A rapidly converging initialisation method to simulate the present-day Greenland ice sheet using the GRISLI ice sheet model (version 1.3)

Abstract. Providing reliable projections of the ice sheet contribution to future sea-level rise has become one of the main challenges of the ice sheet modelling community. To increase confidence in future projections, a good knowledge of the present-day state of ice flow dynamics, which is critically dependent on basal conditions, is strongly needed. The main difficulty is tied to the scarcity of observations at the ice–bed interface at the scale of the whole ice sheet, resulting in poorly constrained parameterisations in ice sheet models. To circumvent this drawback, inverse modelling approaches can be developed to infer initial conditions for ice sheet models that best reproduce available data. Most often such approaches allow for a good representation of the mean present-day state of the ice sheet but are accompanied with unphysical trends. Here, we present an initialisation method for the Greenland ice sheet using the thermo-mechanical hybrid GRISLI (GRenoble Ice Shelf and Land Ice) ice sheet model. Our approach is based on the adjustment of the basal drag coefficient that relates the sliding velocities at the ice–bed interface to basal shear stress in unfrozen bed areas. This method relies on an iterative process in which the basal drag is periodically adjusted in such a way that the simulated ice thickness matches the observed one. The quality of the method is assessed by computing the root mean square errors in ice thickness changes. Because the method is based on an adjustment of the sliding velocities only, the results are discussed in terms of varying ice flow enhancement factors that control the deformation rates. We show that this factor has a strong impact on the minimisation of ice thickness errors and has to be chosen as a function of the internal thermal state of the ice sheet (e.g. a low enhancement factor for a warm ice sheet). While the method performance slightly increases with the duration of the minimisation procedure, an ice thickness root mean square error (RMSE) of 50.3 m is obtained in only 1320 model years. This highlights a rapid convergence and demonstrates that the method can be used for computationally expensive ice sheet models.

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A rapidly converging spin-up method for the present-day Greenland ice sheet using the GRISLI ice-sheet model

10.5194/gmd-2017-322 ◽

2018 ◽

Cited By ~ 3

Author(s):

Sébastien Le clec'h ◽

Aurélien Quiquet ◽

Sylvie Charbit ◽

Christophe Dumas ◽

Masa Kageyama ◽

...

Keyword(s):

Sea Level ◽

Initial Conditions ◽

Ice Sheet ◽

Greenland Ice Sheet ◽

Flow Dynamics ◽

Ice Thickness ◽

Rapid Convergence ◽

Ice Flow ◽

Ice Volume ◽

Basal Shear

Abstract. Providing reliable projections of the ice-sheet contribution to future sea-level rise has become one of the main challenges of the ice-sheet modelling community. To increase confidence in future projections, a good knowledge of the present-day state of the ice flow dynamics, which is critically dependent on basal conditions, is strongly needed. The main difficulty is tied to the scarcity of observations at the ice-bed interface at the scale of the whole ice sheet, resulting in poorly constrained parameterisations in ice-sheet models. To circumvent this drawback, inverse modelling approaches can be developed and validated against available data to infer reliable initial conditions of the ice sheet. Here, we present a spin-up method for the Greenland ice sheet using the thermo-mechanical hybrid GRISLI ice-sheet model. Our approach is based on the adjustment of the basal drag coefficient that relates the sliding velocities at the ice-bed interface to basal shear stress in unfrozen bed areas. This method relies on an iterative process in which the basal drag is periodically adjusted in such as way that the simulated ice thickness matches the observed one. The process depends on three parameters controlling the duration and the number of iterations. The best spin-up parameters are chosen according to two criteria to minimize errors in sea-level projections: the final difference between the simulated and the observed Greenland ice volume as well as the final ice volume trend which must both be as low as possible. To increase confidence in the inferred parameters, we also make sure that the final ice thickness root mean square error from the observations is not greater than a few tens of meters. Our best results are obtained after only 420 years of simulation, highlighting a rapid convergence and demonstrating that our method can be used for computationally expensive ice sheet models.

