Ice Stress Research Articles

Sea-ice mechanical energy balance: nearshore Chukchi Sea, 1982

The mechanical energy balance of sea ice provides information about ice dynamic behavior, driving forces and the constitutive law. The energy balance equation, formed as the product of ice velocity with the ice momentum balance equation, describes changes to the kinetic and potential energy densities as power is input to the ice by wind and current. The momentum balance equation may also be used to describe the ice-stress divergence, air stress, and water stress, but the scalar form of the energy balance is simpler to understand. This paper provides new interpretations of several terms in the energy balance equation, in particular power input by air and water stress and by sea-surface tilt. Barometric pressure fields and drifting buoys deployed on the Chukchi Sea ice cover during 1982 provide wind, ice motion and current measurements that allow each term in the energy balance equation to be evaluated as a function of time. Magnitudes of power input by wind and current show how the energy balance is decomposed and help describe the relative importance of these driving forces. In the nearshore Chukchi Sea during February, March and April 1982, both wind and current provided significant forcing of the ice. Ice stress was also important and, at times, dominated other terms in the mechanical energy balance.

Sea-ice mechanical energy balance: nearshore Chukchi Sea, 1982

The mechanical energy balance of sea ice provides information about ice dynamic behavior, driving forces and the constitutive law. The energy balance equation, formed as the product of ice velocity with the ice momentum balance equation, describes changes to the kinetic and potential energy densities as power is input to the ice by wind and current. The momentum balance equation may also be used to describe the ice-stress divergence, air stress, and water stress, but the scalar form of the energy balance is simpler to understand. This paper provides new interpretations of several terms in the energy balance equation, in particular power input by air and water stress and by sea-surface tilt. Barometric pressure fields and drifting buoys deployed on the Chukchi Sea ice cover during 1982 provide wind, ice motion and current measurements that allow each term in the energy balance equation to be evaluated as a function of time. Magnitudes of power input by wind and current show how the energy balance is decomposed and help describe the relative importance of these driving forces. In the nearshore Chukchi Sea during February, March and April 1982, both wind and current provided significant forcing of the ice. Ice stress was also important and, at times, dominated other terms in the mechanical energy balance.

On the relationship between local stresses and strains in Arctic pack ice

Local ice strains and in situ ice stresses were simultaneously measured on the Coordinated Eastern Arctic Experiment (CEAREX). The experiment took place in the fall of 1988 and was centered about an ice-strengthened ship moored to a multi-year floe in the pack ice northeast of Spitsbergen. During the period of data collection, which extended from early October to late November, the ship and the ice surrounding it drifted from 82°40′N, 32°32′E to 78°54′N, 31°27′E.As soon as ice temperatures were low enough to permit installation, stress sensors were placed at four sites, two sites on each of two adjacent multi-year floes. Principal stress components and the principal stress direction were determined at each sensor. At the same time, microwave transponders, capable of measuring ice deformation to accuracies better than 1 m, were positioned within 1 km of the stress sensors and provided an approximation of the local strain field.What makes this joint dataset particularly interesting is that it includes some large ridging events and a particularly large event which terminated the experiment when the multi-year floes in the local area were broken into small fragments. A wide range of ice stresses was measured during the period. The largest compressive stresses, about 250 kPa, were measured by the near-surface sensors. Although sensors in different locations responded differently to ice movement, the large events were common to all shallow sensors.

Sea-ice dynamics in the Weddell Sea in winter

Observations of ice drift received from an array of ARGOS buoys drifting in the Weddell Sea in winter 1986 are described. Wind and current data are also available, permitting derivation of the complete momentum budget including the internal ice stress computed as residuum. It is shown that the variability of forcing both of the atmosphere and of the ocean is large, and that internal ice stress is not negligible; monthly vector averages amount to about half of the wind and water stresses. Coefficients of shear and bulk viscosity are derived according to Hibler's model of ice rheology; they turn out to be negative occasionally, in particular when small-scale forcing of the atmosphere is large.

