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    A simple stress-based cliff-calving law
    (Göttingen : Copernicus GmbH, 2019) Schlemm, T.; Levermann, A.
    Over large coastal regions in Greenland and Antarctica the ice sheet calves directly into the ocean. In contrast to ice-shelf calving, an increase in calving from grounded glaciers contributes directly to sea-level rise. Ice cliffs with a glacier freeboard larger than ≈100 m are currently not observed, but it has been shown that such ice cliffs are increasingly unstable with increasing ice thickness. This cliff calving can constitute a self-amplifying ice loss mechanism that may significantly alter sea-level projections both of Greenland and Antarctica. Here we seek to derive a minimalist stress-based parametrization for cliff calving from grounded glaciers whose freeboards exceed the 100 m stability limit derived in previous studies. This will be an extension of existing calving laws for tidewater glaciers to higher ice cliffs.

    To this end we compute the stress field for a glacier with a simplified two-dimensional geometry from the two-dimensional Stokes equation. First we assume a constant yield stress to derive the failure region at the glacier front from the stress field within the glacier. Secondly, we assume a constant response time of ice failure due to exceedance of the yield stress. With this strongly constraining but very simple set of assumptions we propose a cliff-calving law where the calving rate follows a power-law dependence on the freeboard of the ice with exponents between 2 and 3, depending on the relative water depth at the calving front. The critical freeboard below which the ice front is stable decreases with increasing relative water depth of the calving front. For a dry water front it is, for example, 75 m. The purpose of this study is not to provide a comprehensive calving law but to derive a particularly simple equation with a transparent and minimalist set of assumptions.

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    Scaling of instability timescales of Antarctic outlet glaciers based on one-dimensional similitude analysis
    (Göttingen : Copernicus GmbH, 2019) Levermann, A.; Feldmann, J.
    Recent observations and ice-dynamic modeling suggest that a marine ice-sheet instability (MISI) might have been triggered in West Antarctica. The corresponding outlet glaciers, Pine Island Glacier (PIG) and Thwaites Glacier (TG), showed significant retreat during at least the last 2 decades. While other regions in Antarctica have the topographic predisposition for the same kind of instability, it is so far unclear how fast these instabilities would unfold if they were initiated. Here we employ the concept of similitude to estimate the characteristic timescales of several potentially MISI-prone outlet glaciers around the Antarctic coast. Our results suggest that TG and PIG have the fastest response time of all investigated outlets, with TG responding about 1.25 to 2 times as fast as PIG, while other outlets around Antarctica would be up to 10 times slower if destabilized. These results have to be viewed in light of the strong assumptions made in their derivation. These include the absence of ice-shelf buttressing, the one-dimensionality of the approach and the uncertainty of the available data. We argue however that the current topographic situation and the physical conditions of the MISI-prone outlet glaciers carry the information of their respective timescale and that this information can be partially extracted through a similitude analysis.
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    MAgPIE 4-a modular open-source framework for modeling global land systems
    (Göttingen : Copernicus GmbH, 2019) Dietrich, J.P.; Bodirsky, B.L.; Humpenöder, F.; Weindl, I.; Stevanović, M.; Karstens, K.; Kreidenweis, U.; Wang, X.; Mishra, A.; Klein, D.; Ambrósio, G.; Araujo, E.; Yalew, A.W.; Baumstark, L.; Wirth, S.; Giannousakis, A.; Beier, F.; Meng-Chuen, Chen, D.; Lotze-Campen, H.; Popp, A.
    The open-source modeling framework MAgPIE (Model of Agricultural Production and its Impact on the Environment) combines economic and biophysical approaches to simulate spatially explicit global scenarios of land use within the 21st century and the respective interactions with the environment. Besides various other projects, it was used to simulate marker scenarios of the Shared Socioeconomic Pathways (SSPs) and contributed substantially to multiple IPCC assessments. However, with growing scope and detail, the non-linear model has become increasingly complex, computationally intensive and non-transparent, requiring structured approaches to improve the development and evaluation of the model. Here, we provide an overview on version 4 of MAgPIE and how it addresses these issues of increasing complexity using new technical features: modular structure with exchangeable module implementations, flexible spatial resolution, in-code documentation, automatized code checking, model/output evaluation and open accessibility. Application examples provide insights into model evaluation, modular flexibility and region-specific analysis approaches. While this paper is focused on the general framework as such, the publication is accompanied by a detailed model documentation describing contents and equations, and by model evaluation documents giving insights into model performance for a broad range of variables. With the open-source release of the MAgPIE 4 framework, we hope to contribute to more transparent, reproducible and collaborative research in the field. Due to its modularity and spatial flexibility, it should provide a basis for a broad range of land-related research with economic or biophysical, global or regional focus.
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    Exploring the sensitivity of Northern Hemisphere atmospheric circulation to different surface temperature forcing using a statistical-dynamical atmospheric model
    (Göttingen : Copernicus GmbH, 2019) Totz, S.; Petri, S.; Lehmann, J.; Peukert, E.; Coumou, D.
    Climate and weather conditions in the mid-latitudes are strongly driven by the large-scale atmosphere circulation. Observational data indicate that important components of the large-scale circulation have changed in recent decades, including the strength and the width of the Hadley cell, jets, storm tracks and planetary waves. Here, we use a new statistical-dynamical atmosphere model (SDAM) to test the individual sensitivities of the large-scale atmospheric circulation to changes in the zonal temperature gradient, meridional temperature gradient and global-mean temperature. We analyze the Northern Hemisphere Hadley circulation, jet streams, storm tracks and planetary waves by systematically altering the zonal temperature asymmetry, the meridional temperature gradient and the global-mean temperature. Our results show that the strength of the Hadley cell, storm tracks and jet streams depend, in terms of relative changes, almost linearly on both the global-mean temperature and the meridional temperature gradient, whereas the zonal temperature asymmetry has little or no influence. The magnitude of planetary waves is affected by all three temperature components, as expected from theoretical dynamical considerations. The width of the Hadley cell behaves nonlinearly with respect to all three temperature components in the SDAM. Moreover, some of these observed large-scale atmospheric changes are expected from dynamical equations and are therefore an important part of model validation.