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Ice-dynamic projections of the Greenland ice sheet in response to atmospheric and oceanic warming

The Cryosphere Discussions ◽

10.5194/tcd-8-3851-2014 ◽

2014 ◽

Vol 8 (4) ◽

pp. 3851-3905 ◽

Cited By ~ 2

Author(s):

J. J. Fürst ◽

H. Goelzer ◽

P. Huybrechts

Keyword(s):

Sea Level Rise ◽

Sea Level ◽

Flow Model ◽

Ice Sheet ◽

Greenland Ice Sheet ◽

Surface Melting ◽

Strong Impact ◽

Ice Dynamics ◽

Ice Flow ◽

Over Time

Abstract. Continuing global warming will have a strong impact on the Greenland ice sheet in the coming centuries. During the last decade, both increased surface melting and enhanced ice discharge from calving glaciers have contributed 0.6 ± 0.1 mm yr−1 to global sea-level rise, roughly in shares of respectively 60 and 40 per cent. Here we use a higher-order ice flow model, initialised to the present state, to simulate future ice volume changes driven by both atmospheric and oceanic temperature changes. For these projections, the ice flow model accounts for runoff-induced basal lubrication and ocean warming-induced discharge increase at the marine margins. For a suite of ten Atmosphere and Ocean General Circulation Models and four Representative Concentration Pathway scenarios, the projected sea-level rise lies in the range of +1.4 to +16.6 cm by the year 2100. For two low emission scenarios, the projections are conducted up to 2300. Ice loss rates are found to either abate when the warming already peaks in this century, allowing to preserve the ice sheet in a geometry close to the present-day state, or to remain at a constant level over three hundred years under moderate warming. The volume loss is predominantly caused by increased surface melting as the contribution from enhanced ice discharge decreases over time and is self-limited by thinning and retreat of the marine margin reducing the ice–ocean contact area. The effect of enhanced basal lubrication on the volume evolution is found to be negligible on centennial time scales. The presented projections show that the observed rates of volume change over the last decades cannot simply be extrapolated over the 21st century on account of a different balance of processes causing ice loss over time. The results also indicate that the largest source of uncertainty arises from the surface mass balance and the underlying climate change projections, and not from ice dynamics.

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An analysis of balance velocities over the Greenland ice sheet and comparison with synthetic aperture radar interferometry

Journal of Glaciology ◽

10.3189/172756500781833412 ◽

2000 ◽

Vol 46 (152) ◽

pp. 67-74 ◽

Cited By ~ 48

Author(s):

J. L. Bamber ◽

R. J. Hardy ◽

I. Joughin

Keyword(s):

Synthetic Aperture Radar ◽

Ice Sheet ◽

Greenland Ice Sheet ◽

Ablation Rate ◽

Sar Interferometry ◽

Synthetic Aperture ◽

Ice Thickness ◽

Good Representation ◽

Elevation Model ◽

Aperture Radar

AbstractBalance velocities for the Greenland ice sheet have been calculated from a new digital elevation model (DEM), accumulation rates and an existing ice-thickness grid, using a fully two-dimensional finite-difference scheme. The pattern of velocities is compared with velocities derived from synthetic-aperture radar (SAR) interferometry for three different regions of the ice sheet. Differences between the two estimates of velocity highlight the respective strengths and weaknesses of the datasets and techniques used. A comparison with ten global positioning system-derived velocities indicates that the balance-velocity scheme and input datasets used here provide a remarkably good representation of the velocity distribution inland from the margins. These balance-velocity data, therefore, could help constrain numerical ice-sheet models. The balance velocities were found to be unreliable close to the ice-sheet margins due to larger errors in ice thickness, surface slope and ablation rate in this region. Comparison of the balance velocities with SAR interferometry in the region of the “Northeast Greenland Ice Stream” indicates the importance of the smoothing distance that must be applied to the DEM before calculating balance velocities. A smoothing distance of 20 times the ice thickness gave good agreement between the two measures of velocity.

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Histamine Control in Raw and Processed Tuna: A Rapid Tool Based on NIR Spectroscopy

Foods ◽

10.3390/foods10040885 ◽

2021 ◽

Vol 10 (4) ◽

pp. 885

Author(s):

Sergio Ghidini ◽

Luca Maria Chiesa ◽

Sara Panseri ◽

Maria Olga Varrà ◽

Adriana Ianieri ◽

...

Keyword(s):

Root Mean Square ◽

Near Infrared ◽

Nir Spectroscopy ◽

Partial Least Square ◽

Least Square ◽

Partial Least Square Regression ◽

Coefficient Of Determination ◽

Mean Square ◽

Tuna Fish ◽

Mean Square Errors

The present study was designed to investigate whether near infrared (NIR) spectroscopy with minimal sample processing could be a suitable technique to rapidly measure histamine levels in raw and processed tuna fish. Calibration models based on orthogonal partial least square regression (OPLSR) were built to predict histamine in the range 10–1000 mg kg−1 using the 1000–2500 nm NIR spectra of artificially-contaminated fish. The two models were then validated using a new set of naturally contaminated samples in which histamine content was determined by conventional high-performance liquid chromatography (HPLC) analysis. As for calibration results, coefficient of determination (r2) > 0.98, root mean square of estimation (RMSEE) ≤ 5 mg kg−1 and root mean square of cross-validation (RMSECV) ≤ 6 mg kg−1 were achieved. Both models were optimal also in the validation stage, showing r2 values > 0.97, root mean square errors of prediction (RMSEP) ≤ 10 mg kg−1 and relative range error (RER) ≥ 25, with better results showed by the model for processed fish. The promising results achieved suggest NIR spectroscopy as an implemental analytical solution in fish industries and markets to effectively determine histamine amounts.

