scholarly journals Stable finite volume element schemes for the shallow-ice approximation

2016 ◽  
Vol 62 (232) ◽  
pp. 230-242 ◽  
Author(s):  
ED BUELER
Keyword(s):  
Steady State ◽  
Finite Volume ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Integral Form ◽  
Conservation Equation ◽  
Volume Element ◽  
Surface Mass ◽  
Finite Volume Element ◽  
Thickness Function

ABSTRACTThe isothermal, non-sliding shallow-ice approximation, combined with mass conservation, is a fundamental model for ice-sheet and glacier flow. It determines the ice extent, geometry and velocity by the solution of a free-boundary problem. In this paper, the steady-state form of this problem is solved directly, without time-stepping, thereby demonstrating a fully implicit scheme with no stability restrictions. The classical Mahaffy (1976) finite difference method is first reinterpreted as a ‘finite volume element’ scheme that has both an everywhere-defined approximate thickness function and an approximation of the conservation equation in flux integral form. From this reinterpretation an improved scheme is built by using better quadrature in the integral and upwinding on that part of the flux which is proportional to the bed gradient. The discrete equations are then solved by a parallel Newton scheme which respects the constraint that ice thickness is non-negative. The results show good accuracy on both flat-bed and bedrock-step exact solutions. The method is then applied at high resolution to model the steady-state geometry of the Greenland ice sheet, using only bedrock elevation and present-day surface mass balance as input data.

scholarly journals The Age-Depth Profile in the Upper Part of a Steady-State Ice Sheet

1989 ◽  
Vol 35 (121) ◽  
pp. 406-417 ◽  
Author(s):  
Niels Reeh
Keyword(s):  
Steady State ◽  
Layer Thickness ◽  
Flow Line ◽  
Numerical Models ◽  
Accumulation Rate ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Thickness ◽  
Western Slope ◽  
Simple Models

AbstractSimple analytical models are developed in order to study how up-stream variations in accumulation rate and ice thickness, and horizontal convergence/ divergence of the flow influence the age and annual layer-thickness profiles in a steady-state ice sheet. Generally, a decrease/increase of the accumulation rate and an increase/decrease of the ice thickness in the up-stream direction (i.e. opposite to the flow direction) results in older/younger ice at a given depth in the ice sheet than would result if the up-stream accumulation rate and ice thickness were constant along the flow line.Convergence/divergence of the up-stream flow will decrease/increase the effect of the accumulation-rate and ice-thickness gradients, whereas convergence/divergence has no influence at all on the age and layer-thickness profiles if the up-stream accumulation rate and ice thickness are constant along the flow line.A modified column-flow model, i.e. a model for which the strain-rate profile (or, equivalently, the horizontal velocity profile) is constant down to the depth corresponding to the Holocene/Wisconsinan transition 10 750 year BP., seems to work well for dating the ice back to 10 000–11 000 year B P. at sites in the slope regions of the Greenland ice sheet. For example, the model predicts the experimentally determined age profile at Dye 3 on the south Greenland ice sheet with a relative root-mean-square error of only 3% back to c. 10 700 year B.P. As illustrated by the Milcent location on the western slope of the central Greenland ice sheet, neglecting up-stream accumulation-rate and ice-thickness gradients, may lead to dating errors as large as 3000–000 years for c. 10 000 year old ice.However, even if these gradients are taken into account, the simple model fails to give acceptable ages for 10 000 year old ice at locations on slightly sloping ice ridges with strongly divergent flow, as for example the Camp Century location. The main reason for this failure is that the site of origin of the ice cannot be determined accurately enough by the simple models, if the flow is strongly divergent.With this exception, the simple models are well suited for dating the ice at locations where the available data or the required accuracy do not justify application of elaborate numerical models. The formulae derived for the age-depth profiles can easily be worked out on a pocket calculator, and in many cases will be a sensible alternative to using numerical flow models.

scholarly journals A finite volume element formulation and error analysis for the non-stationary conduction–convection problem

2012 ◽  
Vol 396 (2) ◽  
pp. 864-879 ◽  
Author(s):  
Hong Li ◽  
Zhendong Luo ◽  
Ping Sun ◽  
Jing An
Keyword(s):  
Error Analysis ◽  
Finite Volume ◽  
Volume Element ◽  
Element Formulation ◽  
Finite Volume Element ◽  
Convection Problem