Sea-ice dynamics in the Weddell Sea in winter

Observations of ice drift received from an array of ARGOS buoys drifting in the Weddell Sea in winter 1986 are described. Wind and current data are also available, permitting derivation of the complete momentum budget including the internal ice stress computed as residuum. It is shown that the variability of forcing both of the atmosphere and of the ocean is large, and that internal ice stress is not negligible; monthly vector averages amount to about half of the wind and water stresses. Coefficients of shear and bulk viscosity are derived according to Hibler's model of ice rheology; they turn out to be negative occasionally, in particular when small-scale forcing of the atmosphere is large.

Forecasting Bering Sea ice edge behavior

A coupled ice/ocean dynamics model is developed to provide Arctic offshore operators with 5‐ to 7‐day forecasts of ice motions, ice conditions, and ice edge motions. An adaptive grid is introduced to follow the ice edge, and the grid may move independently of the ice motion. The grid can be Lagrangian or Eulerian at different locations away from the ice edge. Ice stress is described using an elastic‐plastic model with strength determined by the ice conditions. The ocean dynamics model describes time‐dependent, three‐dimensional behavior, including wind‐driven currents and barotropic and baroclinic flows. The thermal energy budget of the ice cover is coupled to the ocean, with mass and salt interchange accompanying freezing or melting. Near the marginal ice zone (MIZ), surface winds (determined by reducing and turning the geostrophic winds) are enhanced to reflect observed behavior. The model was tested by simulating ice edge motions observed during the 1983 Marginal Ice Zone Experiment‐West and during drilling of the 1983 north Aleutian shelf Continental Offshore Stratigraphic Test well. Simulations of ice edge movement in the Bering Sea compare with observed data to within about 5 km/d. The model correctly describes mixed‐layer evolution in the marginal ice zone as fresh meltwater is mixed downward by turbulence. Along‐edge baroclinic flows due to density gradients across the ice edge are simulated by the model, in agreement with observations. Increased ice drift speeds generate higher melt rates due to increased turbulence levels, with the result that ice edge advance is moderated in spite of higher ice drift speeds.

Super-Critical Reflection of Ocean Waves; A New Factor in Ice-Edge Dynamics?

Movement of the sea-ice edge on short time-scales (<1 d) is due to a balance of forces between several mechanisms (wind stress, sea-surface tilt, internal ice stress, and Coriolis force) which are often comparable in magnitude. Other factors such as the force induced by partial reflection of short seas, internal gravity waves in the pycnocline, etc., may also contribute. Through the momentum equation, these mechanisms affect the dynamics of the ice edge. In this paper we suggest another mechanism which may have importance, namely, a radiation-stress contribution which derives from obliquely incident waves which are totally reflected from the ice edge by a process analogous to total internal reflection in optics. Such reflection generates both normal and shear forces at the ice edge, the former tending to compact the pack ice and the latter to shear the absolute edge. The effect is studied using some recent data collected during the Winter Weddell Sea Project 1986 in Antarctica, where it is found that the contribution to the force balance is significant. For thicker sea ice and icebergs acted upon by oblique seas, the radiation stress-induced force may outweigh more conventional terms in the momentum equation.

Super-Critical Reflection of Ocean Waves; A New Factor in Ice-Edge Dynamics?

Movement of the sea-ice edge on short time-scales (<1 d) is due to a balance of forces between several mechanisms (wind stress, sea-surface tilt, internal ice stress, and Coriolis force) which are often comparable in magnitude. Other factors such as the force induced by partial reflection of short seas, internal gravity waves in the pycnocline, etc., may also contribute. Through the momentum equation, these mechanisms affect the dynamics of the ice edge. In this paper we suggest another mechanism which may have importance, namely, a radiation-stress contribution which derives from obliquely incident waves which are totally reflected from the ice edge by a process analogous to total internal reflection in optics. Such reflection generates both normal and shear forces at the ice edge, the former tending to compact the pack ice and the latter to shear the absolute edge. The effect is studied using some recent data collected during the Winter Weddell Sea Project 1986 in Antarctica, where it is found that the contribution to the force balance is significant. For thicker sea ice and icebergs acted upon by oblique seas, the radiation stress-induced force may outweigh more conventional terms in the momentum equation.

