Impact of spatial resolution on large-scale ice cover modeling of mountainous regions

For reconstructing paleoclimate or studying glacial isostatic effects on the Earth’s lithosphere, increasingly more studies focus on modeling the large-scale ice cover in mountainous regions over long time scales. However, balancing model complexity and the spatial extent with computational costs is challenging. Previous studies of large-scale ice cover simulation in mountain areas such as the European Alps, New Zealand, and the Tibetan Plateau, typically used 1-2 km spatial resolution. However, mountains are characterized by high peaks and steep slopes - topographic features that are crucial for glacier mass balance and dynamics, but poorly resolved in coarse resolution topography. The Instructed Glacier Model (IGM) is a novel 3D ice model equipped with a physics-informed neural network to simulate ice flow. This results in a significant acceleration of run times, and thereby opening the possibility of higher spatial resolution runs. We use IGM to model the glaciation of the European Alps with different resolutions (2 km and 200 m) over a time period of 160,000 years. We apply a linear cooling rate to present-day climate until 6 °C colder to mimic ice age conditions. Preliminary results indicate systematic, resolution-related differences: At the beginning of cooling the 2 km resolution yields slightly more ice volume. However, this trend reverses when ice flows together from high elevations and fill large valleys with thick ice. When the Alps are fully ice covered, we find up to 14% more ice volume in the higher resolution models which, however, is not uniformly distributed in space

Glacial-cycle simulations of the Antarctic Ice Sheet with the Parallel Ice Sheet Model (PISM) – Part 1: Boundary conditions and climatic forcing

Simulations of the glacial–interglacial history of the Antarctic Ice Sheet provide insights into dynamic threshold behavior and estimates of the ice sheet's contributions to global sea-level changes for the past, present and future. However, boundary conditions are weakly constrained, in particular at the interface of the ice sheet and the bedrock. Also climatic forcing covering the last glacial cycles is uncertain, as it is based on sparse proxy data. We use the Parallel Ice Sheet Model (PISM) to investigate the dynamic effects of different choices of input data, e.g., for modern basal heat flux or reconstructions of past changes of sea level and surface temperature. As computational resources are limited, glacial-cycle simulations are performed using a comparably coarse model grid of 16 km and various parameterizations, e.g., for basal sliding, iceberg calving, or for past variations in precipitation and ocean temperatures. In this study we evaluate the model's transient sensitivity to corresponding parameter choices and to different boundary conditions over the last two glacial cycles and provide estimates of involved uncertainties. We also discuss isolated and combined effects of climate and sea-level forcing. Hence, this study serves as a “cookbook” for the growing community of PISM users and paleo-ice sheet modelers in general. For each of the different model uncertainties with regard to climatic forcing, ice and Earth dynamics, and basal processes, we select one representative model parameter that captures relevant uncertainties and motivates corresponding parameter ranges that bound the observed ice volume at present. The four selected parameters are systematically varied in a parameter ensemble analysis, which is described in a companion paper

Combustion of available fossil fuel resources sufficient to eliminate the Antarctic Ice Sheet

The Antarctic Ice Sheet stores water equivalent to 58 m in global sea-level rise. We show in simulations using the Parallel Ice Sheet Model that burning the currently attainable fossil fuel resources is sufficient to eliminate the ice sheet. With cumulative fossil fuel emissions of 10,000 gigatonnes of carbon (GtC), Antarctica is projected to become almost ice-free with an average contribution to sea-level rise exceeding 3 m per century during the first millennium. Consistent with recent observations and simulations, the West Antarctic Ice Sheet becomes unstable with 600 to 800 GtC of additional carbon emissions. Beyond this additional carbon release, the destabilization of ice basins in both West and East Antarctica results in a threshold increase in global sea level. Unabated carbon emissions thus threaten the Antarctic Ice Sheet in its entirety with associated sea-level rise that far exceeds that of all other possible sources

Stabilizing effect of mélange buttressing on the marine ice-cliff instability of the West Antarctic Ice Sheet

