Modeling Thermodynamic Ice–Ocean Interactions at the Base of an Ice Shelf

doi:10.1175/1520-0485(1999)029<1787:MTIOIA>2.0.CO;2

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Modeling Thermodynamic Ice–Ocean Interactions at the Base of an Ice Shelf

Journal Article•DOI•

Modeling Thermodynamic Ice–Ocean Interactions at the Base of an Ice Shelf

David M. Holland¹, Adrian Jenkins²•Institutions (2)

Lamont–Doherty Earth Observatory¹, British Antarctic Survey²

01 Aug 1999-Journal of Physical Oceanography (American Meteorological Society)-Vol. 29, Iss: 8, pp 1787-1800

TL;DR: In this paper, a hierarchy of formulations that could be used to describe the interaction between ice and ocean is presented, with the main difference between them being the treatment of turbulent transfer within the oceanic boundary layer.

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Abstract: Models of ocean circulation beneath ice shelves are driven primarily by the heat and freshwater fluxes that are associated with phase changes at the ice–ocean boundary. Their behavior is therefore closely linked to the mathematical description of the interaction between ice and ocean that is included in the code. An hierarchy of formulations that could be used to describe this interaction is presented. The main difference between them is the treatment of turbulent transfer within the oceanic boundary layer. The computed response to various levels of thermal driving and turbulent agitation in the mixed layer is discussed, as is the effect of various treatments of the conductive heat flux into the ice shelf. The performance of the different formulations that have been used in models of sub-ice-shelf circulation is assessed in comparison with observations of the turbulent heat flux beneath sea ice. Formulations that include an explicit parameterization of the oceanic boundary layer give results that...

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Journal Article•DOI•

Present-Day Atmospheric Simulations Using GISS ModelE: Comparison to In Situ, Satellite, and Reanalysis Data

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Gavin A. Schmidt¹, Reto Ruedy¹, James Hansen¹, Igor Aleinov¹, N. Bell¹, Mike Bauer¹, Susanne E. Bauer¹, Brian Cairns¹, Vittorio Canuto¹, Y. Cheng¹, Anthony D. Del Genio¹, Greg Faluvegi¹, Andrew D. Friend, Timothy M. Hall¹, Yongyun Hu¹, Max Kelley, Nancy Y. Kiang¹, Dorothy Koch¹, Andrew A. Lacis¹, Jean Lerner¹, Ken K. Lo¹, Ron L. Miller¹, Larissa Nazarenko¹, Valdar Oinas¹, J. P. Perlwitz², Judith Perlwitz¹, David Rind¹, Anastasia Romanou¹, Gary L. Russell¹, Makiko Sato¹, Drew Shindell¹, Peter Stone², Shan Sun¹, N. Tausnev¹, Duane Thresher¹, Mao-Sung Yao¹ - Show less +32 more•Institutions (2)

Goddard Institute for Space Studies¹, Massachusetts Institute of Technology²

15 Jan 2006-Journal of Climate

TL;DR: The ModelE version of the GISS atmospheric general circulation model (GCM) and results for present-day climate simulations (ca. 1979) were presented in this article, where the model top is now above the stratopause, the number of vertical layers has increased, a new cloud microphysical scheme is used, vegetation biophysics now incorporates a sensitivity to humidity, atmospheric turbulence is calculated over the whole column, and new land snow and lake schemes are introduced.

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Abstract: A full description of the ModelE version of the Goddard Institute for Space Studies (GISS) atmospheric general circulation model (GCM) and results are presented for present-day climate simulations (ca. 1979). This version is a complete rewrite of previous models incorporating numerous improvements in basic physics, the stratospheric circulation, and forcing fields. Notable changes include the following: the model top is now above the stratopause, the number of vertical layers has increased, a new cloud microphysical scheme is used, vegetation biophysics now incorporates a sensitivity to humidity, atmospheric turbulence is calculated over the whole column, and new land snow and lake schemes are introduced. The performance of the model using three configurations with different horizontal and vertical resolutions is compared to quality-controlled in situ data, remotely sensed and reanalysis products. Overall, significant improvements over previous models are seen, particularly in upper-atmosphere te...