Field measurements of stresses and deformations in a first-year ice cover adjacent to a wide structure

Ice cover movements and stresses were measured near Adams Island from November 1984 to May 1985. The average horizontal movement rate was 0.1 m/day. Global compressive and tensile strains were less than 1 and 4%, respectively. Strain rates (measured over 1 – 2 month periods) were of the order of 10−9 s−1. Maximum stresses and forces in the ice cover were 500 kPa and 400 kN/m, respectively. Key words: ice movements, ice stresses, ice forces, Canadian Arctic Ocean.

Short‐term ice motion modeling with application to the Beaufort Sea

A short‐term, small‐scale ice motion model was developed in order to facilitate the comparison of various conceptual and numerical formulations. This ice motion model is comprised of two basic components: a momentum balance or equation of motion component and a thickness distribution component. The equation of motion component includes the standard terms relating to air stress, water stress, Coriolis force, sea surface tilt, and internal ice stress. In order to describe the internal ice stress, three different constitutive laws were implemented: a standard linear viscous constitutive law, a closed‐form viscous plastic constitutive law, and a piecewise linearized viscous plastic constitutive law. For the thickness distribution component, a choice of either a two‐level or a multicategory model may be used to characterize the spatial and temporal changes in the thickness distribution of the ice cover. The governing equations for both of these basic ice motion model components are presented. The finite element method based on the Galerkin method of weighted residuals is used to spatially integrate the resulting set of nonlinear partial differential equations while a standard recurrence relation is employed for the temporal integration. The selection of an Eulerian or Lagrangian description for both the equations of motion and the thickness distribution equations is also included in the model development. In order to investigate the response of the developed ice motion model and its various options, the model was applied to a 4‐day ice motion episode in the southern Beaufort Sea. The response of the ice motion model was quantified in terms of the magnitude and the spread of the difference between calculated and observed ice displacements. Comparison between the various model options is included and their effect on the overall model performance is discussed.

Nowcasting Sea Ice Movement Through the Bering Strait

Geostrophic wind velocities were calculated using atmospheric pressure data from Bering Strait stations at Uelen (Siberia), Bukhta Provideniya (Siberia) and Nome (Alaska). These velocities were matched to Strait sea ice displacements derived from satellite imagery (1974–1984), resulting in an all-weather ice movement and now-casting model. Also, five ice displacement modes were identified. The first mode is Chukchi to Bering Sea movement when northeasterly winds exceed 11.5 m/s. The second and third modes are Bering to Chukchi Sea movement. Mode two is driven by a pre-existing north-flowing ocean current during weak opposing winds. Mode three is due to winds and currents acting in concert. The first immobilization mode (maximum duration one week) is an apparent balance between northerly wind stress, water stress from the south, and internal ice stresses. The second immobilization mode is due to large, double, solid ice arches jamming the Strait up to four weeks.

The atmospheric environment service regional ice model (RIM) for operational applications

Abstract This paper describes the development of and simulations with a regional scale sea ice dynamics model for obtaining short‐range, real‐time or near real‐time predictions of ice conditions for operational use. This model is an adaptation of the seasonal sea ice dynamic/thermodynamic model developed at the Cold Regions Research and Engineering Laboratory (CRREL). It consists of (1) a momentum equation that includes air‐to‐ice stress, water‐to‐ice stress, internal ice stress, Coriolis force, and the pressure gradient force due to tilt of the sea surface; (2) a constitutive law that relates ice stress to strain rate and ice strength; and (3) continuity equations for ice thickness and concentration. For treating internal ice stress, the model uses a viscous‐plastic constitutive law with plastic strength dependent on thickness and concentration. A finite difference numerical procedure is used for solving the equations. To obtain numerical simulations, the Regional Ice Model (RIM) is applied over the Beau...

