ice thickness of the order of 2 km for the present day near the Ross Embayment. These results underline and quantify the importance of including local GIA feedback effects in ice sheet models when simulating the Antarctic ice sheet evolution over the last glacial cycle.

The strongly varying benthic δ18O levels of the early and mid-Miocene (23 to 14 Myr ago) are primarily caused by a combination of changes in Antarctic Ice Sheet (AIS) volume and deep-ocean temperatures. These factors are coupled since AIS changes affect deep-ocean temperatures. It has recently been argued that this is due to changes in ice sheet area rather than volume because area changes affect the surface albedo. This finding would be important when the transient AIS grows relatively faster in extent than in thickness, which we test here. We analyse simulations of Miocene AIS variability carried out using the three-dimensional ice sheet model IMAU-ICE forced by warm (high CO2, no ice) and cold (low CO2, large East AIS) climate snapshots. These simulations comprise equilibrium and idealized quasi-orbital transient runs with strongly varying CO2 levels (280 to 840 ppm). Our simulations show a limited direct effect of East AIS changes on Miocene orbital-timescale benthic δ18O variability because of the slow build-up of volume. However, we find that relative to the equilibrium ice sheet size, the AIS area adapts significantly faster and more strongly than volume to the applied forcing variability. Consequently, during certain intervals the ice sheet is receding at the margins, while ice is still building up in the interior. That means the AIS does not adapt to a changing equilibrium size at the same rate or with the same sign everywhere. Our results indicate that the Miocene Antarctic Ice Sheet affects deep-ocean temperatures more than its volume suggests.

The Antarctic Ice Sheet represents the largest source of uncertainty in future sea level rise projections, with a contribution to sea level by 2100 ranging from −5 to 43 cm of sea level equivalent under high carbon emission scenarios estimated by the recent Ice Sheet Model Intercomparison for CMIP6 (ISMIP6). ISMIP6 highlighted the different behaviors of the East and West Antarctic ice sheets, as well as the possible role of increased surface mass balance in offsetting the dynamic ice loss in response to changing oceanic conditions in ice shelf cavities. However, the detailed contribution of individual glaciers, as well as the partitioning of uncertainty associated with this ensemble, have not yet been investigated. Here, we analyze the ISMIP6 results for high carbon emission scenarios, focusing on key glaciers around the Antarctic Ice Sheet, and we quantify their projected dynamic mass loss, defined here as mass loss through increased ice discharge into the ocean in response to changing oceanic conditions. We highlight glaciers contributing the most to sea level rise, as well as their vulnerability to changes in oceanic conditions. We then investigate the different sources of uncertainty and their relative role in projections, for the entire continent and for key individual glaciers. We show that, in addition to Thwaites and Pine Island glaciers in West Antarctica, Totten and Moscow University glaciers in East Antarctica present comparable future dynamic mass loss and high sensitivity to ice shelf basal melt. The overall uncertainty in additional dynamic mass loss in response to changing oceanic conditions, compared to a scenario with constant oceanic conditions, is dominated by the choice of ice sheet model, accounting for 52 % of the total uncertainty of the Antarctic dynamic mass loss in 2100. Its relative role for the most dynamic glaciers varies between 14 % for MacAyeal and Whillans ice streams and 56 % for Pine Island Glacier at the end of the century. The uncertainty associated with the choice of climate model increases over time and reaches 13 % of the uncertainty by 2100 for the Antarctic Ice Sheet but varies between 4 % for Thwaites Glacier and 53 % for Whillans Ice Stream. The uncertainty associated with the ice–climate interaction, which captures different treatments of oceanic forcings such as the choice of melt parameterization, its calibration, and simulated ice shelf geometries, accounts for 22 % of the uncertainty at the ice sheet scale but reaches 36 % and 39 % for Institute Ice Stream and Thwaites Glacier, respectively, by 2100. Overall, this study helps inform future research by highlighting the sectors of the ice sheet most vulnerable to oceanic warming over the 21st century and by quantifying the main sources of uncertainty.

A major source of uncertainty in future sea level projections is the ocean-driven basal melt of Antarctic ice shelves. While ice sheet models require a kilometre-scale resolution to realistically resolve ice shelf stability and grounding line migration, global or regional 3D ocean models are computationally too expensive to produce basal melt forcing fields at this resolution on long timescales. To bridge this resolution gap, we introduce the 2D numerical model LADDIE (one-layer Antarctic model for dynamical downscaling of ice–ocean exchanges), which allows for the computationally efficient modelling of detailed basal melt fields. The model is open source and can be applied easily to different geometries or different ocean forcings. The aim of this study is threefold: to introduce the model to the community, to demonstrate its application and performance in two use cases, and to describe and interpret new basal melt patterns simulated by this model. The two use cases are the small Crosson–Dotson Ice Shelf in the warm Amundsen Sea region and the large Filchner–Ronne Ice Shelf in the cold Weddell Sea. At ice-shelf-wide scales, LADDIE reproduces observed patterns of basal melting and freezing in warm and cold environments without the need to re-tune parameters for individual ice shelves. At scales of 0.5–5 km, which are typically unresolved by 3D ocean models and poorly constrained by observations, LADDIE produces plausible basal melt patterns. Most significantly, the simulated basal melt patterns are physically consistent with the applied ice shelf topography. These patterns are governed by the topographic steering and Coriolis deflection of meltwater flows, two processes that are poorly represented in basal melt parameterisations. The kilometre-scale melt patterns simulated by LADDIE include enhanced melt rates in grounding zones and basal channels and enhanced melt or freezing in shear margins. As these regions are critical for ice shelf stability, we conclude that LADDIE can provide detailed basal melt patterns at the essential resolution that ice sheet models require. The physical consistency between the applied geometry and the simulated basal melt fields indicates that LADDIE can play a valuable role in the development of coupled ice–ocean modelling.

The global acceleration of sea-level rise (SLR) during the 20th century is now established. On the local scale, this is harder to establish as several drivers of SLR play a role, which can mask the acceleration. Here, we study the rate of SLR along the coast of the Netherlands from the average of six tide gauge records covering the period 1890–2021. To isolate the effects of the wind field variations and the nodal tide from the local sea-level trend, we use four generalised additive models (GAMs) which include different predictive variables. From the sea-level trend estimates, we obtain the continuous evolution of the rate of SLR and its uncertainty over the observational period. The standard error in the estimation of the rate of SLR is reduced when we account for nodal-tide effects and is reduced further when we also account for the wind effects, meaning these provide better estimates of the rate of SLR. A part of the long-term SLR is due to wind forcing related to a strengthening and northward shift of the jet stream, but this SLR contribution decelerated over the observational period. Additionally, we detect wind-forced sea-level variability on multidecadal timescales with an amplitude of around 1 cm. Using a coherence analysis, we identify both the North Atlantic Oscillation and the Atlantic Multidecadal Variability as its drivers. Crucially, accounting for the nodal-tide and wind effects changes the estimated rate of SLR, unmasking an SLR acceleration that started in the 1960s. Our best-fitting GAM, which accounts for nodal and wind effects, yields a rate of SLR of about 1.72.21.3 mm yr−1 in 1900–1919 and 1.51.91.2 mm yr−1 in 1940–1959 compared to 2.93.52.4 mm yr−1 in 2000–2019 (where the lower and upper bounds denote the 5th and 95th percentiles). If we discount the nodal tide, wind and fluctuation effects and assume a constant rate of SLR, then the probability (p value) of finding a rate difference between 1940–1959 and 2000–2019 of at least our estimate is smaller than 1 %. Consistent with global observations and the expectations based on the physics of global warming, our results show unequivocally that SLR along the Dutch coast has accelerated since the 1960s.

Ice losses from the Greenland and Antarctic ice sheets have accelerated since the 1990s, accounting for a significant increase in the global mean sea level. Here, we present a new 29-year record of ice sheet mass balance from 1992 to 2020 from the Ice Sheet Mass Balance Inter-comparison Exercise (IMBIE). We compare and combine 50 independent estimates of ice sheet mass balance derived from satellite observations of temporal changes in ice sheet flow, in ice sheet volume, and in Earth's gravity field. Between 1992 and 2020, the ice sheets contributed 21.0±1.9 mm to global mean sea level, with the rate of mass loss rising from 105 Gt yr−1 between 1992 and 1996 to 372 Gt yr−1 between 2016 and 2020. In Greenland, the rate of mass loss is 169±9 Gt yr−1 between 1992 and 2020, but there are large inter-annual variations in mass balance, with mass loss ranging from 86 Gt yr−1 in 2017 to 444 Gt yr−1 in 2019 due to large variability in surface mass balance. In Antarctica, ice losses continue to be dominated by mass loss from West Antarctica (82±9 Gt yr−1) and, to a lesser extent, from the Antarctic Peninsula (13±5 Gt yr−1). East Antarctica remains close to a state of balance, with a small gain of 3±15 Gt yr−1, but is the most uncertain component of Antarctica's mass balance. The dataset is publicly available at https://doi.org/10.5285/77B64C55-7166-4A06-9DEF-2E400398E452 (IMBIE Team, 2021).

