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Northern northeastern Brazil (NEB) is a climate change hotspot due to its high biological and social vulnerability to ongoing and future hydroclimate changes. Precipitation in this region is influenced by the Intertropical Convergence Zone (ITCZ), which is largely controlled by the strength of the Atlantic Meridional Overturning Circulation (AMOC). Accordingly, the projected weakening of the AMOC due to anthropogenic global warming may substantially change NEB hydroclimate. Heinrich Stadials (HS), past millennial-scale events during which the AMOC was significantly weaker, provide important insights into the AMOC-ITCZ dynamics. This is especially true for those HS that occurred under similar to modern boundary conditions. HS10 (ca. 110 thousand years ago) was the first HS of Marine Isotope Stage 5, providing an ideal target for investigating AMOC-ITCZ dynamics under relatively warm climate conditions. Here we investigate the response of the surface and deep western equatorial Atlantic (WEA) circulation, as well as NEB precipitation to HS10. Therefore, we use foraminiferal carbon and oxygen stable isotopes and bulk sediment major elemental data from a marine sediment core retrieved from the WEA. Our results record a weakening of the AMOC during HS10 and show a concurrent increased WEA upper stratification and precipitation over NEB. We suggest that the mechanism controlling the WEA upper ocean stratification during HS depends on the background climate. Furthermore, we infer that the southward shift of the ITCZ during HS10 was more limited if compared to the shifts that occurred under colder climate background. Our findings provide useful insights into how a weakening of the AMOC under a relatively warm climate can impact the ITCZ and tropical South American precipitation. 

Abstract Numerical ice sheet models use sliding laws to connect basal shear stress and ice velocity to simulate ice sliding. A sliding‐law parameterβ²is used to control Weertman's sliding law in numerical ice sheet models. Basal reflectivity derived from ice‐penetrating radar also provides information about frozen or thawed conditions underneath glaciers. To assess whether basal reflectivity can be used to constrainβ², we carry out statistical experiments between two recently published datasets:β²inferred from three numerical ice sheet models (ISSM, Úa and STREAMICE) and airborne radar‐derived relative basal reflectivity from the AGASEA‐BBAS mission over Thwaites Glacier (TG). Our results show no robust correlation between theβ²–relative reflectivity pair. Pearson's correlation coefficient, a test of linearity, ranges from −0.26 to −0.38. Spearman's correlation coefficient, which does not require a linear assumption, is also modest (∼−0.35). We conclude thatβ²and relative basal reflectivity underneath TG do not infer similar basal conditions. 

Abstract. Numerical simulations of ice sheets rely on the momentum balance to determine how ice velocities change as the geometry of the system evolves. Ice is generally assumed to follow a Stokes flow with a nonlinear viscosity. Several approximations have been proposed in order to lower the computational cost of a full-Stokes stress balance. A popular option is the Blatter–Pattyn or higher-order model (HO), which consists of a three-dimensional set of equations that solves the horizontal velocities only. However, it still remains computationally expensive for long transient simulations. Here we present a depth-integrated formulation of the HO model, which can be solved on a two-dimensional mesh in the horizontal plane. We employ a specific polynomial function to describe the vertical variation in the velocity, which allows us to integrate the vertical dimension using a semi-analytic integration. We assess the performance of this MOno-Layer Higher-Order (MOLHO) model to compute ice velocities and simulate grounding line dynamics on standard benchmarks (ISMIP-HOM and MISMIP3D). We compare MOLHO results to the ones obtained with the original three-dimensional HO model. We also compare the time performance of both models in time-dependent runs. Our results show that the ice velocities and grounding line positions obtained with MOLHO are in very good agreement with the ones from HO. In terms of computing time, MOLHO requires less than 10 % of the computational time of a typical HO model, for the same simulations. These results suggest that the MOno-Layer Higher-Order formulation provides improved computational time performance and a comparable accuracy compared to the HO formulation, which opens the door to higher-order paleo simulations. 

