William D. Hibler

A Dynamic Thermodynamic Sea Ice Model

Abstract A numerical model for the simulation of sea ice circulation and thickness over a seasonal cycle is presented. This model is used to investigate the effects of ice dynamics on Arctic ice thickness and air-sea heat flux characteristics by carrying out several numerical simulations over the entire Arctic Ocean region. The essential idea in the model is to couple the dynamics to the ice thickness characteristics by allowing the ice interaction to become stronger as the ice becomes thicker and/or contains a lower areas percentage of thin ice. The dynamics in turn causes high oceanic heat losses in regions of ice divergence and reduced heat losses in regions of convergence. TO model these effects consistently the ice is considered to interact in a plastic manner with the plastic strength chosen to depend on the ice thickness and concentration. The thickness and concentration, in turn, evolve according to continuity equations which include changes in ice mass and percent of open water due to advection, ...

Modeling a Variable Thickness Sea Ice Cover

Abstract A numerical framework suitable for simulating a variable thickness sea ice cover over a seasonal cycle is presented. This framework is largely based on the ice thickness distribution model developed by Thorndike et al. (1975). However, the numerical scheme is more general and certain additional developments are included. Namely, a fixed depth mixed-layer formulation including open water heat absorption and lateral melting terms is added, and a mechanical redistribution function consistent with hypothesized and observed physics of the ridging process is proposed. The numerical scheme is formulated in a fixed Eulerian grid and allows an arbitrary number of irregularly spaced thickness levels to be considered. Using this numerical framework in conjunction with a previously developed dynamical model (Hibler, 1979) and a thermodynamic model similar to that of Semtner (1975), a seasonal equilibrium simulation of the Arctic Basin ice cover is carried out. This simulation is performed by doing a 5-year n...

Modeling Pack Ice as a Cavitating Fluid

Abstract Polar ocean circulation is influenced by fluxes of salt and freshwater at the surface as ice freeze in one location, is transported by the winds and currents, and melts again elsewhere. The motion of sea ice, moreover, is strongly affected by internal stresses that arise from the mechanical strength of the ice cover. A simple sea-ice dynamics model, allowing these effects to be included in large-scale climate studies, is presented. In this model a cavitating fluid behaviour is assumed whereby the ice pack does not resist divergence or shear, but does resist convergence. While less realistic than other rheologies that include shear strength, this assumption has certain advantages for long-term climate studies. First, it allows a simple and efficient numerical scheme, in both rectangular and spherical coordinates, which as developed here along with a generation to include shear strength via the Mohr-Coulomb failure criteria. Second, realistic ice transport is maintained, even when the model is driv...

On an efficient numerical method for modeling sea ice dynamics

A computationally efficient numerical method for the solution of nonlinear sea ice dynamics models employing viscous-plastic rheologies is presented. The method is based on a semi-implicit decoupling of the x and y ice momentum equations into a form having better convergence properties than the coupled equations. While this decoupled form also speeds up solutions employing point relaxation methods, a line successive overrelaxation technique combined with a tridiagonal matrix solver procedure was found to converge particularly rapidly. The procedure is also applicable to the ice dynamics equations in orthogonal curvilinear coordinates which are given in explicit form for the special case of spherical coordinates.

Ridging and strength in modeling the thickness distribution of Arctic sea ice

A theory describing evolution of the ice thickness distribution (the probability density of ice thickness) was proposed by Thomdike et al. (1975) and has been used in several sea ice models. The advantage of this theory over the widely used two-level formulation is that it treats ridging explicitly as a redistribution of ice thickness, and ice strength as a function of energy losses incurred by ridge formation. However, the parameterization of these processes remains rather speculative and largely untested, and so our purpose here is to explore these parameterizations using a numerical model based on this theory. The model uses a 160-km resolution grid of the Arctic and 7 years of observed atmospheric forcing data (1979-1985). Monthly oceanic heat flux and current fields are obtained from a 40-km resolution coupled ice-ocean model run separately with the same forcing. By requiring the computed monthly mean ice drift to have the same magnitude as observed buoy drift, we estimate the primary strength parameter : the ratio of total to potential energy change during ridging. This ratio depends on the value of other parameters ; however, the standard case has a ratio of 17 which is within the range estimated by Hopkins (1994) in simulations of individual ridging events. The effects of ridge redistribution and shear ridging parameters are illustrated by a series of sensitivity studies and comparisons between observed and modeled ice thickness distributions and ridge statistics. In addition, these comparisons highlight the following shortcomings of the thickness distribution theory as it is presently implemented : first, the process of first-year to multiyear ridge consolidation is ignored ; and second, the observed preferential melt of thick ridged ice is not reproduced.