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927 citations

Cites background from "Modeling Thermodynamic Ice–Ocean In..."

...The boundary salinity then sets the freezing point for the interface (Holland and Jenkins 1999; Schmidt et al. 2004)....
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DOI•

NEMO ocean engine

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Gurvan Madec

01 Jan 2008

TL;DR: The ocean engine of NEMO (Nucleus for European Modelling of the Ocean) is a primitive equation model adapted to regional and global ocean circulation problems as discussed by the authors, which is intended to be a flexible tool for studying the ocean and its interactions with the others components of the earth climate system over a wide range of space and time scales.

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Abstract: Résumé The ocean engine of NEMO (Nucleus for European Modelling of the Ocean) is a primitive equation model adapted to regional and global ocean circulation problems. It is intended to be a flexible tool for studying the ocean and its interactions with the others components of the earth climate system over a wide range of space and time scales. Prognostic variables are the three-dimensional velocity field, a linear or non-linear sea surface height, the temperature and the salinity. In the horizontal direction, the model uses a curvilinear orthogonal grid and in the vertical direction, a full or partial step z-coordinate, or s-coordinate, or a mixture of the two. The distribution of variables is a three-dimensional Arakawa C-type grid. Various physical choices are available to describe ocean physics, including TKE, GLS and KPP vertical physics. Within NEMO, the ocean is interfaced with a sea-ice model (LIM v2 and v3), passive tracer and biogeochemical models (TOP) and, via the OASIS coupler, with several atmospheric general circulation models. It also support two-way grid embedding via the AGRIF software. Le moteur océanique de NEMO (Nucleus for European Modelling of the Ocean) est un modèle aux équations primitives de la circulation océanique régionale et globale. Il se veut un outil flexible pour étudier sur un vaste spectre spatiotemporel l’océan et ses interactions avec les autres composantes du système climatique terrestre. Les variables pronostiques sont le champ tridimensionnel de vitesse, une hauteur de la mer linéaire ou non, la temperature et la salinité. La distribution des variables se fait sur une grille C d’Arakawa tridimensionnelle utilisant une coordonnée verticale z à niveaux entiers ou partiels, ou une coordonnée s, ou encore une combinaison des deux. Différents choix sont proposés pour décrire la physique océanique, incluant notamment des physiques verticales TKE, GLS et KPP. A travers l’infrastructure NEMO, l’océan est interfacé avec des modèles de glace de mer, de biogéochimie et de traceurs passifs, et, via le coupleur OASIS, à plusieurs modèles de circulation générale atmosphérique. Il supporte également l’emboı̂tement interactif de maillages via le logiciel AGRIF.

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926 citations

Cites background from "Modeling Thermodynamic Ice–Ocean In..."

...See Holland and Jenkins [1999] for all the details on this formulation....
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Journal Article•DOI•

Convection-driven melting near the grounding lines of ice shelves and tidewater glaciers

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Adrian Jenkins¹•Institutions (1)

Natural Environment Research Council¹

01 Dec 2011-Journal of Physical Oceanography

TL;DR: In this paper, the authors used the theory of buoyant plumes that has previously been applied to the study of the larger-scale circulation beneath ice shelves to investigate variability in melting induced by changes in both ocean temperature and subglacial discharge for a number of realistic examples of ice shelves and tidewater glaciers.