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Coherent radar ice thickness measurements over the Greenland ice sheet

Journal of Geophysical Research Atmospheres ◽

10.1029/2001jd900183 ◽

2001 ◽

Vol 106 (D24) ◽

pp. 33761-33772 ◽

Cited By ~ 126

Author(s):

S. Gogineni ◽

D. Tammana ◽

D. Braaten ◽

C. Leuschen ◽

T. Akins ◽

...

Keyword(s):

Ice Sheet ◽

Greenland Ice Sheet ◽

Ice Thickness ◽

Coherent Radar ◽

Thickness Measurements

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

Journal of Glaciology ◽

10.3189/s0022143000009345 ◽

1989 ◽

Vol 35 (121) ◽

pp. 406-417 ◽

Cited By ~ 1

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.

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Ice-dynamic projections of the Greenland ice sheet in response to atmospheric and oceanic warming

The Cryosphere ◽

10.5194/tc-9-1039-2015 ◽

2015 ◽

Vol 9 (3) ◽

pp. 1039-1062 ◽

Cited By ~ 57

Author(s):

J. J. Fürst ◽

H. Goelzer ◽

P. Huybrechts

Keyword(s):

Sea Level Rise ◽

Sea Level ◽

Flow Model ◽

Ice Sheet ◽

Greenland Ice Sheet ◽

Water Runoff ◽

Strong Impact ◽

Ice Dynamics ◽

Over Time ◽

Loss Rates

Abstract. Continuing global warming will have a strong impact on the Greenland ice sheet in the coming centuries. During the last decade (2000–2010), both increased melt-water runoff and enhanced ice discharge from calving glaciers have contributed 0.6 ± 0.1 mm yr−1 to global sea-level rise, with a relative contribution of 60 and 40% respectively. Here we use a higher-order ice flow model, spun up to present day, to simulate future ice volume changes driven by both atmospheric and oceanic temperature changes. For these projections, the flow model accounts for runoff-induced basal lubrication and ocean warming-induced discharge increase at the marine margins. For a suite of 10 atmosphere and ocean general circulation models and four representative concentration pathway scenarios, the projected sea-level rise between 2000 and 2100 lies in the range of +1.4 to +16.6 cm. For two low emission scenarios, the projections are conducted up to 2300. Ice loss rates are found to abate for the most favourable scenario where the warming peaks in this century, allowing the ice sheet to maintain a geometry close to the present-day state. For the other moderate scenario, loss rates remain at a constant level over 300 years. In any scenario, volume loss is predominantly caused by increased surface melting as the contribution from enhanced ice discharge decreases over time and is self-limited by thinning and retreat of the marine margin, reducing the ice–ocean contact area. As confirmed by other studies, we find that the effect of enhanced basal lubrication on the volume evolution is negligible on centennial timescales. Our projections show that the observed rates of volume change over the last decades cannot simply be extrapolated over the 21st century on account of a different balance of processes causing ice loss over time. Our results also indicate that the largest source of uncertainty arises from the surface mass balance and the underlying climate change projections, not from ice dynamics.

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Sensitivity of Greenland Ice Sheet Projections to Model Formulations

Journal of Glaciology ◽

10.3189/2013jog12j182 ◽

2013 ◽

Vol 59 (216) ◽

pp. 733-749 ◽

Cited By ~ 87

Author(s):

H. Goelzer ◽

P. Huybrechts ◽

J.J. Fürst ◽

F.M. Nick ◽

M.L. Andersen ◽

...

Keyword(s):

Regional Climate Model ◽

Sea Level ◽

Flow Model ◽

Climate Model ◽

Regional Climate ◽

Ice Sheet ◽

Greenland Ice Sheet ◽

Ice Flow ◽

Outlet Glacier ◽

Glacier Dynamics

AbstractPhysically based projections of the Greenland ice sheet contribution to future sea-level change are subject to uncertainties of the atmospheric and oceanic climatic forcing and to the formulations within the ice flow model itself. Here a higher-order, three-dimensional thermomechanical ice flow model is used, initialized to the present-day geometry. The forcing comes from a high-resolution regional climate model and from a flowline model applied to four individual marine-terminated glaciers, and results are subsequently extended to the entire ice sheet. The experiments span the next 200 years and consider climate scenario SRES A1B. The surface mass-balance (SMB) scheme is taken either from a regional climate model or from a positive-degree-day (PDD) model using temperature and precipitation anomalies from the underlying climate models. Our model results show that outlet glacier dynamics only account for 6–18% of the sea-level contribution after 200 years, confirming earlier findings that stress the dominant effect of SMB changes. Furthermore, interaction between SMB and ice discharge limits the importance of outlet glacier dynamics with increasing atmospheric forcing. Forcing from the regional climate model produces a 14–31 % higher sea-level contribution compared to a PDD model run with the same parameters as for IPCC AR4.

