Improving the numerical convergence of viscous-plastic sea ice models with the Jacobian-free Newton–Krylov method

Lemieux, Jean‐François; Tremblay, Bruno; Sedláčék, Jan; Tupper, Paul; Thomas, Stephen J.; Huard, David; Auclair, Jean-Pierre

doi:10.1016/j.jcp.2009.12.011

Cited by 58 publications

(43 citation statements)

References 33 publications

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“…This includes research on developing different solvers for the standard VP/EVP rheology (e.g. Lemieux et al, 2010;Kimmritz et al, 2015), different rheologies (e.g. Tremblay and Mysak, 1997;Hopkins, 2004;Schreyer et al, 2006;Wilchinsky and Feltham, 2006;Sulsky et al, 2007;Girard et al, 2011;Tsamados et al, 2013;Herman, 2016;Rabatel et al, 2015;Dansereau et al, 2016), and wind and/or ocean drag parameterisations (e.g.…”

Section: P Rampal Et Al: Nextsim: a New Lagrangian Sea Ice Modelmentioning

confidence: 99%

neXtSIM: a new Lagrangian sea ice model

et al. 2016

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Abstract. The Arctic sea ice cover has changed drastically over the last decades. Associated with these changes is a shift in dynamical regime seen by an increase of extreme fracturing events and an acceleration of sea ice drift. The highly non-linear dynamical response of sea ice to external forcing makes modelling these changes and the future evolution of Arctic sea ice a challenge for current models. It is, however, increasingly important that this challenge be better met, both because of the important role of sea ice in the climate system and because of the steady increase of industrial operations in the Arctic. In this paper we present a new dynamical/thermodynamical sea ice model called neXtSIM that is designed to address this challenge. neXtSIM is a continuous and fully Lagrangian model, whose momentum equation is discretised with the finite-element method. In this model, sea ice physics are driven by the combination of two core components: a model for sea ice dynamics built on a mechanical framework using an elasto-brittle rheology, and a model for sea ice thermodynamics providing damage healing for the mechanical framework. The evaluation of the model performance for the Arctic is presented for the period September 2007 to October 2008 and shows that observed multiscale statistical properties of sea ice drift and deformation are well captured as well as the seasonal cycles of ice volume, area, and extent. These results show that neXtSIM is an appropriate tool for simulating sea ice over a wide range of spatial and temporal scales.

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Section: P Rampal Et Al: Nextsim: a New Lagrangian Sea Ice Modelmentioning

confidence: 99%

neXtSIM: a new Lagrangian sea ice model

et al. 2016

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“…The sea‐ice momentum equations are solved on a Cartesian grid (polar stereographic projection) with

Δ x = Δ y =

10 km spatial resolution. They are discretized on an Arakawa C‐grid and solved numerically using a 1 hour time step and a Jacobian Free Newton‐Krylov (JFNK) method [ Lemieux et al ., ]. In each Newton Loop (NL) of the JFNK solver, the linearized set of equations are solved iteratively using the preconditioned Generalized Minimum RESidual (GMRES) method [ Lemieux et al ., ].…”

Section: Modelmentioning

confidence: 99%

Using sea‐ice deformation fields to constrain the mechanical strength parameters of geophysical sea ice

Bouchat

Tremblay

2017

JGR Oceans

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We investigate the ability of viscous‐plastic (VP) sea‐ice models with an elliptical yield curve and normal flow rule to reproduce the shear and divergence distributions derived from the RADARSAT Geophysical Processor System (RGPS). In particular, we reformulate the VP elliptical rheology to allow independent changes in the ice compressive, shear and isotropic tensile strength parameters ( P∗, S∗, and T∗, respectively) in order to study the sensitivity of the deformation distributions to changes in the ice mechanical strength parameters. Our 10 km VP simulation with standard ice mechanical strength parameters P∗ = 27.5 kN m−2, S∗ = 6.9 kN m−2, and T∗ = 0 kN m−2 (ellipse aspect ratio of e = 2) does not reproduce the large shear and divergence deformations observed in the RGPS deformation fields, and specifically lacks well‐defined, active linear kinematic features (LKFs). Probability density functions (PDFs) for the shear and divergence of are nonetheless not Gaussian. Reducing the ice compressive strength (with constant S∗ and T∗) or increasing the ice shear strength (with constant P∗ and T∗) both results in shear and divergence PDFs in better agreement with RGPS distributions. The isotropic tensile strength of sea ice does not significantly affect the shear and divergence distributions. When considering additional metrics such as the ice drift error, mean ice thickness fields, and spatial scaling of the total deformations, our results suggest that reducing the ice compressive strength P∗ (while keeping S∗ constant, i.e. reducing the ellipse aspect ratio) is a better solution than increasing the shear strength to improve simulations of the Arctic sea‐ice cover with the VP elliptical rheology.

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“…In our model, the dynamics is solved with the implicit‐explicit time integration scheme described in Lemieux et al . [] which is built around a Jacobian‐free Newton‐Krylov solver [ Lemieux et al ., ]. As h, A, and u evolve from one Newton iteration to the next, the

\max

operation for calculating h u (same idea for A u and v u ) is expressed as

h_{u} = \frac{h_{i - 1 j} + h_{i j}}{2} + \frac{h_{i - 1 j}}{2} \tanh true[α (h_{i - 1 j} - h_{i j}) true] + \frac{h_{i j}}{2} \tanh true[α (h_{i j} - h_{i - 1 j}) true],

which provides a smooth transition due to the use of the hyperbolic tangents.…”

Section: Numerical Implementationmentioning

confidence: 99%

A basal stress parameterization for modeling landfast ice

Lemieux

Tremblay

Dupont³

et al. 2015

JGR Oceans

114

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Current large-scale sea ice models represent very crudely or are unable to simulate the formation, maintenance and decay of coastal landfast ice. We present a simple landfast ice parameterization representing the effect of grounded ice keels. This parameterization is based on bathymetry data and the mean ice thickness in a grid cell. It is easy to implement and can be used for two-thickness and multithickness category models. Two free parameters are used to determine the critical thickness required for large ice keels to reach the bottom and to calculate the basal stress associated with the weight of the ridge above hydrostatic balance. A sensitivity study was conducted and demonstrates that the parameter associated with the critical thickness has the largest influence on the simulated landfast ice area. A 6 year (2001)(2002)(2003)(2004)(2005)(2006)(2007) simulation with a 20 km resolution sea ice model was performed. The simulated landfast ice areas for regions off the coast of Siberia and for the Beaufort Sea were calculated and compared with data from the National Ice Center. With optimal parameters, the basal stress parameterization leads to a slightly shorter landfast ice season but overall provides a realistic seasonal cycle of the landfast ice area in the East Siberian, Laptev and Beaufort Seas. However, in the Kara Sea, where ice arches between islands are key to the stability of the landfast ice, the parameterization consistently leads to an underestimation of the landfast area.

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Improving the numerical convergence of viscous-plastic sea ice models with the Jacobian-free Newton–Krylov method

Cited by 58 publications

References 33 publications

neXtSIM: a new Lagrangian sea ice model

neXtSIM: a new Lagrangian sea ice model

Using sea‐ice deformation fields to constrain the mechanical strength parameters of geophysical sea ice

A basal stress parameterization for modeling landfast ice

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