Improved convergence and stability properties in a three-dimensional higher-order ice sheet model

We present a finite difference implementation of a three-dimensional higher-order ice sheet model. In comparison to a conventional centred difference discretisation it enhances both numerical stability and convergence. In order to achieve these benefits the discretisation of the governing force balance equation makes extensive use of information on staggered grid points. Using the same iterative solver, a centred difference discretisation that operates exclusively on the regular grid serves as a reference. The reprise of the ISMIP-HOM experiments indicates that both discretisations are capable of reproducing the higher-order model inter-comparison results. This setup allows a direct comparison of the two numerical implementations also with respect to their convergence behaviour. First and foremost, the new finite difference scheme facilitates convergence by a factor of up to 7 and 2.6 in average. In addition to this decrease in computational costs, the accuracy for the resultant velocity field can be chosen higher in the novel finite difference implementation. Changing the discretisation also prevents build-up of local field irregularites that occasionally cause divergence of the solution for the reference discretisation. <br><br> The improved behaviour makes the new discretisation more reliable for extensive application to real ice geometries. Higher accuracy and robust numerics are crucial in time dependent applications since numerical oscillations in the velocity field of subsequent time steps are attenuated and divergence of the solution is prevented

The Draft Restatement: A Critique from a Securities Regulation Perspective

For the past several years, the American Law Institute has been preparing a proposed revision of the Restatement (Second) of the Foreign Relations Law of the United States (“Draft Restatement”). This article is a critique from a securities regulation perspective of the Draft Restatement\u27s sections 402, 403, 416, 418, 419, 420 and 431.1 In short, the Draft Restatement departs substantially from existing law. It would add dangerous vagueness and uncertainty to the jurisdictional analysis used to determine whether the United States securities laws will be applied to transnational securities activities. In particular, the complicated balancing inquiry required under the Draft would increase litigation by introducing new issues into the jurisdictional analysis and by removing the certainty created by past court decisions. The Draft would make it substantially more difficult to apply United States securities laws where their application is necessary, appropriate and noncontroversial. In addition, the Draft\u27s restrictions on access to information located abroad could impair effective and even-handed enforcement of the securities laws. The Draft Restatement would also make it more difficult for the Securities and Exchange Commission to take summary action which may be necessary for the protection of securities markets in the United States. Section 1905 of the American Law Institute\u27s Federal Securities Code (“Code”), by contrast, retains the benefits of current judicial analysis by substantially codifying that reasoning, while eliminating the drawback of its case-by-case development. Although Section 1905 of the Code was drafted in the context of a general revision of the securities laws, it is a more accurate and workable “restatement” of foreign relations law. The Code also furthers the investor protection purposes of the securities laws because it takes a broader view of the appropriate application of United States securities laws than the Draft Restatement. This article compares and contrasts the analysis used under current law with the analysis that would be used under the Code and under the Draft Restatement. Part I consists of a summary review of current judicial analysis of application of United States law, a comparison of that analysis with that of the Code and the Draft Restatement and illustrations of the differences using five examples. Part II sets forth our principal concerns about the Draft Restatement\u27s approach to application of United States law. Part III critically reviews the Draft\u27s approach to access to information located abroad and the judicial and administrative enforcement mechanisms available to the Commission

Coronal electron temperature in the protracted solar minimum, the cycle 24 mini maximum, and over centuries

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106800/1/jgra50869.pd

Benchmarking the vertically integrated ice-sheet model IMAU-ICE (version 2.0)