Owing to global warming and particularly high regional ocean warming, both Thwaites and Pine Island Glaciers in the Amundsen region of the Antarctic Ice Sheet could lose their buttressing ice shelves over time. We analyse the possible consequences using the parallel ice sheet model (PISM), applying a simple cliff-calving parameterization and an ice mélange-buttressing model. We find that the instantaneous loss of ice-shelf buttressing, due to enforced ice-shelf melting, initiates grounding-line retreat and triggers marine ice sheet instability (MISI). As a consequence, the grounding line progresses into the interior of the West Antarctic Ice Sheet and leads to a sea level contribution of 0.6m within 100a. By subjecting the exposed ice cliffs to cliff calving using our simplified parameterization, we also analyse marine ice cliff instability (MICI). In our simulations it can double or even triple the sea level contribution depending on the only loosely constrained parameter that determines the maximum cliff-calving rate. The speed of MICI depends on this upper bound of the calving rate, which is given by the ice mélange buttressing the glacier. However, stabilization of MICI may occur for geometric reasons. Because the embayment geometry changes as MICI advances into the interior of the ice sheet, the upper bound on calving rates is reduced and the progress of MICI is slowed down. Although we cannot claim that our simulations bear relevant quantitative estimates of the effect of ice-mélange buttressing on MICI, the mechanism has the potential to stop the instability. Further research is needed to evaluate its role for the past and future evolution of the Antarctic Ice Sheet

Interacting tipping elements increase risk of climate domino effects under global warming

With progressing global warming, there is an increased risk that one or several tipping elements in the climate system might cross a critical threshold, resulting in severe consequences for the global climate, ecosystems and human societies. While the underlying processes are fairly well-understood, it is unclear how their interactions might impact the overall stability of the Earth's climate system. As of yet, this cannot be fully analysed with state-of-the-art Earth system models due to computational constraints as well as some missing and uncertain process representations of certain tipping elements. Here, we explicitly study the effects of known physical interactions among the Greenland and West Antarctic ice sheets, the Atlantic Meridional Overturning Circulation (AMOC) and the Amazon rainforest using a conceptual network approach. We analyse the risk of domino effects being triggered by each of the individual tipping elements under global warming in equilibrium experiments. In these experiments, we propagate the uncertainties in critical temperature thresholds, interaction strengths and interaction structure via large ensembles of simulations in a Monte Carlo approach. Overall, we find that the interactions tend to destabilise the network of tipping elements. Furthermore, our analysis reveals the qualitative role of each of the four tipping elements within the network, showing that the polar ice sheets on Greenland and West Antarctica are oftentimes the initiators of tipping cascades, while the AMOC acts as a mediator transmitting cascades. This indicates that the ice sheets, which are already at risk of transgressing their temperature thresholds within the Paris range of 1.5 to 2 ∘C, are of particular importance for the stability of the climate system as a whole

How motifs condition critical thresholds for tipping cascades in complex networks: Linking Micro- to Macro-scales

In this study, we investigate how specific micro interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erd\"os-R\'enyi networks and an exemplary moisture recycling network of the Amazon rainforest. Within these networks, decisive small-scale motifs are the feed forward loop, the secondary feed forward loop, the zero loop and the neighboring loop. Of all motifs, the feed forward loop motif stands out in tipping cascades since it decreases the critical coupling strength necessary to initiate a cascade more than the other motifs. We find that for this motif, the reduction of critical coupling strength is 11% less than the critical coupling of a pair of tipping elements. For highly connected networks, our analysis reveals that coupled feed forward loops coincide with a strong 90% decrease of the critical coupling strength. For the highly clustered moisture recycling network in the Amazon, we observe regions of very high motif occurrence for each of the four investigated motifs suggesting that these regions are more vulnerable. The occurrence of motifs is found to be one order of magnitude higher than in a random Erd\"os-R\'enyi network. This emphasizes the importance of local interaction structures for the emergence of global cascades and the stability of the network as a whole

Global warming due to loss of large ice masses and Arctic summer sea ice

Several large-scale cryosphere elements such as the Arctic summer sea ice, the mountain glaciers, the Greenland and West Antarctic Ice Sheet have changed substantially during the last century due to anthropogenic global warming. However, the impacts of their possible future disintegration on global mean temperature (GMT) and climate feedbacks have not yet been comprehensively evaluated. Here, we quantify this response using an Earth system model of intermediate complexity. Overall, we find a median additional global warming of 0.43 °C (interquartile range: 0.39−0.46 °C) at a CO2 concentration of 400 ppm. Most of this response (55%) is caused by albedo changes, but lapse rate together with water vapour (30%) and cloud feedbacks (15%) also contribute significantly. While a decay of the ice sheets would occur on centennial to millennial time scales, the Arctic might become ice-free during summer within the 21st century. Our findings imply an additional increase of the GMT on intermediate to long time scales

Glacial and erosional contributions to Late Quaternary uplift of the European Alps (GEOLQUEA)