Contemporary (1960–2012) Evolution of the Climate and Surface Mass Balance of the Greenland Ice Sheet

2013 ◽  
Vol 35 (5) ◽  
pp. 1155-1174 ◽  
Author(s):  
J. H. van Angelen ◽  
M. R. van den Broeke ◽  
B. Wouters ◽  
J. T. M. Lenaerts
Keyword(s):  
Mass Balance ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Surface Mass Balance ◽  
Surface Mass

scholarly journals Simulation of the future sea level contribution of Greenland with a new glacial system model

2018 ◽  
Vol 12 (10) ◽  
pp. 3097-3121 ◽  
Author(s):  
Reinhard Calov ◽  
Sebastian Beyer ◽  
Ralf Greve ◽  
Johanna Beckmann ◽  
Matteo Willeit ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Surface Temperature ◽  
Mass Balance ◽  
Sea Level Rise ◽  
Sea Level ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
System Model ◽  
Surface Mass Balance ◽  
Surface Mass

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.

scholarly journals Estimation of the Sea Level Rise by 2100 Resulting from Changes in the Surface Mass Balance of the Greenland Ice Sheet

10.5772/23913 ◽  
2011 ◽  
Author(s):  
Xavier Fettweis ◽  
Alexandre Belleflamme ◽  
Michel Erpicum ◽  
Bruno Franco ◽  
Samuel Nicolay
Keyword(s):  
Mass Balance ◽  
Sea Level Rise ◽  
Sea Level ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Surface Mass Balance ◽  
Surface Mass

scholarly journals Equal Order Discontinuous Finite Volume Element Methods for the Stokes Problem

2015 ◽  
Vol 65 (3) ◽  
pp. 956-978 ◽  
Author(s):  
Sarvesh Kumar ◽  
Ricardo Ruiz-Baier
Keyword(s):  
Finite Volume ◽  
Stokes Problem ◽  
Volume Element ◽  
Finite Volume Element

scholarly journals Seasonal mass variations show timing and magnitude of meltwater storage in the Greenland Ice Sheet

2018 ◽  
Vol 12 (9) ◽  
pp. 2981-2999 ◽  
Author(s):  
Jiangjun Ran ◽  
Miren Vizcaino ◽  
Pavel Ditmar ◽  
Michiel R. van den Broeke ◽  
Twila Moon ◽  
...  
Keyword(s):  
Mass Balance ◽  
Climate Model ◽  
Spatial Scales ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Surface Mass Balance ◽  
High Accumulation ◽  
Outlet Glacier ◽  
Surface Mass ◽  
Meltwater Runoff

Abstract. The Greenland Ice Sheet (GrIS) is currently losing ice mass. In order to accurately predict future sea level rise, the mechanisms driving the observed mass loss must be better understood. Here, we combine data from the satellite gravimetry mission Gravity Recovery and Climate Experiment (GRACE), surface mass balance (SMB) output of the Regional Atmospheric Climate Model v. 2 (RACMO2), and ice discharge estimates to analyze the mass budget of Greenland at various temporal and spatial scales. We find that the mean rate of mass variations in Greenland observed by GRACE was between −277 and −269 Gt yr−1 in 2003–2012. This estimate is consistent with the sum (i.e., -304±126 Gt yr−1) of individual contributions – surface mass balance (SMB, 216±122 Gt yr−1) and ice discharge (520±31 Gt yr−1) – and with previous studies. We further identify a seasonal mass anomaly throughout the GRACE record that peaks in July at 80–120 Gt and which we interpret to be due to a combination of englacial and subglacial water storage generated by summer surface melting. The robustness of this estimate is demonstrated by using both different GRACE-based solutions and different meltwater runoff estimates (namely, RACMO2.3, SNOWPACK, and MAR3.9). Meltwater storage in the ice sheet occurs primarily due to storage in the high-accumulation regions of the southeast and northwest parts of Greenland. Analysis of seasonal variations in outlet glacier discharge shows that the contribution of ice discharge to the observed signal is minor (at the level of only a few gigatonnes) and does not explain the seasonal differences between the total mass and SMB signals. With the improved quantification of meltwater storage at the seasonal scale, we highlight its importance for understanding glacio-hydrological processes and their contributions to the ice sheet mass variability.

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