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

PLISMIP-ANT, an ice-sheet model intercomparison project

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

A High-End Estimate of Sea Level Rise for Practitioners

Sea level rise (SLR) is a long-lasting consequence of climate change because global anthropogenic warming takes centuries to millennia to equilibrate for the deep ocean and ice sheets. SLR projections based on climate models support policy analysis, risk assessment and adaptation planning today, despite their large uncertainties. The central range of the SLR distribution is estimated by process-based models. However, risk-averse practitioners often require information about plausible future conditions that lie in the tails of the SLR distribution, which are poorly defined by existing models. Here, a community effort combining scientists and practitioners builds on a framework of discussing physical evidence to quantify high-end global SLR for practitioners. The approach is complementary to the IPCC AR6 report and provides further physically plausible high-end scenarios. High-end estimates for the different SLR components are developed for two climate scenarios at two timescales. For global warming of +2°C in 2100 (RCP2.6/SSP1-2.6) relative to pre-industrial values our high-end global SLR estimates are up to 0.9 m in 2100 and 2.5 m in 2300. Similarly, for a (RCP8.5/SSP5-8.5), we estimate up to 1.6 m in 2100 and up to 10.4 m in 2300. The large and growing differences between the scenarios beyond 2100 emphasize the long-term benefits of mitigation. However, even a modest 2°C warming may cause multi-meter SLR on centennial time scales with profound consequences for coastal areas. Earlier high-end assessments focused on instability mechanisms in Antarctica, while here we emphasize the importance of the timing of ice shelf collapse around Antarctica. This is highly uncertain due to low understanding of the driving processes. Hence both process understanding and emission scenario control high-end SLR

Eastern Pacific Warm Pool paleosalinity and climate variability : 0–30 kyr

Author Posting. © American Geophysical Union, 2006. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Paleoceanography 21 (2006): PA3008, doi:10.1029/2005PA001208.Multi-proxy geologic records of δ18O and Mg/Ca in fossil foraminifera from sediments under the Eastern Pacific Warm Pool (EPWP) region west of Central America document variations in upper ocean temperature, pycnocline strength, and salinity (i.e., net precipitation) over the past 30 ky. Although evident in the paleotemperature record, there is no glacial-interglacial difference in paleosalinity, suggesting that tropical hydrologic changes do not respond passively to high-latitude ice sheets and oceans. Millennial variations in paleosalinity with amplitudes as high as ~4 PSU occur with a dominant period of ~3-5 ky during the glacial/deglacial interval and ~1.0-1.5 ky during the Holocene. The amplitude of the EPWP paleosalinity changes greatly exceeds that of published Caribbean and western tropical Pacific paleosalinity records. EPWP paleosalinity changes correspond to millennial-scale climate changes in the surface and deep Atlantic and the high northern latitudes, with generally higher (lower) paleosalinity during cold (warm) events. In addition to Intertropical Convergence Zone (ITCZ) dynamics, which play an important role in tropical hydrologic variability, changes in Atlantic-Pacific moisture transport, which is closely linked to ITCZ dynamics, may also contribute to hydrologic variations in the EPWP. Calculations of interbasin salinity average and interbasin salinity contrast between the EPWP and the Caribbean help differentiate long-term changes in mean ITCZ position and Atlantic-Pacific moisture transport, respectively.Support for this research was provided by the U.S. National Science Foundation

initMIP-Antarctica: an ice sheet model initialization experiment of ISMIP6

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

Asynchronous Antarctic and Greenland ice-volume contributions to the last interglacial sea-level highstand

The last interglacial (LIG; ~130 to ~118 thousand years ago, ka) was the last time global sea level rose well above the present level. Greenland Ice Sheet (GrIS) contributions were insufficient to explain the highstand, so that substantial Antarctic Ice Sheet (AIS) reduction is implied. However, the nature and drivers of GrIS and AIS reductions remain enigmatic, even though they may be critical for understanding future sea-level rise. Here we complement existing records with new data, and reveal that the LIG contained an AIS-derived highstand from ~129.5 to ~125 ka, a lowstand centred on 125–124 ka, and joint AIS + GrIS contributions from ~123.5 to ~118 ka. Moreover, a dual substructure within the first highstand suggests temporal variability in the AIS contributions. Implied rates of sea-level rise are high (up to several meters per century; m c−1), and lend credibility to high rates inferred by ice modelling under certain ice-shelf instability parameterisations