scholarly journals Mathematical Analysis of a Stefan Problem with Dirichlet–Signorini Boundary Conditions Appearing in Polythermic Ice Sheet Modeling

2001 ◽  
Vol 262 (2) ◽  
pp. 577-600 ◽  
Author(s):  
N. Calvo ◽  
J. Durany ◽  
C. Vázquez
1993 ◽  
Vol 39 (131) ◽  
pp. 91-98 ◽  
Author(s):  
Douglas R. MacAyeal

AbstractControl methods are recommended as an efficient means to estimate undetermined physical parameters and boundary conditions and, in so doing, to improve the fidelity of a given ice-sheet flow model to specific ice-sheet velocity observations. To accomplish this task, the underlying dynamics of the model are inverted. This permits model-tuning adjustments to be represented explicitly in terms of model/observation misfit. Advantages of the control method over trial-and-error techniques in common use are: (1) it is readily automated with little additional programming effort, (2) the tuning parameters and boundary conditions it achieves are assured to give the best possible fit between model and observation, and (3) it quantifies the uncertainty of tuning parameters and boundary conditions in situations where they are not uniquely determined.


1993 ◽  
Vol 39 (131) ◽  
pp. 91-98 ◽  
Author(s):  
Douglas R. MacAyeal

AbstractControl methods are recommended as an efficient means to estimate undetermined physical parameters and boundary conditions and, in so doing, to improve the fidelity of a given ice-sheet flow model to specific ice-sheet velocity observations. To accomplish this task, the underlying dynamics of the model are inverted. This permits model-tuning adjustments to be represented explicitly in terms of model/observation misfit. Advantages of the control method over trial-and-error techniques in common use are: (1) it is readily automated with little additional programming effort, (2) the tuning parameters and boundary conditions it achieves are assured to give the best possible fit between model and observation, and (3) it quantifies the uncertainty of tuning parameters and boundary conditions in situations where they are not uniquely determined.


2014 ◽  
Vol 10 (5) ◽  
pp. 1817-1836 ◽  
Author(s):  
F. A. Ziemen ◽  
C. B. Rodehacke ◽  
U. Mikolajewicz

Abstract. In the standard Paleoclimate Modelling Intercomparison Project (PMIP) experiments, the Last Glacial Maximum (LGM) is modeled in quasi-equilibrium with atmosphere–ocean–vegetation general circulation models (AOVGCMs) with prescribed ice sheets. This can lead to inconsistencies between the modeled climate and ice sheets. One way to avoid this problem would be to model the ice sheets explicitly. Here, we present the first results from coupled ice sheet–climate simulations for the pre-industrial times and the LGM. Our setup consists of the AOVGCM ECHAM5/MPIOM/LPJ bidirectionally coupled with the Parallel Ice Sheet Model (PISM) covering the Northern Hemisphere. The results of the pre-industrial and LGM simulations agree reasonably well with reconstructions and observations. This shows that the model system adequately represents large, non-linear climate perturbations. A large part of the drainage of the ice sheets occurs in ice streams. Most modeled ice stream systems show recurring surges as internal oscillations. The Hudson Strait Ice Stream surges with an ice volume equivalent to about 5 m sea level and a recurrence interval of about 7000 yr. This is in agreement with basic expectations for Heinrich events. Under LGM boundary conditions, different ice sheet configurations imply different locations of deep water formation.


2018 ◽  
Vol 12 (10) ◽  
pp. 3097-3121 ◽  
Author(s):  
Reinhard Calov ◽  
Sebastian Beyer ◽  
Ralf Greve ◽  
Johanna Beckmann ◽  
Matteo Willeit ◽  
...  

