Sensitivity and uncertainty analysis of a short‐term sea ice motion model

A finite-element algorithm is constructed for a material coordinate formulation of the equations of sea-ice dynamics, using quadratic elements and fully implicit time steps. The material coordinate description allows the nodes of a fixed finite-element mesh to define the same material elements as time proceeds, which avoids interpolation of nodal values on a changing spatial mesh as the pack evolves, quadratic elements preserve continuity of second derivatives, and this time stepping is stable and accurate in standard problems. An earlier finite-element study of a wind-driven pack with two free boundary sections, using spatial coordinates and implicit time steps without iteration, gave rise to numerical instability when the constitutive law for the ice stress induced by floe interactions imposes zero stress in diverging flow. The present more accurate study of the same problem, using a material description and fully implicit time steps, with a smoothed transition to zero stress in diverging flow, significantly extends the time over which a stable solution is obtained. Stability and accuracy of the present algorithm is first demonstrated by comparison with a class of exact solutions to specific problems using linearly viscous relations in converging flow and abrupt transition to zero stress in diverging flow, for which an expanding region of diverging flow is initiated after a finite time at an interior point, either following convergence everywhere, or following an expanded region of neutral flow. The previous problem with two free boundary sections is then solved with the same rheology to demonstrate a stable solution over an extended time period. Next, a general nonlinearly viscous relation is constructed which ensures that the stress lies close to a yield envelope during strongly converging flow, to reflect the commonly used viscous-plastic model without the disjoint stress relations in different regimes. This is applied to a pack flow with a dramatically deforming free boundary driven by a vortex wind, which demonstrates how well the present material formulation can capture large deformations.

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“…Less common are finite-element treatments, and few examples include Thomson et al . (1988), Thomson & Sykes (1990), and Schulkes et al . (1998).…”

Section: Finite-element Algorithmmentioning

confidence: 95%

A material coordinate treatment of the sea–ice dynamics equations

Morland

Staroszczyk

1998

Proc. R. Soc. Lond. A

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A finite-element treatment of sea ice dynamics for different ice rheologies

Schulkes

Morland

Staroszczyk

1998

Int. J. Numer. Anal. Meth. Geomech.

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SUMMARYIn this paper the effects of four different rheologies on the evolution of a large-scale sea ice pack are determined and compared. Two rheologies are of viscous-plastic form, and two are viscous fluid relations. The initial pack domain is rectangular, and the motion is driven by wind stress and resisted by ocean drag. Two adjacent edges are rigid shore boundaries, and the other two are free boundaries at open water which move during the pack motion, so that the pack domain changes in time. Two different forms of boundary conditions at the rigid shore edges are considered, which also influence the evolution. The governing equations are solved numerically using a finite-element method, and, unlike previous numerical treatments, no artificial viscosity is incorporated to stabilise the algorithm near interfaces between converging and diverging flow. Instability arises when any tensile stress is abruptly cut-off when diverging flow is initiated, and an alternative view is offered.

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Evaluation of physical processes in an idealized extratropical cyclone using adjoint sensitivity

Langland¹,

Elsberry²,

Errico³

1995

Quart J Royal Meteoro Soc

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SUMMARYAn adjoint model is used to examine the sensitivity of an idealized dry extratropical cyclogenesis simulation to perturbations of predictive variables and parameters during the cyclone life cycle. The adjoint sensitivity indicates how small perturbations of model variables or parameters anywhere in the model domain can influence cyclone central pressure. Largest sensitivity for both temperature and wind perturbations is located between 600 and 900 hPa in the baroclinic zone above the developing cyclone. Perturbations of a given size have more influence on cyclone intensity when located in high-sensitivity regions (the middle and lower troposphere in this simulation). The effects of physical processescan be interpreted with adjoint sensitivity by considering perturbations that are proportional to temperature and wind tendencies in the basic state (nonlinear forecast). In the early phase of the cyclone life cycle, temperature advection near the steering level in the lower troposphere (about 800 hPa) is strongly cyclogenetic and resembles a Charney mode of baroclinic instability. During the phase of most rapid deepening, temperature advection in the lower troposphere remains important, while interpretation of sensitivity to wind perturbations suggests that increased vorticity in the middle and upper troposphere above the surface low-pressure centre may also be significant for cyclone intensification.Adjoint techniques can provide insight into spatial and temporal sensitivity not easily obtained from other methods. Higher sea surface temperature (SST) has a cyclogenetic effect mainly in a localized region corresponding to the cyclone warm sector. Outside the areas of high sensitivity, small perturbations of SST have very little effect on central pressure of the forecast cyclone. When strong upward sensible-heat flux, F?, exists, it can have a cyclogenetic (preconditioning) influence early in the cyclone life cycle, although downward Fs in the cyclone warm sector is anticyclogenetic during the phase of most rapid deepening. The sensitivity indicates that Fs can be cyclogenetic in one location and anticyclogenetic at the same time in another location, so that F, effects on cyclone intensity are partially self-cancelling. Surface momentum stress is anticyclogenetic, with sensitivity highly localized in the cyclone warm sector.

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Sensitivity and uncertainty analysis of a short‐term sea ice motion model

Cited by 4 publications

References 11 publications

A material coordinate treatment of the sea–ice dynamics equations

A material coordinate treatment of the sea–ice dynamics equations

A finite-element treatment of sea ice dynamics for different ice rheologies

Evaluation of physical processes in an idealized extratropical cyclone using adjoint sensitivity

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