Search

For better projections of sea level rise, two things are needed: an improved understanding of the contributing processes and their accurate representation in climate models. A major process is basal melting of ice shelves and glacier tongues by the ocean, which reduces ice sheet stability and increases ice discharge into the ocean. We study marine melting of Greenland's largest floating ice tongue, the 79° North Glacier, using a high‐resolution, 2D‐vertical ocean model. While our fjord model is idealized, the results agree with observations of melt rate and overturning strength. Our setup is the first application of adaptive vertical coordinates to an ice cavity. Their stratification‐zooming allows a vertical resolution finer than 1 m in the entrainment layer of the meltwater plume, which is important for the plume development. We find that the plume development is dominated by entrainment only initially. In the stratified upper part of the cavity, the subglacial plume shows continuous detrainment. It reaches neutral buoyancy near 100 m depth, detaches from the ice, and transports meltwater out of the fjord. Melting almost stops there. In a sensitivity study, we show that the detachment depth depends primarily on stratification. Our results contribute to the understanding of ice–ocean interactions in glacier cavities. Furthermore, we suggest that our modeling approach with stratification‐zooming coordinates will improve the representation of these interactions in global ocean models. Finally, our idealized model topography and forcing are close to a real fjord and completely defined analytically, making the setup an interesting reference case for future model developments. Plain Language Summary: The global increase of sea levels is a consequence of human‐induced climate change. It presents a threat to coastal regions and demands action to protect human life and infrastructure near the coast. Planning protective measures requires projections of sea level rise, computed with climate models. We present an approach to improve the simulation of an important contributor to sea level rise: melting of floating ice shelves by ocean circulation. Our modeling approach uses a vertical model grid that evolves over time. The temporal evolution depends on the density structure of the ocean. Large density differences appear just below an ice shelf, where fresh meltwater mixes with salty seawater. The adaptive grid of our model resolves this mixing process in great detail. This is important for an accurate computation of the melt rate and enables us to study in depth the ice shelf–ocean interactions. We study them at the glacier tongue of the 79° North Glacier, which is Greenland's largest ice shelf. The physical understanding gained from our simulations is also applicable to other floating glacier tongues and ice shelves. We suggest that using the presented model technique in global ocean models can improve projections of melting and sea level rise. Key Points: Melting of the 79° North Glacier ice tongue by turbulent ocean currents is studied with an idealized 2D‐vertical fjord modelThe subglacial plume behaves like an entraining plume close to the grounding line and like a detraining gravity current further downstreamA vertical resolution finer than 1 m is achieved in the subglacial plume by using adaptive vertical coordinates that zoom to stratification [ABSTRACT FROM AUTHOR]

We examine ocean tides in the barotropic version of the Model for Prediction Across Scales (MPAS‐Ocean), the ocean component of the Department of Energy Earth system model. We focus on four factors that affect tidal accuracy: self‐attraction and loading (SAL), model resolution, details of the underlying bathymetry, and parameterized topographic wave drag. The SAL term accounts for the tidal loading of Earth's crust and the self‐gravitation of the ocean and the load‐deformed Earth. A common method for calculating SAL is to decompose mass anomalies into their spherical harmonic constituents. Here, we compare a scalar SAL approximation versus an inline SAL using a fast spherical harmonic transform package. Wave drag accounts for energy lost by breaking internal tides that are produced by barotropic tidal flow over topographic features. We compare a series of successively finer quasi‐uniform resolution meshes (62.9, 31.5, 15.7, and 7.87 km) to a variable resolution (45 to 5 km) configuration. We ran MPAS‐Ocean in a single‐layer barotropic mode forced by five tidal constituents. The 45 to 5 km variable resolution mesh obtained the best total root‐mean‐square error (5.4 cm) for the deep ocean (> $ > $1,000 m) M2 ${\mathrm{M}}_{2}$ tide compared to TPXO8 and ran twice as fast as the quasi‐uniform 8 km mesh, which had an error of 5.8 cm. This error is comparable to those found in other forward (non‐assimilative) ocean tide models. In future work, we plan to use MPAS‐Ocean to study tidal interactions with other Earth system components, and the tidal response to climate change. Plain Language Summary: Over the next century, climate change impacts on coastal regions will include floods, droughts, erosion, and severe weather events. The Department of Energy (DoE) is funding the Integrated Coastal Modeling Project to understand these potential risks better. In this paper, we implement tides in the DoE ocean model. Tides themselves respond to climate change, altering coastal flooding risk assessments. We explore the sensitivity of tides to model resolution (the spacing of model gridpoints), ocean‐floor topography, and the so‐called "self‐attraction and loading" (SAL) effect. Self‐attraction and loading occurs as the mass of water in a location fluctuates, causing a deformation of the Earth's crust and changes in the gravitational potential, which must be accounted for when modeling tides. We present a computationally efficient method of calculating the SAL effects and show that it is more accurate than other commonly used approximations. In future work we will examine interactions of tides with other components of the climate system, including sea ice, floating ice shelves, rivers, and current systems. Key Points: We calculate the full self‐attraction and loading (SAL) term inline, in a barotropic configuration of Model for Prediction Across Scales (MPAS‐Ocean)Inclusion of the inline SAL and higher resolution meshes yield improved tidal accuracy in stand‐alone barotropic MPAS‐Ocean configurationsA 45 to 5‐km variable‐resolution mesh provides reduced tidal errors with better computational performance than a quasi‐uniform 8‐km mesh [ABSTRACT FROM AUTHOR]