Subglacial bed roughness is one of the main factors controlling the rate of future Antarctic ice-sheet retreat and also one of the most uncertain. A common technique to constrain the bed roughness using ice-sheet models is basal inversion, tuning the roughness to reproduce the observed present-day ice-sheet geometry and/or surface velocity. However, many other factors affecting ice-sheet evolution, such as the englacial temperature and viscosity, the surface and basal mass balance, and the subglacial topography, also contain substantial uncertainties. Using a basal inversion technique intrinsically causes any errors in these other quantities to lead to compensating errors in the inverted bed roughness. Using a set of idealised-geometry experiments, we quantify these compensating errors and investigate their effect on the dynamic response of the ice sheet to a prescribed forcing. We find that relatively small errors in ice viscosity and subglacial topography require substantial compensating errors in the bed roughness in order to produce the same steady-state ice sheet, obscuring the realistic spatial variability in the bed roughness. When subjected to a retreat-inducing forcing, we find that these different parameter combinations, which per definition of the inversion procedure result in the same steady-state geometry, lead to a rate of ice volume loss that can differ by as much as a factor of 2. This implies that ice-sheet models that use basal inversion to initialise their model state can still display a substantial model bias despite having an initial state which is close to the observations.

Background: Differentiation between uncomplicated and complicated postoperative wound drainage after arthroplasty is crucial to prevent unnecessary reoperation. Prospective data about the duration and amount of postoperative wound drainage in patients with and without prosthetic joint infection (PJI) are currently absent. Methods: A multicentre cohort study was conducted to assess the duration and amount of wound drainage in patients after arthroplasty. During 30 postoperative days after arthroplasty, patients recorded their wound status in a previously developed wound care app and graded the amount of wound drainage on a 5-point scale. Data about PJI in the follow-up period were extracted from the patient files. Results: Of the 1019 included patients, 16 patients (1.6 %) developed a PJI. Minor wound drainage decreased from the first to the fourth postoperative week from 50 % to 3 %. Both moderate to severe wound drainage in the third week and newly developed wound drainage in the second week after a week without drainage were strongly associated with PJI (odds ratio (OR) 103.23, 95 % confidence interval (CI) 26.08 to 408.57, OR 80.71, 95 % CI 9.12 to 714.52, respectively). The positive predictive value (PPV) for PJI was 83 % for moderate to heavy wound drainage in the third week. Conclusion: Moderate to heavy wound drainage and persistent wound drainage were strongly associated with PJI. The PPV of wound drainage for PJI was high for moderate to heavy drainage in the third week but was low for drainage in the first week. Therefore, additional parameters are needed to guide the decision to reoperate on patients for suspected acute PJI.

During the last glacial cycle (LGC), ice sheets covered large parts of Eurasia and North America, which resulted in ∼120 m of sea level change. Ice sheet–climate interactions have considerable influence on temperature and precipitation patterns and therefore need to be included when simulating this time period. Ideally, ice sheet–climate interactions are simulated by a high-resolution Earth system model. While these models are capable of simulating climates at a certain point in time, such as the pre-industrial (PI) or the Last Glacial Maximum (LGM; 21 000 years ago), a full transient glacial cycle is currently computationally unfeasible as it requires a too-large amount of computation time. Nevertheless, ice sheet models require forcing that captures the gradual change in climate over time to calculate the accumulation and melt of ice and its effect on ice sheet extent and volume changes. Here we simulate the LGC using an ice sheet model forced by LGM and PI climates. The gradual change in climate is modelled by transiently interpolating between pre-calculated results from a climate model for the LGM and the PI. To assess the influence of ice sheet–climate interactions, we use two different interpolation methods: the climate matrix method, which includes a temperature–albedo and precipitation–topography feedback, and the glacial index method, which does not. To investigate the sensitivity of the results to the prescribed climate forcing, we use the output of several models that are part of the Paleoclimate Modelling Intercomparison Project Phase III (PMIP3). In these simulations, ice volume is prescribed, and the climate is reconstructed with a general circulation model (GCM). Here we test those models by using their climate to drive an ice sheet model over the LGC. We find that the ice volume differences caused by the climate forcing exceed the differences caused by the interpolation method. Some GCMs produced unrealistic LGM volumes, and only four resulted in reasonable ice sheets, with LGM Northern Hemisphere sea level contribution ranging between 74–113 m with respect to the present day. The glacial index and climate matrix methods result in similar ice volumes at the LGM but yield a different ice evolution with different ice domes during the inception phase of the glacial cycle and different sea level rates during the deglaciation phase. The temperature–albedo feedback is the main cause of differences between the glacial index and climate matrix methods.

Ice-dynamical processes constitute a large uncertainty in future projections of sea-level rise caused by anthropogenic climate change. Improving our understanding of these processes requires ice-sheet models that perform well at simulating both past and future ice-sheet evolution. Here, we present version 2.0 of the ice-sheet model IMAU-ICE, which uses the depth-integrated viscosity approximation (DIVA) to solve the stress balance. We evaluate its performance in a range of benchmark experiments, including simple analytical solutions and both schematic and realistic model intercomparison exercises. IMAU-ICE has adopted recent developments in the numerical treatment of englacial stress and sub-shelf melt near the grounding line, which result in good performance in experiments concerning grounding-line migration (MISMIP, MISMIP+) and buttressing (ABUMIP). This makes it a model that is robust, versatile, and user-friendly, which will provide a firm basis for (palaeo-)glaciological research in the coming years.

Benthic δ18O levels vary strongly during the warmer-than-modern early and mid-Miocene (23 to 14 Myr ago), suggesting a dynamic Antarctic ice sheet (AIS). So far, however, realistic simulations of the Miocene AIS have been limited to equilibrium states under different CO2 levels and orbital settings. Earlier transient simulations lacked ice-sheet–atmosphere interactions and used a present-day rather than Miocene Antarctic bedrock topography. Here, we quantify the effect of ice-sheet–atmosphere interactions, running the ice-sheet model IMAU-ICE using climate forcing from Miocene simulations by the general circulation model GENESIS. Utilising a recently developed matrix interpolation method enables us to interpolate the climate forcing based on CO2 levels (between 280 and 840 ppm), as well as varying ice-sheet configurations (between no ice and a large East Antarctic Ice Sheet). We furthermore implement recent reconstructions of Miocene Antarctic bedrock topography. We find that the positive albedo–temperature feedback, partly compensated for by a negative feedback between ice volume and precipitation, increases hysteresis in the relation between CO2 and ice volume. Together, these ice-sheet–atmosphere interactions decrease the amplitude of Miocene AIS variability in idealised transient simulations. Forced by quasi-orbital 40 kyr forcing CO2 cycles, the ice volume variability reduces by 21 % when ice-sheet–atmosphere interactions are included compared to when forcing variability is only based on CO2 changes. Thereby, these interactions also diminish the contribution of AIS variability to benthic δ18O fluctuations. Evolving bedrock topography during the early and mid-Miocene also reduces ice volume variability by 10 % under equal 40 kyr cycles of atmosphere and ocean forcing.

Introduction: Two-stage revision surgery is the most frequently performed procedure in patients with a chronic periprosthetic joint infection (PJI). The infection eradication rates in the current literature differ between 54 % and 100 %, which could be attributed to different treatment strategies. The aim of this study was to retrospectively evaluate the infection eradication rate in patients with chronic PJI treated with two-stage revision surgery of the hip or knee in primary and re-revision cases. Methods: All patients treated with a two-stage revision for chronic PJI between 2005 and 2011 were analysed. Patient and infection characteristics were retrieved. Primary outcome was successful infection eradication at last follow-up. Successful eradication is specified as no need for subsequent revision surgery or suppressive antibiotic treatment. Results: Forty-seven patients were treated with a two-stage revision. Infection eradication was achieved in 36 out of 47 cases. Thirty-eight patients had positive cultures: 35 monomicrobial infections and 3 polymicrobial infections. Nine cases of culture-negative infections were identified. Accompanying eradication rates were 26 out of 35 cases, 2 out of 3 cases, and 8 out of 9 cases respectively. Mean follow-up was 128 (27–186) months. For hip and knee revisions the eradication rates were 22 out of 31 cases and 14 out of 16 cases respectively. After primary arthroplasty the infection was eradicated in 29 out of 38 cases and after re-revision in 7 out of 9 cases. Conclusion: In this study, the infection eradication rate for two-stage revision surgery after PJI of the hip and knee in primary and re-revision cases was 77 %. No statistically significant patient, infection and micro-organism characteristics were found which influence the infection eradication rates at long-term follow-up of 128 (27–186) months.