Abstract. Time-dependent simulations of ice sheets require two equations to be solved:the mass transport equation, derived from the conservation of mass, and thestress balance equation, derived from the conservation of momentum. The masstransport equation controls the advection of ice from the interior of the icesheet towards its periphery, thereby changing its geometry. Because it isbased on an advection equation, a stabilization scheme needs to beemployed when solved using the finite-element method. Several stabilizationschemes exist in the finite-element method framework, but their respectiveaccuracy and robustness have not yet been systematically assessed forglaciological applications. Here, we compare classical schemes used in thecontext of the finite-element method: (i) artificial diffusion, (ii)streamline upwinding, (iii) streamline upwind Petrov–Galerkin, (iv)discontinuous Galerkin, and (v) flux-corrected transport. We also look at thestress balance equation, which is responsible for computing the ice velocitythat “advects” the ice downstream. To improve the velocity computationaccuracy, the ice-sheet modeling community employs several sub-elementparameterizations of physical processes at the grounding line, the point wherethe grounded ice starts to float onto the ocean. Here, we introduce a newsub-element parameterization for the driving stress, the force that drives theice-sheet flow. We analyze the response of each stabilization scheme byrunning transient simulations forced by ice-shelf basal melt. The simulationsare based on an idealized ice-sheet geometry for which there is no influenceof bedrock topography. We also perform transient simulations of the AmundsenSea Embayment, West Antarctica, where real bedrock and surface elevations areemployed. In both idealized and real ice-sheet experiments, stabilizationschemes based on artificial diffusion lead systematically to a bias towardsmore mass loss in comparison to the other schemes and therefore should beavoided or employed with a sufficiently high mesh resolution in the vicinityof the grounding line. We also run diagnostic simulations to assess theaccuracy of the driving stress parameterization, which, in combination with anadequate parameterization for basal stress, provides improved numericalconvergence in ice speed computations and more accurate results. 

Abstract. Among the most important challenges faced by ice flow models is how to represent basal and rheological conditions, which are challenging to obtain from direct observations. A common practice is to use numerical inversions to calculate estimates for the unknown properties, but there are many possible methods and not one standardised approach. As such, every ice flow model has a unique initialisation procedure. Here we compare the outputs of inversions from three different ice flow models, each employing a variant of adjoint-based optimisation to calculate basal sliding coefficients and flow rate factors using the same observed surface velocities and ice thickness distribution. The region we focus on is the Amundsen Sea Embayment in West Antarctica, the subject of much investigation due to rapid changes in the area over recent decades. We find that our inversions produce similar distributions of basal sliding across all models, despite using different techniques, implying that the methods used are highly robust and represent the physical equations without much influence by individual model behaviours. Transferring the products of inversions between models results in time-dependent simulations displaying variability on the order of or lower than existing model intercomparisons. Focusing on contributions to sea level, the highest variability we find in simulations run in the same model with different inversion products is 32 %, over a 40-year period, a difference of 3.67 mm. There is potential for this to be improved with further standardisation of modelling processes, and the lowest variability within a single model is 13 %, or 1.82 mm over 40 years. While the successful transfer of inversion outputs from one model to another requires some extra effort and technical knowledge of the particular models involved, it is certainly possible and could indeed be useful for future intercomparison projects. 