We develop a generalized interpolation material point method (GIMPM) for the shallow shelf approximation (SSA) of ice flow. The GIMPM, which can be viewed as a particle version of the finite element method, is used here to solve the shallow shelf approximations of the momentum balance and ice thickness evolution equations. We introduce novel numerical schemes for particle splitting and integration at domain boundaries to accurately simulate the spreading of an ice shelf. The advantages of the proposed GIMPM‐SSA framework include efficient advection of history or internal state variables without diffusion errors, automated tracking of the ice front and grounding line at sub‐element scales, and a weak formulation based on well‐established conventions of the finite element method with minimal additional computational cost. We demonstrate the numerical accuracy and stability of the GIMPM using 1‐D and 2‐D benchmark examples. We also compare the accuracy of the GIMPM with the standard material point method (sMPM) and a reweighted form of the sMPM. We find that the grid‐crossing error is very severe for SSA simulations with the sMPM, whereas the GIMPM successfully mitigates this error. While the grid‐crossing error can be reasonably reduced in the sMPM by implementing a simple material point reweighting scheme, this approach it not as accurate as the GIMPM. Thus, we illustrate that the GIMPM‐SSA framework is viable for the simulation of ice sheet‐shelf evolution and enables boundary tracking and error‐free advection of history or state variables, such as ice thickness or damage. Plain Language Summary: Ice shelves largely govern the evolution of the Antarctic ice sheet by buttressing grounded ice flow into the ocean. This buttressing is sensitive to changes in ice thickness, upstream ice flow, ice front position, contact with bedrock, fracture‐induced weakening, and calving. The current generation of ice flow models are particularly ill‐suited for capturing the processes associated with fracture and boundary tracking because they solve equations using exclusively mesh‐based methods. For large‐deformation ice flow, these methods produce diffusion errors when advecting history variables (e.g., fracture variables) and often rely on overly approximate or cumbersome schemes to track the ice front position. Here, we introduce an ice shelf flow model based on the material point method, a particle variation of the finite element method where boundaries are naturally tracked and advection errors are alleviated. A mesh is only needed when solving the momentum equations, where the particles serve as moving integration points. As part of our implementation, we introduce new schemes for particle splitting and integration at domain boundaries, and we test several shape functions for mapping between the particles and the grid. We demonstrate the accuracy and stability of the method with a series of benchmark examples. Key Points: Our material point method for ice shelf flow enables error‐free advection of history variables, such as damage, and ice front trackingThe method can be readily implemented into existing finite element software (here, Elmer/Ice), and is suitable for large‐scale applicationThe method is verified against analytical solutions for steady‐state flow and front evolution, and tested on an idealized marine ice sheet [ABSTRACT FROM AUTHOR]

Ice shelf fracture is responsible for roughly half of Antarctic ice mass loss in the form of calving and can weaken buttressing of upstream ice flow. Large uncertainties associated with the ice sheet response to climate variations are due to a poor understanding of these fracture processes and how to model them. Here, we address these problems by implementing an anisotropic, nonlocal integral formulation of creep damage within a large‐scale shallow‐shelf ice flow model. This model can be used to study the full evolution of fracture from initiation of crevassing to rifting that eventually causes tabular calving. While previous ice shelf fracture models have largely relied on simple expressions to estimate crevasse depths, our model parameterizes fracture as a progressive damage evolution process in three‐dimensions (3‐D). We also implement an efficient numerical framework based on the material point method, which avoids advection errors. Using an idealized marine ice sheet, we test the creep damage model and a crevasse‐depth based damage model, including a modified version of the latter that accounts for damage evolution due to necking and mass balance. We demonstrate that the creep damage model is best suited for capturing weakening and rifting over shorter (monthly/yearly) timescales, and that anisotropic damage reproduces typically observed fracture patterns better than isotropic damage. Because necking and mass balance can significantly influence damage on longer (decadal) timescales, we discuss the potential for a combined approach between models to best represent mechanical weakening and tabular calving within long‐term simulations. Plain Language Summary: Floating ice shelves buttress the flow of grounded ice into the ocean. Ice shelf fracture decreases this buttressing and in the form of calving, accounts for approximately half of Antarctic ice mass loss. Here, we introduce a "creep damage" framework that parameterizes large‐scale ice shelf fracture evolution in three‐dimensions (3‐D) and captures the weakening effect of fracture on flow. This framework is based on a previous approach for modeling individual crevasses, where the damage parameters were calibrated to laboratory tests. We use the material point method to avoid diffusion errors while transporting the damage field and ensure computational efficiency. Using an idealized ice configuration, we demonstrate that our methods represent fracture evolution ranging from crevasse initiation to rifting. We find that our modeled rift patterns best match typically observed patterns when we account for fracture orientation, or damage anisotropy. Furthermore, we show how a previously proposed damage framework that parameterizes crevasse depths is ill‐suited for modeling rifting, although it's modified form accounts for the impact of ice accumulation/melt and necking on damage, which we find is significant on decadal timescales. We conclude by discussing potential approaches for implementing these additional processes into the creep damage model. Key Points: Our shallow‐shelf creep damage model can represent the full evolution of ice shelf fracture from crevasse initiation to tabular calvingStrongly anisotropic creep damage produces sharp, arcuate rift patterns more consistent with observations than isotropic creep damageThe zero‐stress damage model poorly captures rifting, but a modified form accounts for damage evolution due to mass balance and necking [ABSTRACT FROM AUTHOR]