Improving our confidence in future projections of sea-level rise requires models that can simulate ice-sheet evolution both in the future and in the geological past. A physically accurate treatment of large changes in ice-sheet geometry requires a proper treatment of processes near the margin, like grounding line dynamics, which in turn requires a high spatial resolution in that specific region, so that small-scale topographical features are resolved. This leads to a demand for computationally efficient models, where such a high resolution can be feasibly applied in simulations of 105–107 years in duration. Here, we present and evaluate a new ice-sheet model that solves the hybrid SIA–SSA approximation of the stress balance, including a heuristic rule for the grounding-line flux. This is done on a dynamic adaptive mesh which is adapted to the modelled ice-sheet geometry during a simulation. Mesh resolution can be configured to be fine only at specified areas, such as the calving front or the grounding line, as well as specified point locations such as ice-core drill sites. This strongly reduces the number of grid points where the equations need to be solved, increasing the computational efficiency. A high resolution allows the model to resolve small geometrical features, such as outlet glaciers and sub-shelf pinning points, which can significantly affect large-scale ice-sheet dynamics. We show that the model reproduces the analytical solutions or model intercomparison benchmarks for a number of schematic ice-sheet configurations, indicating that the numerical approach is valid. Because of the unstructured triangular mesh, the number of vertices increases less rapidly with resolution than in a square-grid model, greatly reducing the required computation time for high resolutions. A simulation of all four continental ice sheets during an entire 120 kyr glacial cycle, with a 4 km resolution near the grounding line, is expected to take 100–200 wall clock hours on a 16-core system (1600–3200 core hours), implying that this model can be feasibly used for high-resolution palaeo-ice-sheet simulations.

Understanding the evolution of, and the interactions between, ice sheets and the global climate over geological timescales is important for being able to project their future evolution. However, direct observational evidence of past CO2 concentrations, and the implied radiative forcing, only exists for the past 800 000 years. Records of benthic δ18O date back millions of years but contain signals from both land ice volume and ocean temperature. In recent years, inverse forward modelling has been developed as a method to disentangle these two signals, resulting in mutually consistent reconstructions of ice volume, temperature, and CO2. We use this approach to force a hybrid ice-sheet–climate model with a benthic δ18O stack, reconstructing the evolution of the ice sheets, global mean sea level, and atmospheric CO2 during the late Pliocene and the Pleistocene, from 3.6 million years (Myr) ago to the present day. During the warmer-than-present climates of the late Pliocene, reconstructed CO2 varies widely, from 320–440 ppmv for warm periods to 235–250 ppmv for the early glacial excursion ∼3.3 million years ago. Sea level is relatively stable during this period, with maxima of 6–14 m and minima of 12–26 m during glacial episodes. Both CO2 and sea level are within the wide ranges of values covered by available proxy data for this period. Our results for the Pleistocene agree well with the ice-core CO2 record, as well as with different available sea-level proxy data. For the Early Pleistocene, 2.6–1.2 Myr ago, we simulate 40 kyr glacial cycles, with interglacial CO2 decreasing from 280–300 ppmv at the beginning of the Pleistocene to 250–280 ppmv just before the Mid-Pleistocene Transition (MPT). Peak glacial CO2 decreases from 220–250 to 205–225 ppmv during this period. After the MPT, when the glacial cycles change from 40 to 80 120 kyr cyclicity, the glacial–interglacial contrast increases, with interglacial CO2 varying between 250–320 ppmv and peak glacial values decreasing to 170–210 ppmv.

Tidal flats provide valuable ecosystem services such as flood protection and carbon sequestration. Erosion and accretion processes govern the ecogeomorphic evolution of intertidal ecosystems (marshes and bare flats) and, hence, substantially affect their valuable ecosystem services. To understand the intertidal ecosystem development, high-frequency bed-level change data are thus needed. However, such datasets are scarce due to the lack of suitable methods that do not involve excessive labour and/or costly instruments. By applying newly developed surface elevation dynamics (SED) sensors, we obtained unique high-resolution daily bed-level change datasets in the period 2013–2017 from 10 marsh–mudflat sites situated in the Netherlands, Belgium, and the United Kingdom in contrasting physical and biological settings. At each site, multiple sensors were deployed for 9–20 months to ensure sufficient spatial and temporal coverage of highly variable bed-level change processes. The bed-level change data are provided with synchronized hydrodynamic data, i.e. water level, wave height, tidal current velocity, medium sediment grain size (D50), and chlorophyll a level at four sites. This dataset has revealed diverse spatial morphodynamics patterns over daily to seasonal scales, which are valuable to theoretical and model development. On the daily scale, this dataset is particularly instructive, as it includes a number of storm events, the response to which can be detected in the bed-level change observations. Such data are rare but useful to study tidal flat response to highly energetic conditions. The dataset is available from 4TU.ResearchData (https://doi.org/10.4121/12693254.v4; Hu et al., 2020), which is expected to expand with additional SED sensor data from ongoing and planned surveys.

Introduction: Debridement, antibiotics and implant retention (DAIR) procedures are effective treatments for acute postoperative or acute hematogenous periprosthetic joint infections. However, literature reporting on the effectiveness of DAIR procedures performed after a one- or two-stage revision because of a prosthetic joint infection (PJI) (PJI-related revision arthroplasty) is scarce. The aim of this study is to retrospectively evaluate the infection control after 1 year of a DAIR procedure in the case of an early postoperative infection either after primary arthroplasty or after PJI-related revision arthroplasty. Materials and methods: All patients treated with a DAIR procedure within 3 months after onset of PJI between 2009 and 2017 were retrospectively included. Data were collected on patient and infection characteristics. All infections were confirmed by applying the Musculoskeletal Infection Society (MSIS) 2014 criteria. The primary outcome was successful control of infection at 1 year after a DAIR procedure, which was defined as the absence of clinical signs, such as pain, swelling, and erythema; radiological signs, such as protheses loosening; or laboratory signs, such as C-reactive protein (CRP) () with no use of antibiotic therapy. Results: Sixty-seven patients were treated with a DAIR procedure (41 hips and 26 knees). Successful infection control rates of a DAIR procedure after primary arthroplasty (n=51) and after prior PJI-related revision arthroplasty (n=16) were 69 % and 56 %, respectively (p=0.38). The successful infection control rates of a DAIR procedure after an early acute infection (n=35) and after a hematogenous infection (n=16) following primary arthroplasty were both 69 % (p=1.00). Conclusion: In this limited study population, no statistically significant difference is found in infection control after 1 year between DAIR procedures after primary arthroplasty and PJI-related revision arthroplasty.

Observations and models agree that the Greenland Ice Sheet (GrIS) surface mass balance (SMB) has decreased since the end of the 1990s due to an increase in meltwater runoff and that this trend will accelerate in the future. However, large uncertainties remain, partly due to different approaches for modelling the GrIS SMB, which have to weigh physical complexity or low computing time, different spatial and temporal resolutions, different forcing fields, and different ice sheet topographies and extents, which collectively make an inter-comparison difficult. Our GrIS SMB model intercomparison project (GrSMBMIP) aims to refine these uncertainties by intercomparing 13 models of four types which were forced with the same ERA-Interim reanalysis forcing fields, except for two global models. We interpolate all modelled SMB fields onto a common ice sheet mask at 1 km horizontal resolution for the period 1980–2012 and score the outputs against (1) SMB estimates from a combination of gravimetric remote sensing data from GRACE and measured ice discharge; (2) ice cores, snow pits and in situ SMB observations; and (3) remotely sensed bare ice extent from MODerate-resolution Imaging Spectroradiometer (MODIS). Spatially, the largest spread among models can be found around the margins of the ice sheet, highlighting model deficiencies in an accurate representation of the GrIS ablation zone extent and processes related to surface melt and runoff. Overall, polar regional climate models (RCMs) perform the best compared to observations, in particular for simulating precipitation patterns. However, other simpler and faster models have biases of the same order as RCMs compared with observations and therefore remain useful tools for long-term simulations or coupling with ice sheet models. Finally, it is interesting to note that the ensemble mean of the 13 models produces the best estimate of the present-day SMB relative to observations, suggesting that biases are not systematic among models and that this ensemble estimate can be used as a reference for current climate when carrying out future model developments. However, a higher density of in situ SMB observations is required, especially in the south-east accumulation zone, where the model spread can reach 2 m w.e. yr−1 due to large discrepancies in modelled snowfall accumulation.