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Evidence That Supertriangles Exist in Nature from the Vertical Projections of Koelreuteria paniculata Fruit

Symmetry ◽

10.3390/sym14010023 ◽

2021 ◽

Vol 14 (1) ◽

pp. 23

Author(s):

Yuping Li ◽

Brady K. Quinn ◽

Johan Gielis ◽

Yirong Li ◽

Peijian Shi

Keyword(s):

Root Mean Square ◽

Goodness Of Fit ◽

Mean Square ◽

Sea Stars ◽

Different Types ◽

Koelreuteria Paniculata ◽

Two Parameters ◽

Mean Square Errors

Many natural radial symmetrical shapes (e.g., sea stars) follow the Gielis equation (GE) or its twin equation (TGE). A supertriangle (three triangles arranged around a central polygon) represents such a shape, but no study has tested whether natural shapes can be represented as/are supertriangles or whether the GE or TGE can describe their shape. We collected 100 pieces of Koelreuteria paniculata fruit, which have a supertriangular shape, extracted the boundary coordinates for their vertical projections, and then fitted them with the GE and TGE. The adjusted root mean square errors (RMSEadj) of the two equations were always less than 0.08, and >70% were less than 0.05. For 57/100 fruit projections, the GE had a lower RMSEadj than the TGE, although overall differences in the goodness of fit were non-significant. However, the TGE produces more symmetrical shapes than the GE as the two parameters controlling the extent of symmetry in it are approximately equal. This work demonstrates that natural supertriangles exist, validates the use of the GE and TGE to model their shapes, and suggests that different complex radially symmetrical shapes can be generated by the same equation, implying that different types of biological symmetry may result from the same biophysical mechanisms.

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Winter drainage of surface lakes on the Greenland Ice Sheet from Sentinel-1 SAR imagery

The Cryosphere ◽

10.5194/tc-15-1587-2021 ◽

2021 ◽

Vol 15 (3) ◽

pp. 1587-1606

Author(s):

Corinne L. Benedek ◽

Ian C. Willis

Keyword(s):

Ice Sheet ◽

Greenland Ice Sheet ◽

Shape From Shading ◽

Lake Area ◽

Ice Flow ◽

Surface Mass ◽

Flow Acceleration ◽

Optical Imagery ◽

Sar Imagery ◽

Lake Drainage

Abstract. Surface lakes on the Greenland Ice Sheet play a key role in its surface mass balance, hydrology and biogeochemistry. They often drain rapidly in the summer via hydrofracture, which delivers lake water to the ice sheet base over timescales of hours to days and then can allow meltwater to reach the base for the rest of the summer. Rapid lake drainage, therefore, influences subglacial drainage evolution; water pressures; ice flow; biogeochemical activity; and ultimately the delivery of water, sediments and nutrients to the ocean. It has generally been assumed that rapid lake drainage events are confined to the summer, as this is typically when observations are made using satellite optical imagery. Here we develop a method to quantify backscatter changes in satellite radar imagery, which we use to document the drainage of six different lakes during three winters (2014/15, 2015/16 and 2016/17) in fast-flowing parts of the Greenland Ice Sheet. Analysis of optical imagery from before and after the three winters supports the radar-based evidence for winter lake drainage events and also provides estimates of lake drainage volumes, which range between 0.000046 ± 0.000017 and 0.0200 ± 0.002817 km3. For three of the events, optical imagery allows repeat photoclinometry (shape from shading) calculations to be made showing mean vertical collapse of the lake surfaces ranging between 1.21 ± 1.61 and 7.25 ± 1.61 m and drainage volumes of 0.002 ± 0.002968 to 0.044 ± 0.009858 km3. For one of these three, time-stamped ArcticDEM strips allow for DEM differencing, which demonstrates a mean collapse depth of 2.17 ± 0.28 m across the lake area. The findings show that lake drainage can occur in the winter in the absence of active surface melt and notable ice flow acceleration, which may have important implications for subglacial hydrology and biogeochemical processes.

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