Iterative improvement of the shallow-ice approximation

Souček, Ondřej; Martinec, Zdenĕk

doi:10.3189/002214308787779924

Cited by 11 publications

(11 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Most intermediate models are developed with the aim of improving the SIA model by accounting for the effects of LSG (Hubbard, 2000). As examples of this approach, Nye (1969), Shoemaker and Morland (1984), Kamb and Echelmeyer (1986), Marshall and others (2005) and Souček and Martinec (2008) introduce different physical or numerical means of parameterizing LSG effects. These methods are not completely satisfactory, however, as they add considerable mathematical and numerical complexity without fully describing the dynamical system.…”

Section: Introductionmentioning

confidence: 99%

Improvements to shear-deformational models of glacier dynamics through a longitudinal stress factor

Adhikari¹,

Marshall²

2011

J. Glaciol.

View full text Add to dashboard Cite

In a two-dimensional (plane strain) glacier domain, gravity-driven ice flow is balanced by basal drag and the resistance associated with longitudinal stress gradients. The plane strain Stokes model accommodates both these resistances, whereas several simpler models only account for basal drag. Solving the Stokes equations is numerically challenging and computationally expensive, but simpler models may lead to unrealistic dynamical behaviour. Here, we propose a factor which can be introduced in shear-deformational flow models to yield results comparable to those from the plane strain Stokes model. As this factor adapts simpler models to capture the effects of missing dynamics, i.e. longitudinal stress gradients, we refer to it as the longitudinal stress (L L-)factor. We assess the usefulness of this factor for idealized domains with complex basal topography and evolving geometry. We apply the model to Haig Glacier, Canadian Rockies, in order to present an illustration of how simulations of glacier response to climate forcing can be improved through the introduction of the L-factor in a shear-deformational flow model.

show abstract

Section: Introductionmentioning

confidence: 99%

Improvements to shear-deformational models of glacier dynamics through a longitudinal stress factor

Adhikari¹,

Marshall²

2011

J. Glaciol.

View full text Add to dashboard Cite

show abstract

“…While it is possible in the model to improve the SIA solution by an iterative algorithm, described in Souček and Martinec (2008) and successfully tested in Pattyn et al (2008), only the first step of the algorithm, corresponding to the SIA solution, is used in the presented simulation. The model is numerically implemented by a finite difference technique (Souček, 2010;Souček and Martinec, 2011).…”

Section: Description Of the Numerical Modelmentioning

confidence: 99%

A 3 Ga old polythermal ice sheet in Isidis Planitia, Mars: Dynamics and thermal regime inferred from numerical modeling

Souček

Bourgeois

Pochat

et al. 2015

Earth and Planetary Science Letters

Self Cite

View full text Add to dashboard Cite

“…The convergence of the iterative algorithm which is controlled by two projection parameters, is ensured by choosing the parameters sufficiently small. Souček & Martinec (2008) applied this iterative technique on modelling of glacier flow. These ideas warrant further investigation, because a non-trivial contribution of the toroidal-poloidal mode coupled magnetic signals to the geomagnetic field at ground-based magnetic observatories situated close to the shoreline necessitates accounting for it in geomagnetic coastal-effect modelling.…”

Section: O N C L U S I O N S a N D F U T U R E W O R Kmentioning

confidence: 99%

The modelling of the toroidal magnetic field induced by tidal ocean circulation

Dostál

Martinec

Thomas

2012

Geophysical Journal International

Self Cite

View full text Add to dashboard Cite

S U M M A R YObservations of the ocean-induced magnetic field by the CHAMP magnetic space mission have the potential to be used as a constraint when examining ocean dynamics. This has initiated theoretical studies on the prediction of the poloidal magnetic field induced by the horizontal ocean-circulation flow. This study deals with the computation and analysis of the toroidal magnetic field induced by the tidal ocean-circulation flow on the background of the main Earth's geomagnetic field. Since the induced toroidal magnetic field cannot be modelled by the single-layer approximation model used to predict the poloidal magnetic field, we treat the ocean as a spherical layer of a finite thickness and compute the toroidal magnetic field by a matrix-propagator technique with a source of electric currents in the ocean layer.Our numerical simulations based on the OMCT tidal ocean velocities show that the induced toroidal magnetic field is extremely sensitive to the vertical gradient of horizontal ocean flow. The larger this gradient, the stronger the induced toroidal magnetic field. Specifically, its magnitudes vary from 10 −2 nT for barotropic flow to several nT for baroclinic flow. We show that the induced toroidal magnetic field generated by M 2 tidal forcing is comparable in amplitude to the induced poloidal part of the field. The induced toroidal and poloidal magnetic fields differ, however, in their spatial behaviour.

show abstract

Iterative improvement of the shallow-ice approximation

Cited by 11 publications

References 16 publications

Improvements to shear-deformational models of glacier dynamics through a longitudinal stress factor

Improvements to shear-deformational models of glacier dynamics through a longitudinal stress factor

A 3 Ga old polythermal ice sheet in Isidis Planitia, Mars: Dynamics and thermal regime inferred from numerical modeling

The modelling of the toroidal magnetic field induced by tidal ocean circulation

Contact Info

Product

Resources

About