Ice flow models of the Antarctic ice sheet are commonly used to simulate its future evolution in response to different climate scenarios and assess the mass loss that would contribute to future sea level rise. However, there is currently no consensus on estimates of the future mass balance of the ice sheet, primarily because of differences in the representation of physical processes, forcings employed and initial states of ice sheet models. This study presents results from ice flow model simulations from 13 international groups focusing on the evolution of the Antarctic ice sheet during the period 2015–2100 as part of the Ice Sheet Model Intercomparison for CMIP6 (ISMIP6). They are forced with outputs from a subset of models from the Coupled Model Intercomparison Project Phase 5 (CMIP5), representative of the spread in climate model results. Simulations of the Antarctic ice sheet contribution to sea level rise in response to increased warming during this period varies between −7.8 and 30.0 cm of sea level equivalent (SLE) under Representative Concentration Pathway (RCP) 8.5 scenario forcing. These numbers are relative to a control experiment with constant climate conditions and should therefore be added to the mass loss contribution under climate conditions similar to present-day conditions over the same period. The simulated evolution of the West Antarctic ice sheet varies widely among models, with an overall mass loss, up to 18.0 cm SLE, in response to changes in oceanic conditions. East Antarctica mass change varies between −6.1 and 8.3 cm SLE in the simulations, with a significant increase in surface mass balance outweighing the increased ice discharge under most RCP 8.5 scenario forcings. The inclusion of ice shelf collapse, here assumed to be caused by large amounts of liquid water ponding at the surface of ice shelves, yields an additional simulated mass loss of 28 mm compared to simulations without ice shelf collapse. The largest sources of uncertainty come from the climate forcing, the ocean-induced melt rates, the calibration of these melt rates based on oceanic conditions taken outside of ice shelf cavities and the ice sheet dynamic response to these oceanic changes. Results under RCP 2.6 scenario based on two CMIP5 climate models show an additional mass loss of 0 and 3 cm of SLE on average compared to simulations done under present-day conditions for the two CMIP5 forcings used and display limited mass gain in East Antarctica.

The Greenland ice sheet is one of the largest contributors to global mean sea-level rise today and is expected to continue to lose mass as the Arctic continues to warm. The two predominant mass loss mechanisms are increased surface meltwater run-off and mass loss associated with the retreat of marine-terminating outlet glaciers. In this paper we use a large ensemble of Greenland ice sheet models forced by output from a representative subset of the Coupled Model Intercomparison Project (CMIP5) global climate models to project ice sheet changes and sea-level rise contributions over the 21st century. The simulations are part of the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6). We estimate the sea-level contribution together with uncertainties due to future climate forcing, ice sheet model formulations and ocean forcing for the two greenhouse gas concentration scenarios RCP8.5 and RCP2.6. The results indicate that the Greenland ice sheet will continue to lose mass in both scenarios until 2100, with contributions of 90±50 and 32±17 mm to sea-level rise for RCP8.5 and RCP2.6, respectively. The largest mass loss is expected from the south-west of Greenland, which is governed by surface mass balance changes, continuing what is already observed today. Because the contributions are calculated against an unforced control experiment, these numbers do not include any committed mass loss, i.e. mass loss that would occur over the coming century if the climate forcing remained constant. Under RCP8.5 forcing, ice sheet model uncertainty explains an ensemble spread of 40 mm, while climate model uncertainty and ocean forcing uncertainty account for a spread of 36 and 19 mm, respectively. Apart from those formally derived uncertainty ranges, the largest gap in our knowledge is about the physical understanding and implementation of the calving process, i.e. the interaction of the ice sheet with the ocean.

As the primary energy and carbon source in aquatic food webs, phytoplankton generally display spatial heterogeneity due to complicated biotic and abiotic controls; however our understanding of the causes of this spatial heterogeneity is challenging, as it involves multiple regulatory mechanisms. We applied a combination of field observation, numerical modeling, and remote sensing to display and interpret the spatial gradient of phytoplankton biomass in a Dutch tidal bay (the Eastern Scheldt) on the east coast of the North Sea. The 19 years (1995–2013) of monitoring data reveal a seaward increasing trend in chlorophyll-a (chl a) concentrations during the spring bloom. Using a calibrated and validated three-dimensional hydrodynamic–biogeochemical model, two idealized model scenarios were run: switching off the suspension feeders and halving the open-boundary nutrient and phytoplankton loading. Results reveal that bivalve grazing exerts a dominant control on phytoplankton in the bay and that the tidal import mainly influences algal biomass near the mouth. Satellite data captured a post-bloom snapshot that indicated the temporally variable phytoplankton distribution. Based on a literature review, we found five common spatial phytoplankton patterns in global estuarine–coastal ecosystems for comparison with the Eastern Scheldt case: seaward increasing, seaward decreasing, concave with a chlorophyll maximum, weak spatial gradients, and irregular patterns. We highlight the temporal variability of these spatial patterns and the importance of anthropogenic and environmental influences.

Projection of the contribution of ice sheets to sea level change as part of the Coupled Model Intercomparison Project Phase 6 (CMIP6) takes the form of simulations from coupled ice sheet–climate models and stand-alone ice sheet models, overseen by the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6). This paper describes the experimental setup for process-based sea level change projections to be performed with stand-alone Greenland and Antarctic ice sheet models in the context of ISMIP6. The ISMIP6 protocol relies on a suite of polar atmospheric and oceanic CMIP-based forcing for ice sheet models, in order to explore the uncertainty in projected sea level change due to future emissions scenarios, CMIP models, ice sheet models, and parameterizations for ice–ocean interactions. We describe here the approach taken for defining the suite of ISMIP6 stand-alone ice sheet simulations, document the experimental framework and implementation, and present an overview of the ISMIP6 forcing to be used by participating ice sheet modeling groups.

Future sea-level change projections with process-based stand-alone ice sheet models are typically driven with surface mass balance (SMB) forcing derived from climate models. In this work we address the problems arising from a mismatch of the modelled ice sheet geometry with the geometry used by the climate model. We present a method for applying SMB forcing from climate models to a wide range of Greenland ice sheet models with varying and temporally evolving geometries. In order to achieve that, we translate a given SMB anomaly field as a function of absolute location to a function of surface elevation for 25 regional drainage basins, which can then be applied to different modelled ice sheet geometries. The key feature of the approach is the non-locality of this remapping process. The method reproduces the original forcing data closely when remapped to the original geometry. When remapped to different modelled geometries it produces a physically meaningful forcing with smooth and continuous SMB anomalies across basin divides. The method considerably reduces non-physical biases that would arise by applying the SMB anomaly derived for the climate model geometry directly to a large range of modelled ice sheet model geometries.

The Barents Sea is situated on a continental margin and was home to a large ice sheet at the Last Glacial Maximum. Studying the solid Earth response to the removal of this ice sheet (glacial isostatic adjustment; GIA) can give insight into the subsurface rheology of this region. However, because the region is currently covered by ocean, uplift measurements from the center of the former ice sheet are not available. The Gravity Recovery and Climate Experiment (GRACE) gravity data have been shown to be able to constrain GIA. Here we analyze GRACE data for the period 2003–2015 in the Barents Sea and use the data to constrain GIA models for the region. We study the effect of uncertainty in non-tidal ocean mass models that are used to correct GRACE data and find that it should be taken into account when studying solid Earth signals in oceanic areas from GRACE. We compare GRACE-derived gravity disturbance rates with GIA model predictions for different ice deglaciation chronologies of the last glacial cycle and find that best-fitting models have an upper mantle viscosity equal or higher than 3×1020 Pa s. Following a similar procedure for Fennoscandia we find that the preferred upper mantle viscosity there is a factor 2 larger than in the Barents Sea for a range of lithospheric thickness values. This factor is shown to be consistent with the ratio of viscosities derived for both regions from global seismic models. The viscosity difference can serve as constraint for geodynamic models of the area.

Estimating the contribution of marine ice sheets to sea-level rise is complicated by ice grounded below sea level that is replaced by ocean water when melted. The common approach is to only consider the ice volume above floatation, defined as the volume of ice to be removed from an ice column to become afloat. With isostatic adjustment of the bedrock and external sea-level forcing that is not a result of mass changes of the ice sheet under consideration, this approach breaks down, because ice volume above floatation can be modified without actual changes in the sea-level contribution. We discuss a consistent and generalised approach for estimating the sea-level contribution from marine ice sheets.