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Abstract: Subglacial meltwater draining along the bed of fast-flowing, marine-terminating glaciers emerges at the groundingline,wheretheiceeithergoesafloattoformaniceshelforterminates inacalvingface.Theinputof freshwater to the ocean provides a source of buoyancy and drives convective motion alongside the ice‐ocean interface. This process is modeled using the theory of buoyant plumes that has previously been applied to the study of the larger-scale circulation beneath ice shelves. The plume grows through entrainment of ocean waters, and the heat brought into the plume as a result drives melting at the ice‐ocean interface. The equations are nondimensionalized by using scales appropriate for the region where the subglacial drainage, rather than the subsequent addition of meltwater, supplies the majority of the buoyancy forcing. It is found that the melt rate within this region can be approximated reasonably well by a function that is linear in ocean temperature, has a cube root dependence on the flux of subglacial meltwater, and has a complex dependency on the slope of the ice‐ocean interface. The model is used to investigate variability in melting induced by changes in both ocean temperature and subglacial discharge for a number of realistic examples of ice shelves and tidewater glaciers. The results show how warming ocean waters and increasing subglacial drainage both generate increases in melting near the grounding line.

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391 citations

Cites background or methods from "Modeling Thermodynamic Ice–Ocean In..."

...…second term on the left-hand side of (7) represents the heat conducted into the ice shelf; is derived by considering steady-state, one-dimensional advection and diffusion perpendicular to the melting interface; and is applicable for Péclet numbers greater than about 5 (Holland and Jenkins 1999)....
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...The second term on the left-hand side of (7) represents the heat conducted into the ice shelf; is derived by considering steady-state, one-dimensional advection and diffusion perpendicular to the melting interface; and is applicable for Péclet numbers greater than about 5 (Holland and Jenkins 1999). Equation (9) is a linearization of the liquidus relationship that facilitates algebraic solution of (7)–(9). The last term gives the dependence of the freezing point on the depth of the ice shelf base Zb. Jenkins (1991) used expressions for the thermal and haline Stanton numbers, Cd GT and Cd GS, that were derived from laboratory studies of boundary layers adjacent to hydraulically smooth surfaces (Kader and Yaglom 1972, 1977)....
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...The second term on the left-hand side of (7) represents the heat conducted into the ice shelf; is derived by considering steady-state, one-dimensional advection and diffusion perpendicular to the melting interface; and is applicable for Péclet numbers greater than about 5 (Holland and Jenkins 1999). Equation (9) is a linearization of the liquidus relationship that facilitates algebraic solution of (7)–(9). The last term gives the dependence of the freezing point on the depth of the ice shelf base Zb. Jenkins (1991) used expressions for the thermal and haline Stanton numbers, Cd GT and Cd GS, that were derived from laboratory studies of boundary layers adjacent to hydraulically smooth surfaces (Kader and Yaglom 1972, 1977). However, the weak dependence of the derived expressions on plume Reynolds number is unvalidated by geophysical-scale observations, and constant Stanton numbers appear to be at least as good a choice (McPhee 1992; McPhee et al. 1999; Jenkins et al. 2010). Equations (3) and (4) are slightly modified from their original form to ensure conservation of heat and salt (Jenkins et al. 2001). Values adopted for the physical constants are given in Table 1. McPhee (1992) and McPhee et al....
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...The second term on the left-hand side of (7) represents the heat conducted into the ice shelf; is derived by considering steady-state, one-dimensional advection and diffusion perpendicular to the melting interface; and is applicable for Péclet numbers greater than about 5 (Holland and Jenkins 1999). Equation (9) is a linearization of the liquidus relationship that facilitates algebraic solution of (7)–(9). The last term gives the dependence of the freezing point on the depth of the ice shelf base Zb. Jenkins (1991) used expressions for the thermal and haline Stanton numbers, Cd GT and Cd GS, that were derived from laboratory studies of boundary layers adjacent to hydraulically smooth surfaces (Kader and Yaglom 1972, 1977). However, the weak dependence of the derived expressions on plume Reynolds number is unvalidated by geophysical-scale observations, and constant Stanton numbers appear to be at least as good a choice (McPhee 1992; McPhee et al. 1999; Jenkins et al. 2010). Equations (3) and (4) are slightly modified from their original form to ensure conservation of heat and salt (Jenkins et al. 2001). Values adopted for the physical constants are given in Table 1. McPhee (1992) and McPhee et al. (1999) recommend the use of a simpler formulation for the heat balance at the ice–ocean interface,...
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...The second term on the left-hand side of (7) represents the heat conducted into the ice shelf; is derived by considering steady-state, one-dimensional advection and diffusion perpendicular to the melting interface; and is applicable for Péclet numbers greater than about 5 (Holland and Jenkins 1999)....
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Journal Article•DOI•