Given two (di)graphs G, H and a cost function c:V(G) x V(H) -> Q_{>= 0} cup {+infty}, in the minimum cost homomorphism problem, MinHOM(H), we are interested in finding a homomorphism f:V(G)-> V(H) (a.k.a H-coloring) that minimizes sum limits_{v in V(G)}c(v,f(v)). The complexity of exact minimization of this problem is well understood [Pavol Hell and Arash Rafiey, 2012], and the class of digraphs H, for which the MinHOM(H) is polynomial time solvable is a small subset of all digraphs. In this paper, we consider the approximation of MinHOM within a constant factor. In terms of digraphs, MinHOM(H) is not approximable if H contains a digraph asteroidal triple (DAT). We take a major step toward a dichotomy classification of approximable cases. We give a dichotomy classification for approximating the MinHOM(H) when H is a graph (i.e. symmetric digraph). For digraphs, we provide constant factor approximation algorithms for two important classes of digraphs, namely bi-arc digraphs (digraphs with a conservative semi-lattice polymorphism or min-ordering), and k-arc digraphs (digraphs with an extended min-ordering). Specifically, we show that: - Dichotomy for Graphs: MinHOM(H) has a 2|V(H)|-approximation algorithm if graph H admits a conservative majority polymorphims (i.e. H is a bi-arc graph), otherwise, it is inapproximable; - MinHOM(H) has a |V(H)|^2-approximation algorithm if H is a bi-arc digraph; - MinHOM(H) has a |V(H)|^2-approximation algorithm if H is a k-arc digraph. In conclusion, we show the importance of these results and provide insights for achieving a dichotomy classification of approximable cases. Our constant factors depend on the size of H. However, the implementation of our algorithms provides a much better approximation ratio. It leaves open to investigate a classification of digraphs H, where MinHOM(H) admits a constant factor approximation algorithm that is independent of |V(H)|. 

Given two (di)graphs G, H and a cost function c:V(G) x V(H) -> Q_{>= 0} cup {+infty}, in the minimum cost homomorphism problem, MinHOM(H), we are interested in finding a homomorphism f:V(G)-> V(H) (a.k.a H-coloring) that minimizes sum limits_{v in V(G)}c(v,f(v)). The complexity of exact minimization of this problem is well understood [Pavol Hell and Arash Rafiey, 2012], and the class of digraphs H, for which the MinHOM(H) is polynomial time solvable is a small subset of all digraphs. In this paper, we consider the approximation of MinHOM within a constant factor. In terms of digraphs, MinHOM(H) is not approximable if H contains a digraph asteroidal triple (DAT). We take a major step toward a dichotomy classification of approximable cases. We give a dichotomy classification for approximating the MinHOM(H) when H is a graph (i.e. symmetric digraph). For digraphs, we provide constant factor approximation algorithms for two important classes of digraphs, namely bi-arc digraphs (digraphs with a conservative semi-lattice polymorphism or min-ordering), and k-arc digraphs (digraphs with an extended min-ordering). Specifically, we show that: - Dichotomy for Graphs: MinHOM(H) has a 2|V(H)|-approximation algorithm if graph H admits a conservative majority polymorphims (i.e. H is a bi-arc graph), otherwise, it is inapproximable; - MinHOM(H) has a |V(H)|^2-approximation algorithm if H is a bi-arc digraph; - MinHOM(H) has a |V(H)|^2-approximation algorithm if H is a k-arc digraph. In conclusion, we show the importance of these results and provide insights for achieving a dichotomy classification of approximable cases. Our constant factors depend on the size of H. However, the implementation of our algorithms provides a much better approximation ratio. It leaves open to investigate a classification of digraphs H, where MinHOM(H) admits a constant factor approximation algorithm that is independent of |V(H)|. 

Abstract Thwaites and Pine Island Glaciers as well as other ice streams in West Antarctica have been changing dramatically over the past decades. Although changes in ocean conditions are likely the primary driver of these changes, it remains unclearwhereother processes could cause more mass loss. By employing Automatic Differentiation and two independent ice‐sheet models, we construct maps of the sensitivity of the volume above floatation to changes in ocean‐induced melt rates, ice rigidity, basal friction, and surface mass balance. We find that changes in basal melt close to the grounding lines and along shear margins have a larger impact on the glaciers' final volume. The glaciers are sensitive to changes in basal friction on regions close to the grounding lines, while changes in ice rigidity has a larger impact along the shear margins of Pine Island. The sensitivity to surface mass balance is uniform over grounded ice.