Abstract. We introduce the coupled model of the Greenland glacial system IGLOO 1.0, including the polythermal ice sheet model SICOPOLIS (version 3.3) with hybrid dynamics, the model of basal hydrology HYDRO and a parameterization of submarine melt for marine-terminated outlet glaciers. The aim of this glacial system model is to gain a better understanding of the processes important for the future contribution of the Greenland ice sheet to sea level rise under future climate change scenarios. The ice sheet is initialized via a relaxation towards observed surface elevation, imposing the palaeo-surface temperature over the last glacial cycle. As a present-day reference, we use the 1961–1990 standard climatology derived from simulations of the regional atmosphere model MAR with ERA reanalysis boundary conditions. For the palaeo-part of the spin-up, we add the temperature anomaly derived from the GRIP ice core to the years 1961–1990 average surface temperature field. For our projections, we apply surface temperature and surface mass balance anomalies derived from RCP 4.5 and RCP 8.5 scenarios created by MAR with boundary conditions from simulations with three CMIP5 models. The hybrid ice sheet model is fully coupled with the model of basal hydrology. With this model and the MAR scenarios, we perform simulations to estimate the contribution of the Greenland ice sheet to future sea level rise until the end of the 21st and 23rd centuries. Further on, the impact of elevation–surface mass balance feedback, introduced via the MAR data, on future sea level rise is inspected. In our projections, we found the Greenland ice sheet to contribute between 1.9 and 13.0 cm to global sea level rise until the year 2100 and between 3.5 and 76.4 cm until the year 2300, including our simulated additional sea level rise due to elevation–surface mass balance feedback. Translated into additional sea level rise, the strength of this feedback in the year 2100 varies from 0.4 to 1.7 cm, and in the year 2300 it ranges from 1.7 to 21.8 cm. Additionally, taking the Helheim and Store glaciers as examples, we investigate the role of ocean warming and surface runoff change for the melting of outlet glaciers. It shows that ocean temperature and subglacial discharge are about equally important for the melting of the examined outlet glaciers.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Michael E. Weber ◽  
Nicholas R. Golledge ◽  
Chris J. Fogwill ◽  
Chris S. M. Turney ◽  
Zoë A. Thomas

AbstractEmerging ice-sheet modeling suggests once initiated, retreat of the Antarctic Ice Sheet (AIS) can continue for centuries. Unfortunately, the short observational record cannot resolve the tipping points, rate of change, and timescale of responses. Iceberg-rafted debris data from Iceberg Alley identify eight retreat phases after the Last Glacial Maximum that each destabilized the AIS within a decade, contributing to global sea-level rise for centuries to a millennium, which subsequently re-stabilized equally rapidly. This dynamic response of the AIS is supported by (i) a West Antarctic blue ice record of ice-elevation drawdown >600 m during three such retreat events related to globally recognized deglacial meltwater pulses, (ii) step-wise retreat up to 400 km across the Ross Sea shelf, (iii) independent ice sheet modeling, and (iv) tipping point analysis. Our findings are consistent with a growing body of evidence suggesting the recent acceleration of AIS mass loss may mark the beginning of a prolonged period of ice sheet retreat and substantial global sea level rise.


2020 ◽  
Author(s):  
Sophie Nowicki ◽  
Antony J. Payne ◽  
Heiko Goelzer ◽  
Helene Seroussi ◽  
William H. Lipscomb ◽  
...  

Abstract. Projection of the contribution of ice sheets to sea-level change as part of the Coupled Model Intercomparison Project – phase 6 (CMIP6) takes the form of simulations from coupled ice-sheet-climate models and standalone ice sheet models, overseen by the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6). This paper describes the experimental setup for process-based sea-level change projections to be performed with standalone Greenland and Antarctic ice sheet models in the context of ISMIP6. The ISMIP6 protocol relies on a suite of polar atmospheric and oceanic CMIP-based forcing for ice sheet models, in order to explore the uncertainty in projected sea-level change due to future emissions scenarios, CMIP models, ice sheet models, and parameterizations for ice-ocean interactions. We describe here the approach taken for defining the suite of ISMIP6 standalone ice sheet simulations, document the experimental framework and implementation, as well as present an overview of the ISMIP6 forcing to be used by participating ice sheet modeling groups.


2002 ◽  
Vol 35 ◽  
pp. 503-509 ◽  
Author(s):  
Olivier Gagliardini ◽  
Jacques Meyssonnier

AbstractA local two-dimensional flow model which accounts for the anisotropic behaviour of polar ice and the evolution of its strain-induced anisotropy is briefly reviewed. Due to its complexity, it is not yet possible to use this model to simulate the flow of a whole ice sheet, and its potential applications are presently restricted to limited spatial domains around existing drilling sites. In order to calculate the local flow of ice, boundary conditions must be applied on the lateral edges of the studied domain. Since these limits correspond to fictitious sections of the ice sheet, the type of boundary condition to adopt is not obvious. In the present paper, different kinds of boundary conditions of the Dirichlet type, applied at the lateral boundary of an idealized ice sheet of simplified geometry, are discussed. This will serve as a first step towards the coupling of the local flow model with a global ice-sheet flow model.


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