The sea level contribution of the Antarctic ice sheet constitutes a large uncertainty in future sea level projections. Here we apply a linear response theory approach to 16 state-of-the-art ice sheet models to estimate the Antarctic ice sheet contribution from basal ice shelf melting within the 21st century. The purpose of this computation is to estimate the uncertainty of Antarctica's future contribution to global sea level rise that arises from large uncertainty in the oceanic forcing and the associated ice shelf melting. Ice shelf melting is considered to be a major if not the largest perturbation of the ice sheet's flow into the ocean. However, by computing only the sea level contribution in response to ice shelf melting, our study is neglecting a number of processes such as surface-mass-balance-related contributions. In assuming linear response theory, we are able to capture complex temporal responses of the ice sheets, but we neglect any self-dampening or self-amplifying processes. This is particularly relevant in situations in which an instability is dominating the ice loss. The results obtained here are thus relevant, in particular wherever the ice loss is dominated by the forcing as opposed to an internal instability, for example in strong ocean warming scenarios. In order to allow for comparison the methodology was chosen to be exactly the same as in an earlier study (Levermann et al., 2014) but with 16 instead of 5 ice sheet models. We include uncertainty in the atmospheric warming response to carbon emissions (full range of CMIP5 climate model sensitivities), uncertainty in the oceanic transport to the Southern Ocean (obtained from the time-delayed and scaled oceanic subsurface warming in CMIP5 models in relation to the global mean surface warming), and the observed range of responses of basal ice shelf melting to oceanic warming outside the ice shelf cavity. This uncertainty in basal ice shelf melting is then convoluted with the linear response functions of each of the 16 ice sheet models to obtain the ice flow response to the individual global warming path. The model median for the observational period from 1992 to 2017 of the ice loss due to basal ice shelf melting is 10.2 mm, with a likely range between 5.2 and 21.3 mm. For the same period the Antarctic ice sheet lost mass equivalent to 7.4 mm of global sea level rise, with a standard deviation of 3.7 mm (Shepherd et al., 2018) including all processes, especially surface-mass-balance changes. For the unabated warming path, Representative Concentration Pathway 8.5 (RCP8.5), we obtain a median contribution of the Antarctic ice sheet to global mean sea level rise from basal ice shelf melting within the 21st century of 17 cm, with a likely range (66th percentile around the mean) between 9 and 36 cm and a very likely range (90th percentile around the mean) between 6 and 58 cm. For the RCP2.6 warming path, which will keep the global mean temperature below 2 ∘C of global warming and is thus consistent with the Paris Climate Agreement, the procedure yields a median of 13 cm of global mean sea level contribution. The likely range for the RCP2.6 scenario is between 7 and 24 cm, and the very likely range is between 4 and 37 cm. The structural uncertainties in the method do not allow for an interpretation of any higher uncertainty percentiles. We provide projections for the five Antarctic regions and for each model and each scenario separately. The rate of sea level contribution is highest under the RCP8.5 scenario. The maximum within the 21st century of the median value is 4 cm per decade, with a likely range between 2 and 9 cm per decade and a very likely range between 1 and 14 cm per decade.

In order to investigate the relation between ice sheets and climate in a warmer-than-present world, recent research has focussed on the Late Pliocene, 3.6 to 2.58 million years ago. It is the most recent period in Earth's history when such a warm climate state existed for a significant duration of time. Marine Isotope Stage (MIS) M2 (∼3.3 Myr ago) is a strong positive excursion in benthic oxygen records in the middle of the otherwise warm and relatively stable Late Pliocene. However, the relative contributions to the benthic δ18O signal from deep ocean cooling and growing ice sheets are still uncertain. Here, we present results from simulations of the Late Pliocene with a hybrid ice-sheet–climate model, showing a reconstruction of ice sheet geometry, sea level and atmospheric CO2. Initial experiments simulating the last four glacial cycles indicate that this model yields results which are in good agreement with proxy records in terms of global mean sea level, benthic oxygen isotope abundance, ice-core-derived surface temperature and atmospheric CO2 concentration. For the Late Pliocene, our results show an atmospheric CO2 concentration during MIS M2 of 233–249 ppmv and a drop in global mean sea level of 10 to 25 m. Uncertainties are larger during the warmer periods leading up to and following MIS M2. CO2 concentrations during the warm intervals in the Pliocene, with sea-level high stands of 8–14 m above the present day, varied between 320 and 400 ppmv, lower than indicated by some proxy records but in line with earlier model reconstructions.

Visualization can greatly benefit understanding of concepts and processes, which in soil science and geology can be done using real-life snapshots of soils and sediments in lacquer peels and glue peels. While it may seem complicated, anyone can make such a soil peel for use in classrooms, public places, homes, and offices for teaching, outreach, decoration, and awareness. Technological development has considerably simplified the making of soil peels, but this methodological innovation has not been described in the literature. Here, we report on a thoroughly tested and simple method for taking peels of sandy soils using readily available tools and materials. Our method follows the main previously published steps of preparing a soil face, impregnating the soil face with a fixation agent in the field, extracting the resulting peel, and mounting it on a wooden panel. Yet instead of using lacquers and thinning agents, we use strong though flexible contact adhesive (glue), which has the major advantage that it no longer requires use and mixing of toxic chemicals in the field or reinforcement of the peel to prevent breaking. Moreover, the preservation potential is much higher than with the old method. This new twist to old methods makes creation of soil peels safer, simpler, and more successful, and thereby a true DIY (do-it-yourself) activity. The resulting increased accessibility of making soil and sediment peels can benefit research, teaching, and science communication and can thereby bring the value and beauty of the ground below our feet to students, schools, policy makers, and the general public.

Ice sheet numerical modeling is an important tool to estimate the dynamic contribution of the Antarctic ice sheet to sea level rise over the coming centuries. The influence of initial conditions on ice sheet model simulations, however, is still unclear. To better understand this influence, an initial state intercomparison exercise (initMIP) has been developed to compare, evaluate, and improve initialization procedures and estimate their impact on century-scale simulations. initMIP is the first set of experiments of the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6), which is the primary Coupled Model Intercomparison Project Phase 6 (CMIP6) activity focusing on the Greenland and Antarctic ice sheets. Following initMIP-Greenland, initMIP-Antarctica has been designed to explore uncertainties associated with model initialization and spin-up and to evaluate the impact of changes in external forcings. Starting from the state of the Antarctic ice sheet at the end of the initialization procedure, three forward experiments are each run for 100 years: a control run, a run with a surface mass balance anomaly, and a run with a basal melting anomaly beneath floating ice. This study presents the results of initMIP-Antarctica from 25 simulations performed by 16 international modeling groups. The submitted results use different initial conditions and initialization methods, as well as ice flow model parameters and reference external forcings. We find a good agreement among model responses to the surface mass balance anomaly but large variations in responses to the basal melting anomaly. These variations can be attributed to differences in the extent of ice shelves and their upstream tributaries, the numerical treatment of grounding line, and the initial ocean conditions applied, suggesting that ongoing efforts to better represent ice shelves in continental-scale models should continue.

We present an intercomparison study of four airborne imaging DOAS instruments, dedicated to the retrieval and high-resolution mapping of tropospheric nitrogen dioxide (NO2) vertical column densities (VCDs). The AROMAPEX campaign took place in Berlin, Germany, in April 2016 with the primary objective to test and intercompare the performance of experimental airborne imagers. The imaging DOAS instruments were operated simultaneously from two manned aircraft, performing synchronised flights: APEX (VITO–BIRA-IASB) was operated from DLR's DO-228 D-CFFU aircraft at 6.2 km in altitude, while AirMAP (IUP-Bremen), SWING (BIRA-IASB), and SBI (TNO–TU Delft–KNMI) were operated from the FUB Cessna 207T D-EAFU at 3.1 km. Two synchronised flights took place on 21 April 2016. NO2 slant columns were retrieved by applying differential optical absorption spectroscopy (DOAS) in the visible wavelength region and converted to VCDs by the computation of appropriate air mass factors (AMFs). Finally, the NO2 VCDs were georeferenced and mapped at high spatial resolution. For the sake of harmonising the different data sets, efforts were made to agree on a common set of parameter settings, AMF look-up table, and gridding algorithm. The NO2 horizontal distribution, observed by the different DOAS imagers, shows very similar spatial patterns. The NO2 field is dominated by two large plumes related to industrial compounds, crossing the city from west to east. The major highways A100 and A113 are also identified as line sources of NO2. Retrieved NO2 VCDs range between 1×1015 molec cm−2 upwind of the city and 20×1015 molec cm−2 in the dominant plume, with a mean of 7.3±1.8×1015 molec cm−2 for the morning flight and between 1 and 23×1015 molec cm−2 with a mean of 6.0±1.4×1015 molec cm−2 for the afternoon flight. The mean NO2 VCD retrieval errors are in the range of 22 % to 36 % for all sensors. The four data sets are in good agreement with Pearson correlation coefficients better than 0.9, while the linear regression analyses show slopes close to unity and generally small intercepts.