Continental scale, high order, high spatial resolution, ice sheet modeling using the Ice Sheet System Model (ISSM)

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Eric Larour¹, Helene Seroussi², Helene Seroussi¹, Mathieu Morlighem¹, Mathieu Morlighem², Eric Rignot¹, Eric Rignot³ - Show less +3 more•Institutions (3)

California Institute of Technology¹, École Centrale Paris², University of California, Irvine³

01 Mar 2012-Journal of Geophysical Research

TL;DR: In this article, the authors present a new thermomechanical finite element model of ice flow named ISSM (Ice Sheet System Model) that includes higher-order stresses, high spatial resolution capability and data assimilation techniques to better capture ice dynamics and produce realistic simulations of ice sheet flow at the continental scale.

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Abstract: Ice flow models used to project the mass balance of ice sheets in Greenland and Antarctica usually rely on the Shallow Ice Approximation (SIA) and the Shallow-Shelf Approximation (SSA), sometimes combined into so-called hybrid models. Such models, while computationally efficient, are based on a simplified set of physical assumptions about the mechanical regime of the ice flow, which does not uniformly apply everywhere on the ice sheet/ice shelf system, especially near grounding lines, where rapid changes are taking place at present. Here, we present a new thermomechanical finite element model of ice flow named ISSM (Ice Sheet System Model) that includes higher-order stresses, high spatial resolution capability and data assimilation techniques to better capture ice dynamics and produce realistic simulations of ice sheet flow at the continental scale. ISSM includes several approximations of the momentum balance equations, ranging from the two-dimensional SSA to the three-dimensional full-Stokes formulation. It also relies on a massively parallelized architecture and state-of-the-art scalable tools. ISSM employs data assimilation techniques, at all levels of approximation of the momentum balance equations, to infer basal drag at the ice-bed interface from satellite radar interferometry-derived observations of ice motion. Following a validation of ISSM with standard benchmarks, we present a demonstration of its capability in the case of the Greenland Ice Sheet. We show ISSM is able to simulate the ice flow of an entire ice sheet realistically at a high spatial resolution, with higher-order physics, thereby providing a pathway for improving projections of ice sheet evolution in a warming climate. Copyright 2012 by the American Geophysical Union.

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389 citations

Cites methods from "Modeling Thermodynamic Ice–Ocean In..."

...Under floating ice, we use the simple parameterization from Holland and Jenkins [1999]:...
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Journal Article•DOI•

Strong Sensitivity of Pine Island Ice-Shelf Melting to Climatic Variability

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Pierre Dutrieux¹, Jan De Rydt¹, Adrian Jenkins¹, Paul R. Holland¹, Ho Kyung Ha², SangHoon Lee², Eric J. Steig³, Qinghua Ding³, E. Povl Abrahamsen¹, Michael Schröder⁴ - Show less +6 more•Institutions (4)

Natural Environment Research Council¹, Korean Ocean Research and Development Institute², University of Washington³, Alfred Wegener Institute for Polar and Marine Research⁴

10 Jan 2014-Science

TL;DR: Observations and numerical modeling reveal large fluctuations in the ocean heat available in the adjacent bay and enhanced sensitivity of ice-shelf melting to water temperatures at intermediate depth, as a seabed ridge blocks the deepest and warmest waters from reaching the thickest ice.