Isostatic adjustments of the Earth’s surface to changes in water, ice, and sediment loading are important contributions to present-day uplift/subsidence rates in many regions on Earth. In the absence of significant horizontal tectonic shortening in the central and western parts of the European Alps, uplift rates larger than 2 mm/yr are difficult to explain by geodynamic processes and have been a matter of debate for many decades. Here we examine the likely contribution of glacial isostatic adjustment in the European Alps in response to changes in ice loading using state of the art ice flow and lithospheric numerical modeling. In contrast to a similar previous approach (Mey et al., 2016), we employ a transient ice sheet model over the last glacial cycle (100 kyr) in combination with a spherical viscoelastic solid earth model. We present ice model results using the Instructed Glacier Model (Jouvet et al., 2021), in which we tested the effect of spatial resolution on the growth and extent of the European ice cap. We found significant differences using a model resolution of 200 m compared to a resolution of 2000 m, which is commonly used in large-scale glacier modeling studies. These differences result in near-steady state volumetric differences at the maximum ice extent of +13% for the high compared to the low-resolution model. In addition, we observed periods of marked ice growth that initiated at significantly different times for the different resolution models. Therefore, we conclude that a realistic ice loading history requires a sufficiently high spatial resolution, which is significantly higher than used in previous models. Based on the modeled ice loading histories, we used the lithosphere and mantle model VILMA (Klemann et al., 2008, J. Geodyn.) to predict the vertical land motion. These estimates are based on a global 60 km thick elastic lithosphere, followed by a 200 km thick viscous layer with a viscosity of 1020 Pa s, which increases to 5 x 1020 Pa s down to 670 km depth, and 3.16 x 1021 Pa s to the core mantle boundary. Preliminary results indicate similar first-order lithospheric responses, with spatiotemporal differences in the magnitude of postglacial response. We hope to present more results based on further ice models that are forced by a more realistic climate history

Basin stability and limit cycles in a conceptual model for climate tipping cascades

Tipping elements in the climate system are large-scale subregions of the Earth that might possess threshold behavior under global warming with large potential impacts on human societies. Here, we study a subset of five tipping elements and their interactions in a conceptual and easily extendable framework: the Greenland and West Antarctic Ice Sheets, the Atlantic Meridional Overturning Circulation (AMOC), the El-Nino Southern Oscillation (ENSO) and the Amazon rainforest. In this nonlinear and multistable system, we perform a basin stability analysis to detect its stable states and their associated Earth system resilience. Using this approach, we perform a system-wide and comprehensive robustness analysis with more than 3.5 billion ensemble members. Further, we investigate dynamic regimes where some of the states lose stability and oscillations appear using a newly developed basin bifurcation analysis methodology. Our results reveal that the state of four or five tipped elements has the largest basin volume for large levels of global warming beyond 4 {\deg}C above pre-industrial climate conditions. For lower levels of warming, states including disintegrated ice sheets on West Antarctica and Greenland have higher basin volume than other state configurations. Therefore in our model, we find that the large ice sheets are of particular importance for Earth system resilience. We also detect the emergence of limit cycles for 0.6% of all ensemble members at rare parameter combinations. Such limit cycle oscillations mainly occur between the Greenland Ice Sheet and AMOC (86%), due to their negative feedback coupling. These limit cycles point to possibly dangerous internal modes of variability in the climate system that could have played a role in paleoclimatic dynamics such as those unfolding during the Pleistocene ice age cycles.Comment: 50 pages, 10 figures, 2 table

Emergence of cascading dynamics in interacting tipping elements of ecology and climate

In ecology, climate and other fields, (sub)systems have been identified that can transition into a qualitatively different state when a critical threshold or tipping point in a driving process is crossed. An understanding of those tipping elements is of great interest given the increasing influence of humans on the biophysical Earth system. Complex interactions exist between tipping elements, e.g. physical mechanisms connect subsystems of the climate system. Based on earlier work on such coupled nonlinear systems, we systematically assessed the qualitative long-term behaviour of interacting tipping elements. We developed an understanding of the consequences of interactions on the tipping behaviour allowing for tipping cascades to emerge under certain conditions. The (narrative) application of these qualitative results to real-world examples of interacting tipping elements indicates that tipping cascades with profound consequences may occur: the interacting Greenland ice sheet and thermohaline ocean circulation might tip before the tipping points of the isolated subsystems are crossed. The eutrophication of the first lake in a lake chain might propagate through the following lakes without a crossing of their individual critical nutrient input levels. The possibility of emerging cascading tipping dynamics calls for the development of a unified theory of interacting tipping elements and the quantitative analysis of interacting real-world tipping elements.Comment: 22 pages, 8 figure