Ice flow forced by gravity is governed by the full Stokes (FS) equations, which are computationally expensive to solve due to the nonlinearity introduced by the rheology. Therefore, approximations to the FS equations are commonly used, especially when modeling a marine ice sheet (ice sheet, ice shelf, and/or ice stream) for 103 years or longer. The shallow ice approximation (SIA) and shallow shelf approximation (SSA) are commonly used but are accurate only for certain parts of an ice sheet. Here, we report a novel way of iteratively coupling FS and SSA that has been implemented in Elmer/Ice and applied to conceptual marine ice sheets. The FS–SSA coupling appears to be very accurate; the relative error in velocity compared to FS is below 0.5 % for diagnostic runs and below 5 % for prognostic runs. Results for grounding line dynamics obtained with the FS–SSA coupling are similar to those obtained from an FS model in an experiment with a periodical temperature forcing over 3000 years that induces grounding line advance and retreat. The rapid convergence of the FS–SSA coupling shows a large potential for reducing computation time, such that modeling a marine ice sheet for thousands of years should become feasible in the near future. Despite inefficient matrix assembly in the current implementation, computation time is reduced by 32 %, when the coupling is applied to a 3-D ice shelf.

Fully coupled ice-sheet–climate modelling over 10 000–100 000-year timescales at high spatial and temporal resolution remains beyond the capability of current computational systems. Forcing an ice-sheet model with precalculated output from a general circulation model (GCM) offers a middle ground, balancing the need to accurately capture both long-term processes, in particular circulation-driven changes in precipitation, and processes requiring a high spatial resolution like ablation. Here, we present and evaluate a model set-up that forces the ANICE 3-D thermodynamic ice-sheet–shelf model calculating the four large continental ice sheets (Antarctica, Greenland, North America, and Eurasia) with precalculated output from two steady-state simulations with the HadCM3 (GCM) using a so-called matrix method of coupling both components, whereby simulations with various levels of pCO2 and ice-sheet configuration are combined to form a time-continuous transient climate forcing consistent with the modelled ice sheets. We address the difficulties in downscaling low-resolution GCM output to the higher-resolution grid of an ice-sheet model and account for differences between GCM and ice-sheet model surface topography ranging from interglacial to glacial conditions. Although the approach presented here can be applied to a matrix with any number of GCM snapshots, we limited our experiments to a matrix of only two snapshots. As a benchmark experiment to assess the validity of this model set-up, we perform a simulation of the entire last glacial cycle from 120 kyr ago to present day. The simulated eustatic sea-level drop at the Last Glacial Maximum (LGM) for the combined Antarctic, Greenland, Eurasian, and North American ice sheets amounts to 100 m, in line with many other studies. The simulated ice sheets at the LGM agree well with the ICE-5G reconstruction and the more recent DATED-1 reconstruction in terms of total volume and geographical location of the ice sheets. Moreover, modelled benthic oxygen isotope abundance and the relative contributions from global ice volume and deep-water temperature agree well with available data, as do surface temperature histories for the Greenland and Antarctic ice sheets. This model strategy can be used to create time-continuous ice-sheet distribution and sea-level reconstructions for geological periods up to several million years in duration, capturing climate-model-driven variations in the mass balance of the ice sheet.

Observational evidence, including offshore moraines and sediment cores, confirm that at the Last Glacial Maximum (LGM) the Greenland ice sheet (GrIS) expanded to a significantly larger spatial extent than seen at present, grounding into Baffin Bay and out onto the continental shelf break. Given this larger spatial extent and its close proximity to the neighbouring Laurentide Ice Sheet (LIS) and Innuitian Ice Sheet (IIS), it is likely these ice sheets will have had a strong non-local influence on the spatial and temporal behaviour of the GrIS. Most previous paleo ice-sheet modelling simulations recreated an ice sheet that either did not extend out onto the continental shelf or utilized a simplified marine ice parameterization which did not fully include the effect of ice shelves or neglected the sensitivity of the GrIS to this non-local bedrock signal from the surrounding ice sheets. In this paper, we investigated the evolution of the GrIS over the two most recent glacial–interglacial cycles (240 ka BP to the present day) using the ice-sheet–ice-shelf model IMAU-ICE. We investigated the solid earth influence of the LIS and IIS via an offline relative sea level (RSL) forcing generated by a glacial isostatic adjustment (GIA) model. The RSL forcing governed the spatial and temporal pattern of sub-ice-shelf melting via changes in the water depth below the ice shelves. In the ensemble of simulations, at the glacial maximums, the GrIS coalesced with the IIS to the north and expanded to the continental shelf break to the southwest but remained too restricted to the northeast. In terms of the global mean sea level contribution, at the Last Interglacial (LIG) and LGM the ice sheet added 1.46 and −2.59 m, respectively. This LGM contribution by the GrIS is considerably higher (∼ 1.26 m) than most previous studies whereas the contribution to the LIG highstand is lower (∼ 0.7 m). The spatial and temporal behaviour of the northern margin was highly variable in all simulations, controlled by the sub-ice-shelf melting which was dictated by the RSL forcing and the glacial history of the IIS and LIS. In contrast, the southwestern part of the ice sheet was insensitive to these forcings, with a uniform response in all simulations controlled by the surface air temperature, derived from ice cores.

Earlier large-scale Greenland ice sheet sea-level projections (e.g. those run during the ice2sea and SeaRISE initiatives) have shown that ice sheet initial conditions have a large effect on the projections and give rise to important uncertainties. The goal of this initMIP-Greenland intercomparison exercise is to compare, evaluate, and improve the initialisation techniques used in the ice sheet modelling community and to estimate the associated uncertainties in modelled mass changes. initMIP-Greenland is the first in a series of ice sheet model intercomparison activities within ISMIP6 (the Ice Sheet Model Intercomparison Project for CMIP6), which is the primary activity within the Coupled Model Intercomparison Project Phase 6 (CMIP6) focusing on the ice sheets. Two experiments for the large-scale Greenland ice sheet have been designed to allow intercomparison between participating models of (1) the initial present-day state of the ice sheet and (2) the response in two idealised forward experiments. The forward experiments serve to evaluate the initialisation in terms of model drift (forward run without additional forcing) and in response to a large perturbation (prescribed surface mass balance anomaly); they should not be interpreted as sea-level projections. We present and discuss results that highlight the diversity of data sets, boundary conditions, and initialisation techniques used in the community to generate initial states of the Greenland ice sheet. We find good agreement across the ensemble for the dynamic response to surface mass balance changes in areas where the simulated ice sheets overlap but differences arising from the initial size of the ice sheet. The model drift in the control experiment is reduced for models that participated in earlier intercomparison exercises.

We evaluate modelled Greenland ice sheet (GrIS) near-surface climate, surface energy balance (SEB) and surface mass balance (SMB) from the updated regional climate model RACMO2 (1958–2016). The new model version, referred to as RACMO2.3p2, incorporates updated glacier outlines, topography and ice albedo fields. Parameters in the cloud scheme governing the conversion of cloud condensate into precipitation have been tuned to correct inland snowfall underestimation: snow properties are modified to reduce drifting snow and melt production in the ice sheet percolation zone. The ice albedo prescribed in the updated model is lower at the ice sheet margins, increasing ice melt locally. RACMO2.3p2 shows good agreement compared to in situ meteorological data and point SEB/SMB measurements, and better resolves the spatial patterns and temporal variability of SMB compared with the previous model version, notably in the north-east, south-east and along the K-transect in south-western Greenland. This new model version provides updated, high-resolution gridded fields of the GrIS present-day climate and SMB, and will be used for projections of the GrIS climate and SMB in response to a future climate scenario in a forthcoming study.

Basal melting below ice shelves is a major factor in mass loss from the Antarctic Ice Sheet, which can contribute significantly to possible future sea-level rise. Therefore, it is important to have an adequate description of the basal melt rates for use in ice-dynamical models. Most current ice models use rather simple parametrizations based on the local balance of heat between ice and ocean. In this work, however, we use a recently derived parametrization of the melt rates based on a buoyant meltwater plume travelling upward beneath an ice shelf. This plume parametrization combines a non-linear ocean temperature sensitivity with an inherent geometry dependence, which is mainly described by the grounding-line depth and the local slope of the ice-shelf base. For the first time, this type of parametrization is evaluated on a two-dimensional grid covering the entire Antarctic continent. In order to apply the essentially one-dimensional parametrization to realistic ice-shelf geometries, we present an algorithm that determines effective values for the grounding-line depth and basal slope in any point beneath an ice shelf. Furthermore, since detailed knowledge of temperatures and circulation patterns in the ice-shelf cavities is sparse or absent, we construct an effective ocean temperature field from observational data with the purpose of matching (area-averaged) melt rates from the model with observed present-day melt rates. Our results qualitatively replicate large-scale observed features in basal melt rates around Antarctica, not only in terms of average values, but also in terms of the spatial pattern, with high melt rates typically occurring near the grounding line. The plume parametrization and the effective temperature field presented here are therefore promising tools for future simulations of the Antarctic Ice Sheet requiring a more realistic oceanic forcing.