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Abstract: Pine Island Glacier has thinned and accelerated over recent decades, significantly contributing to global sea-level rise. Increased oceanic melting of its ice shelf is thought to have triggered those changes. Observations and numerical modeling reveal large fluctuations in the ocean heat available in the adjacent bay and enhanced sensitivity of ice-shelf melting to water temperatures at intermediate depth, as a seabed ridge blocks the deepest and warmest waters from reaching the thickest ice. Oceanic melting decreased by 50% between January 2010 and 2012, with ocean conditions in 2012 partly attributable to atmospheric forcing associated with a strong La Nina event. Both atmospheric variability and local ice shelf and seabed geometry play fundamental roles in determining the response of the Antarctic Ice Sheet to climate.

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354 citations

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References

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A First Course in Turbulence

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Henk Tennekes, John L. Lumley

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TL;DR: In this paper, the authors present a reference record created on 2005-11-18, modified on 2016-08-08 and used for the analysis of turbulence and transport in the context of energie.

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Abstract: Keywords: turbulence ; transport ; contraintes ; transport ; couche : limite ; ecoulement ; tourbillon ; energie Reference Record created on 2005-11-18, modified on 2016-08-08

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8,276 citations

"Modeling Thermodynamic Ice–Ocean In..." refers background in this paper

...Values for the first three of these are given in Table 1, while we estimate the sublayer thickness to be (Tennekes and Lumley 1972, p. 160) n h 5 5 ....
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Mathematical Methods for Physicists

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The Physics of Glaciers

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W.S.B. Paterson, John T. Andrews

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TL;DR: In this paper, the transformation of snow to ice mass balance heat budget and climatology structure and deformation of ice hydraulics and glaciers glacier sliding deformation, subglacial till structures and fabrics in glaciers and ice sheets distribution of temperature in glaciers, flow of ice shelves and ice streams non-steady flow of glaciers, ice sheets surging and tidewater glaciers ice core studies.

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Abstract: The transformation of snow to ice mass balance heat budget and climatology structure and deformation of ice hydraulics and glaciers glacier sliding deformation of subglacial till structures and fabrics in glaciers and ice sheets distribution of temperature in glaciers and ice sheets steady flow of glaciers and ice sheets flow of ice shelves and ice streams non-steady flow of glaciers and ice sheets surging and tidewater glaciers ice core studies.

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4,450 citations

"Modeling Thermodynamic Ice–Ocean In..." refers methods in this paper

...(19) reduces to the equation used by Wexler (1960) (see also discussion by Paterson 1994, p. 204): 2] T w ]TI I I1 5 0, (22) 2 T]z k ]zI where rMw 5 w ....
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Mathematical methods for physicists

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George B. Arfken, Hans Weber

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"Modeling Thermodynamic Ice–Ocean In..." refers background in this paper

...(27) is ill-defined for a melt rate of zero, a problem that may be overcome by rewriting the right-hand side as a power series (Arfken 1970) of the form...
[...]

Journal Article•DOI•

Circulation and bottom water production in the Weddell Sea

[...]

A.E. Gill¹•Institutions (1)

University of Cambridge¹

01 Feb 1973-Deep Sea Research and Oceanographic Abstracts

TL;DR: In this article, a study of the distribution of temperature and salinity in the Weddell Sea is presented, showing that there is a circulation on the shelf in the vertical plane which carries about 106 m3sec−1 of water off the shelf.

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425 citations

"Modeling Thermodynamic Ice–Ocean In..." refers background in this paper

...It is commonly assumed that atmospheric forcing of the ocean and ice cover is the primary driving mechanism behind the deep convection that occurs over the continental slope (e.g., Gill 1973)....
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...It is commonly assumed that atmospheric forcing of the ocean and ice cover is the primary driving mechanism behind the deep convection that occurs over the continental slope (e.g., Gill 1973 )....
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