Arctic Ice–Ocean Modeling with and without Climate Restoring

Abstract A coupled ice–mixed layer–ocean model is constructed for the Arctic Ocean, the Barents Sea, and the Greenland–Iceland–Norwegian Sea. The model is used to address Arctic numerical modeling with and without climate restoring. The model without climate restoring reproduces basic observed features of the Arctic ice–ocean circulation. The simulated oceanic processes adjust to the surface and lateral fluxes and transport heat and mass in a way that achieves a rough salt and heat balance in the Arctic in the integration period of seven decades. The main deficiency of the model is its prediction of unrealistically high salinity in the central Arctic, which tends to weaken the ocean currents. The introduction of corrective salinity and temperature restoring terms has a significant impact on prediction of the ice–ocean circulation in the Arctic. The impact results from a chain reaction. First, the restoring terms change the salinity and thermal states in the oceanic mixed layer and below. The altered densi...

On Modeling Seasonal and Interannual Fluctuations of Arctic Sea Ice

Abstract Some results from a series of three-year aperiodic simulations of the Northern Hemisphere sea ice cover are reported. The simulations employ the dynamic-thermodynamics sea ice model developed by Hibler (1979) and use a one-day timestep on a 35×31 grid with a resolution of 222 km. Atmospheric data from the years 1973–75 are used to drive the simulations. The simulations yield a seasonal cycle with excessive amounts of ice in the North Atlantic during winter and with somewhat excessive amounts of open water in the central Arctic during summer. Despite the seasonal bias, the simulated and observed interannual fluctuations are similar in magnitude and are positively correlated. The correlations with observed data are noticeably smaller when dynamical processes are omitted from the model. The simulated outflow of ice through the Greenland-Spitsbergen passage undergoes large fluctuations both seasonally and on an interannual basis. The outflow correlates highly with the simulated fluctuations of ice co...

On modeling the anisotropic failure and flow of flawed sea ice

The failure and flow of sea ice on scales small and large is characterized by the propagation of oriented leads and cracks. In this paper a theory for the dynamical treatment of anisotropic oriented flaws in sea ice is developed and used to examine the interaction of these oriented flaws under idealized stress forcing. The essential idea of the theory is to take one or more oriented weak leads imbedded in thick ice. A constitutive law for both the thin and thick ice is taken to be similar to laboratory observations, which are consistent with Mohr Coulomb-like failure. Application of normal continuum mechanics boundary conditions leads to anisotropic flow and failure characteristics of this anisotropic composite under both near- and far-field forcing. The local failure characteristics show that there is a preferred orientation for failure with the intersection between “leads” increasing as confinement increases. For spatially separated interacting flaws the theory predicts a preference for the weakening of flaws in a narrow range of angles of ∼10°–20° relative to the principal far-field stress. Imbedding isolated flaws leads to simulated damage directions consistent with local failure characteristics. In the case where the ice is considered to have available flaws in all directions, fracture propagation is found to proceed by picking out oriented flaws alternating in direction along large-scale damage strikes with individual flaw alignments of ∼20° relative to far-field principal stresses. The mechanisms responsible for these results and how this anisotropic sea ice rheology might be implemented in current dynamic/thermodynamic sea ice models are discussed.

Arctic Ocean Study: Synthesis of Model Results and Observations

Model development and simulations represent a comprehensive synthesis of observations with advances in numerous disciplines (physics; mathematics; and atmospheric, oceanic, cryospheric, and related sciences), enabling hypothesis testing via numerical experiments. For the Arctic Ocean, modeling has become one of the major instruments for understanding past conditions and explaining recently observed changes. In this context, the international Arctic Ocean Model Intercomparison Project (AOMiphttp://fish.cims.nyu.edu/project_aomip/overview. html) has investigated various aspects of ocean and sea ice changes for the time period 1948 to present. Among the major AOMIP themes are investigations of the origin and variability of Atlantic water (AW) circulation, mechanisms of accumulation and release of fresh water (FW), causes of sea level rise, and the role of tides in shaping climate.

Multinational effort studies differences among arctic ocean models

The Arctic Ocean is an important component of the global climate system. The processes occurring in the Arctic Ocean affect the rate of deep and bottom water formation in the convective regions of the high North Atlantic and influence ocean circulation across the globe. This fact is highlighted by global climate modeling studies that consistently show the Arctic to be one of the most sensitive regions to climate change. But an identification of the differences among models and model systematic errors in the Arctic Ocean remains unchecked, despite being essential to interpreting the simulation results and their implications for climate variability. For this reason, the Arctic Ocean Model Intercomparison Project (AOMIP), an international effort, was recently established to carry out a thorough analysis of model differences and errors. The geographical focus of this effort is shown in Figure 1.