Currently a paradigm shift is made from global averaged to spatially variable sea level change (SLC) projections. Traditionally, the contribution from ice sheet mass loss to SLC is considered to be symmetrically distributed. However, several assessments suggest that the probability distribution of dynamical ice sheet mass loss is asymmetrically distributed towards higher SLC values. Here we show how asymmetric probability distributions of dynamical ice sheet mass loss impact the high-end uncertainties of regional SLC projections across the globe. For this purpose we use distributions of dynamical ice sheet mass loss presented by Church et al. (2013), De Vries and Van de Wal (2015) and Ritz et al. (2015). The global average median can be 0.18 m higher compared to symmetric distributions based on IPCC-AR5, but the change in the global average 95th percentile SLC is considerably larger with a shift of 0.32 m. Locally the 90th, 95th and 97.5th SLC percentiles exceed +1.4, +1.6 and +1.8 m. The high-end percentiles of SLC projections are highly sensitive to the precise shape of the probability distributions of dynamical ice sheet mass loss. The shift towards higher values is of importance for coastal safety strategies as they are based on the high-end percentiles of projections.

Models for glacial isostatic adjustment (GIA) routinely include the effects of meltwater redistribution and changes in topography and coastlines. Since the sediment transport related to the dynamics of ice sheets may be comparable to that of sea level rise in terms of surface pressure, the loading effect of sediment deposition could cause measurable ongoing viscous readjustment. Here, we study the loading effect of glacially induced sediment redistribution (GISR) related to the Weichselian ice sheet in Fennoscandia and the Barents Sea. The surface loading effect and its effect on the gravitational potential is modeled by including changes in sediment thickness in the sea level equation following the method of Dalca et al. (2013). Sediment displacement estimates are estimated in two different ways: (i) from a compilation of studies on local features (trough mouth fans, large-scale failures, and basin flux) and (ii) from output of a coupled ice–sediment model. To account for uncertainty in Earth's rheology, three viscosity profiles are used. It is found that sediment transport can lead to changes in relative sea level of up to 2 m in the last 6000 years and larger effects occurring earlier in the deglaciation. This magnitude is below the error level of most of the relative sea level data because those data are sparse and errors increase with length of time before present. The effect on present-day uplift rates reaches a few tenths of millimeters per year in large parts of Norway and Sweden, which is around the measurement error of long-term GNSS (global navigation satellite system) monitoring networks. The maximum effect on present-day gravity rates as measured by the GRACE (Gravity Recovery and Climate Experiment) satellite mission is up to tenths of microgal per year, which is larger than the measurement error but below other error sources. Since GISR causes systematic uplift in most of mainland Scandinavia, including GISR in GIA models would improve the interpretation of GNSS and GRACE observations there.

Since the inception of the Antarctic ice sheet at the Eocene–Oligocene transition (∼ 34 Myr ago), land ice has played a crucial role in Earth's climate. Through feedbacks in the climate system, land ice variability modifies atmospheric temperature changes induced by orbital, topographical, and greenhouse gas variations. Quantification of these feedbacks on long timescales has hitherto scarcely been undertaken. In this study, we use a zonally averaged energy balance climate model bidirectionally coupled to a one-dimensional ice sheet model, capturing the ice–albedo and surface–height–temperature feedbacks. Potentially important transient changes in topographic boundary conditions by tectonics and erosion are not taken into account but are briefly discussed. The relative simplicity of the coupled model allows us to perform integrations over the past 38 Myr in a fully transient fashion using a benthic oxygen isotope record as forcing to inversely simulate CO2. Firstly, we find that the results of the simulations over the past 5 Myr are dependent on whether the model run is started at 5 or 38 Myr ago. This is because the relation between CO2 and temperature is subject to hysteresis. When the climate cools from very high CO2 levels, as in the longer transient 38 Myr run, temperatures in the lower CO2 range of the past 5 Myr are higher than when the climate is initialised at low temperatures. Consequently, the modelled CO2 concentrations depend on the initial state. Taking the realistic warm initialisation into account, we come to a best estimate of CO2, temperature, ice-volume-equivalent sea level, and benthic δ18O over the past 38 Myr. Secondly, we study the influence of ice sheets on the evolution of global temperature and polar amplification by comparing runs with ice sheet–climate interaction switched on and off. By passing only albedo or surface height changes to the climate model, we can distinguish the separate effects of the ice–albedo and surface–height–temperature feedbacks. We find that ice volume variability has a strong enhancing effect on atmospheric temperature changes, particularly in the regions where the ice sheets are located. As a result, polar amplification in the Northern Hemisphere decreases towards warmer climates as there is little land ice left to melt. Conversely, decay of the Antarctic ice sheet increases polar amplification in the Southern Hemisphere in the high-CO2 regime. Our results also show that in cooler climates than the pre-industrial, the ice–albedo feedback predominates the surface–height–temperature feedback, while in warmer climates they are more equal in strength.

The albedo of the surface of ice sheets changes as a function of time due to the effects of deposition of new snow, ageing of dry snow, bare ice exposure, melting and run-off. Currently, the calculation of the albedo of ice sheets is highly parameterized within the earth system model EC-Earth by taking a constant value for areas with thick perennial snow cover. This is an important reason why the surface mass balance (SMB) of the Greenland ice sheet (GrIS) is poorly resolved in the model. The purpose of this study is to improve the SMB forcing of the GrIS by evaluating different parameter settings within a snow albedo scheme. By allowing ice-sheet albedo to vary as a function of wet and dry conditions, the spatial distribution of albedo and melt rate improves. Nevertheless, the spatial distribution of SMB in EC-Earth is not significantly improved. As a reason for this, we identify omissions in the current snow albedo scheme, such as separate treatment of snow and ice and the effect of refreezing. The resulting SMB is downscaled from the lower-resolution global climate model topography to the higher-resolution ice-sheet topography of the GrIS, such that the influence of these different SMB climatologies on the long-term evolution of the GrIS is tested by ice-sheet model simulations. From these ice-sheet simulations we conclude that an albedo scheme with a short response time of decaying albedo during wet conditions performs best with respect to long-term simulated ice-sheet volume. This results in an optimized albedo parameterization that can be used in future EC-Earth simulations with an interactive ice-sheet component.

N2O is currently the third most important anthropogenic greenhouse gas in terms of radiative forcing and its atmospheric mole fraction is rising steadily. To quantify the growth rate and its causes over the past decades, we performed a multi-site reconstruction of the atmospheric N2O mole fraction and isotopic composition using new and previously published firn air data collected from Greenland and Antarctica in combination with a firn diffusion and densification model. The multi-site reconstruction showed that while the global mean N2O mole fraction increased from (290 ± 1) nmol mol−1 in 1940 to (322 ± 1) nmol mol−1 in 2008, the isotopic composition of atmospheric N2O decreased by (−2.2 ± 0.2) ‰ for δ15Nav, (−1.0 ± 0.3) ‰ for δ18O, (−1.3 ± 0.6) ‰ for δ15Nα, and (−2.8 ± 0.6) ‰ for δ15Nβ over the same period. The detailed temporal evolution of the mole fraction and isotopic composition derived from the firn air model was then used in a two-box atmospheric model (comprising a stratospheric box and a tropospheric box) to infer changes in the isotopic source signature over time. The precise value of the source strength depends on the choice of the N2O lifetime, which we choose to fix at 123 years. The average isotopic composition over the investigated period is δ15Nav = (−7.6 ± 0.8) ‰ (vs. air-N2), δ18O = (32.2 ± 0.2) ‰ (vs. Vienna Standard Mean Ocean Water – VSMOW) for δ18O, δ15Nα = (−3.0 ± 1.9) ‰ and δ15Nβ = (−11.7 ± 2.3) ‰. δ15Nav, and δ15Nβ show some temporal variability, while for the other signatures the error bars of the reconstruction are too large to retrieve reliable temporal changes. Possible processes that may explain trends in 15N are discussed. The 15N site preference ( = δ15Nα − δ15Nβ) provides evidence of a shift in emissions from denitrification to nitrification, although the uncertainty envelopes are large.

Many processes govern the deglaciation of ice sheets. One of the processes that is usually ignored is the calving of ice in lakes that temporarily surround the ice sheet. In order to capture this process a “flood-fill algorithm” is needed. Here we present and evaluate several optimizations to a standard flood-fill algorithm in terms of computational efficiency. As an example, we determine the land–ocean mask for a 1 km resolution digital elevation model (DEM) of North America and Greenland, a geographical area of roughly 7000 by 5000 km (roughly 35 million elements), about half of which is covered by ocean. Determining the land–ocean mask with our improved flood-fill algorithm reduces computation time by 90 % relative to using a standard stack-based flood-fill algorithm. This implies that it is now feasible to include the calving of ice in lakes as a dynamical process inside an ice-sheet model. We demonstrate this by using bedrock elevation, ice thickness and geoid perturbation fields from the output of a coupled ice-sheet–sea-level equation model at 30 000 years before present and determine the extent of Lake Agassiz, using both the standard and improved versions of the flood-fill algorithm. We show that several optimizations to the flood-fill algorithm used for filling a depression up to a water level, which is not defined beforehand, decrease the computation time by up to 99 %. The resulting reduction in computation time allows determination of the extent and volume of depressions in a DEM over large geographical grids or repeatedly over long periods of time, where computation time might otherwise be a limiting factor. The algorithm can be used for all glaciological and hydrological models, which need to trace the evolution over time of lakes or drainage basins in general.

This paper accompanies the second OBLIMAP open-source release. The package is developed to map climate fields between a general circulation model (GCM) and an ice sheet model (ISM) in both directions by using optimal aligned oblique projections, which minimize distortions. The curvature of the surfaces of the GCM and ISM grid differ, both grids may be irregularly spaced and the ratio of the grids is allowed to differ largely. OBLIMAP's stand-alone version is able to map data sets that differ in various aspects on the same ISM grid. Each grid may either coincide with the surface of a sphere, an ellipsoid or a flat plane, while the grid types might differ. Re-projection of, for example, ISM data sets is also facilitated. This is demonstrated by relevant applications concerning the major ice caps. As the stand-alone version also applies to the reverse mapping direction, it can be used as an offline coupler. Furthermore, OBLIMAP 2.0 is an embeddable GCM–ISM coupler, suited for high-frequency online coupled experiments. A new fast scan method is presented for structured grids as an alternative for the former time-consuming grid search strategy, realising a performance gain of several orders of magnitude and enabling the mapping of high-resolution data sets with a much larger number of grid nodes. Further, a highly flexible masked mapping option is added. The limitation of the fast scan method with respect to unstructured and adaptive grids is discussed together with a possible future parallel Message Passing Interface (MPI) implementation.

In this study, we use satellite gravimetry data from the Gravity Recovery and Climate Experiment (GRACE) to estimate regional mass change of the Greenland ice sheet (GrIS) and neighboring glaciated regions using a least squares inversion approach. We also consider results from the input–output method (IOM). The IOM quantifies the difference between the mass input and output of the GrIS by studying the surface mass balance (SMB) and the ice discharge (D). We use the Regional Atmospheric Climate Model version 2.3 (RACMO2.3) to model the SMB and derive the ice discharge from 12 years of high-precision ice velocity and thickness surveys. We use a simulation model to quantify and correct for GRACE approximation errors in mass change between different subregions of the GrIS, and investigate the reliability of pre-1990s ice discharge estimates, which are based on the modeled runoff. We find that the difference between the IOM and our improved GRACE mass change estimates is reduced in terms of the long-term mass change when using a reference discharge derived from runoff estimates in several subareas. In most regions our GRACE and IOM solutions are consistent with other studies, but differences remain in the northwestern GrIS. We validate the GRACE mass balance in that region by considering several different GIA models and mass change estimates derived from data obtained by the Ice, Cloud and land Elevation Satellite (ICESat). We conclude that the approximated mass balance between GRACE and IOM is consistent in most GrIS regions. The difference in the northwest is likely due to underestimated uncertainties in the IOM solutions.

It is still an open question how equilibrium warming in response to increasing radiative forcing – the specific equilibrium climate sensitivity S – depends on background climate. We here present palaeodata-based evidence on the state dependency of S, by using CO2 proxy data together with a 3-D ice-sheet-model-based reconstruction of land ice albedo over the last 5 million years (Myr). We find that the land ice albedo forcing depends non-linearly on the background climate, while any non-linearity of CO2 radiative forcing depends on the CO2 data set used. This non-linearity has not, so far, been accounted for in similar approaches due to previously more simplistic approximations, in which land ice albedo radiative forcing was a linear function of sea level change. The latitudinal dependency of ice-sheet area changes is important for the non-linearity between land ice albedo and sea level. In our set-up, in which the radiative forcing of CO2 and of the land ice albedo (LI) is combined, we find a state dependence in the calculated specific equilibrium climate sensitivity, S[CO2,LI], for most of the Pleistocene (last 2.1 Myr). During Pleistocene intermediate glaciated climates and interglacial periods, S[CO2,LI] is on average ~ 45 % larger than during Pleistocene full glacial conditions. In the Pliocene part of our analysis (2.6–5 Myr BP) the CO2 data uncertainties prevent a well-supported calculation for S[CO2,LI], but our analysis suggests that during times without a large land ice area in the Northern Hemisphere (e.g. before 2.82 Myr BP), the specific equilibrium climate sensitivity, S[CO2,LI], was smaller than during interglacials of the Pleistocene. We thus find support for a previously proposed state change in the climate system with the widespread appearance of northern hemispheric ice sheets. This study points for the first time to a so far overlooked non-linearity in the land ice albedo radiative forcing, which is important for similar palaeodata-based approaches to calculate climate sensitivity. However, the implications of this study for a suggested warming under CO2 doubling are not yet entirely clear since the details of necessary corrections for other slow feedbacks are not fully known and the uncertainties that exist in the ice-sheet simulations and global temperature reconstructions are large.

We discuss Greenland Ice Sheet (GrIS) surface mass balance (SMB) differences between the updated polar version of the RACMO climate model (RACMO2.3) and the previous version (RACMO2.1). Among other revisions, the updated model includes an adjusted rainfall-to-snowfall conversion that produces exclusively snowfall under freezing conditions; this especially favours snowfall in summer. Summer snowfall in the ablation zone of the GrIS has a pronounced effect on melt rates, affecting modelled GrIS SMB in two ways. By covering relatively dark ice with highly reflective fresh snow, these summer snowfalls have the potential to locally reduce melt rates in the ablation zone of the GrIS through the snow-albedo-melt feedback. At larger scales, SMB changes are driven by differences in orographic precipitation following a shift in large-scale circulation, in combination with enhanced moisture to precipitation conversion for warm to moderately cold conditions. A detailed comparison of model output with observations from automatic weather stations, ice cores and ablation stakes shows that the model update generally improves the simulated SMB-elevation gradient as well as the representation of the surface energy balance, although significant biases remain.

We performed detailed 2H isotope diffusion measurements in the upper 3 m of firn at Summit, Greenland. Using a small snow gun, a thin snow layer was formed from 2H-enriched water over a 6 × 6 m2 area. We followed the diffusion process, quantified as the increase of the δ2H diffusion length, over a 4-year period, by retrieving the layer once per year by drilling a firn core and slicing it into 1 cm layers and measuring the δ2H signal of these layers. We compared our experimental findings to calculations based on the model by Johnsen et al. (2000) and found substantial differences. The diffusion length in our experiments increased much less over the years than in the model. We discuss the possible causes for this discrepancy and conclude that several aspects of the diffusion process in firn are still poorly constrained, in particular the tortuosity.

In the context of future climate change, understanding the nature and behaviour of ice sheets during warm intervals in Earth history is of fundamental importance. The late Pliocene warm period (also known as the PRISM interval: 3.264 to 3.025 million years before present) can serve as a potential analogue for projected future climates. Although Pliocene ice locations and extents are still poorly constrained, a significant contribution to sea-level rise should be expected from both the Greenland ice sheet and the West and East Antarctic ice sheets based on palaeo sea-level reconstructions. Here, we present results from simulations of the Antarctic ice sheet by means of an international Pliocene Ice Sheet Modeling Intercomparison Project (PLISMIP-ANT). For the experiments, ice-sheet models including the shallow ice and shelf approximations have been used to simulate the complete Antarctic domain (including grounded and floating ice). We compare the performance of six existing numerical ice-sheet models in simulating modern control and Pliocene ice sheets by a suite of five sensitivity experiments. We include an overview of the different ice-sheet models used and how specific model configurations influence the resulting Pliocene Antarctic ice sheet. The six ice-sheet models simulate a comparable present-day ice sheet, considering the models are set up with their own parameter settings. For the Pliocene, the results demonstrate the difficulty of all six models used here to simulate a significant retreat or re-advance of the East Antarctic ice grounding line, which is thought to have happened during the Pliocene for the Wilkes and Aurora basins. The specific sea-level contribution of the Antarctic ice sheet at this point cannot be conclusively determined, whereas improved grounding line physics could be essential for a correct representation of the migration of the grounding-line of the Antarctic ice sheet during the Pliocene.

The concept of a positive feedback between ice flow and enhanced melt rates in a warmer climate fuelled the debate regarding the temporal and spatial controls on seasonal ice acceleration. Here we combine melt, basal water pressure and ice velocity data. Using 20 years of data covering the whole ablation area, we show that there is not a strong positive correlation between annual ice velocities and melt rates. Annual velocities even slightly decreased with increasing melt. Results also indicate that melt variations are most important for velocity variations in the upper ablation zone up to the equilibrium line altitude. During the extreme melt in 2012, a large velocity response near the equilibrium line was observed, highlighting the possibility of meltwater to have an impact even high on the ice sheet. This may lead to an increase of the annual ice velocity in the region above S9 and requires further monitoring.