Sea Ice Tracking by Nested Correlations

Spatial differences in sea ice displacement affect ice stress, ice production, and the mass balance of the ice cover. Our concepts about the spatial structure of this field have been undernourished because of a paucity of data with high spatial detail and because of the tedium of extracting such measurements from images manually. A method is described that measures displacements from synthetic aperture radar digital imagery with fine spatial resolution, and does so fully automatically. Many small areas of ice common to two images are identified by correlating the two images. The strategy is to acquire a crude displacement field first from highly averaged images, and to refine this field with images of successively higher resolution. The median discrepancy between automatically and manually measured displacements is three pixels (0.075 km). The algorithm operates successfully on compact ice with large floes and modest rotation rates; we believe it will prove applicable to most of the arctic ice cover throughout the year.

Sea ice drift near Bering Strait during 1982

Six Argos ice stations were deployed in the northeastern Bering Sea in January and February 1982. Four moved north through Bering Strait and made between one and five passes through the strait before they sank or were crushed by the ice, and two remained in western Norton Sound and Shpanberg Strait. Net winds in the region were directed toward the southwest and were relatively uniform geographically. Net currents were northward, and both mean velocity and mean speed were greater at Bering Strait than at Shpanberg Strait. Norton Sound contributed ice northward through Bering Strait in the mean during winter and spring. There was also a net divergence of ice near Cap Lisburne. A theory for open‐shelf shallow water ice drift is developed that adds terms for bottom drag and stress feedback from the water column. A stress analysis for a station that remained in western Norton Sound and Shpanberg Strait showed that bottom drag did not contribute significantly but that stress feedback from the accelerated shallow water current can be of the same order as the Coriolis force. However, the analysis contained a residual, possibly associated with internal ice stress, coastal setup, or unknown measurement error, which was of roughly the same order as the wind and current stress.

Water stress and ocean current measurements under first‐year sea ice in the Canadian Arctic

Ocean current profiles were measured to calculate the ice‐water drag coefficent for tidal currents under landfast ice at the intersection of Lancaster Sound and Navy Board Inlet in the Canadian Arctic. Under‐ice current profiles showed 1–3 m of a logarithmic layer with a friction velocity ranging from 0.3 to 1.0 cm/s. No significant Ekman veering was found below the logarithmic layer, which suggests a strong modulation of the surface current by tidal currents. The ice‐water drag coefficients at 1‐m depth, calculated from the mean current profiles, ranged from 0.0053 to 0.0093, reflecting a nonhomogeneous rough surface and ridges. It was shown that the present estimate of the drag coefficient was consistent with previously measured values of the ice stress.

Estimating ice thickness and internal pressure and stress forces in pack ice using Lagrangian data

A methodology is presented which allows one to calculate an ice thickness term using observed ice motion and wind data. Since the wind data can come from atmospheric pressure fields or numerical models, the methodology is in fact a remote‐sensing capability which relies on ice motion data from satellite imagery, buoys drifting on the ice, etc. The thickness term is shown to be an effective ice thickness which reflects the strength of the ice as a result of the true ice thickness plus the added mass effect of the horizontal gradients of pressure and internal ice stresses. The method for estimating the actual ice thickness and then calculating the forces due to pressure and internal stresses is also outlined. Examples of the temporal variations of the effective ice thickness in the Beaufort Sea are presented. These variations are explained in terms of the compactness of the ice field as the motion is toward or away from the ice pack.

Spin‐down of baroclinic eddies under sea ice

A linear model is used to examine the spin‐down of a baroclinic eddy under the sea ice. For anti‐cyclonic eddies the ice stress, besides directly spinning down the azimuthal flow within the mixed layer, generates an Ekman divergence that raises the pycnocline near the eddy axis. For eddies of the size of the baroclinic radius of deformation (based on the unperturbed mixed layer depth H and the density jump across the pycnocline), the doming reaches a quasi‐stationary state on the frictional time scale T (defined as H/α, where α is the resistence coefficient at the ice‐water interface), which generally is of the order of days. Upward entrainment of the fluid across the pycnocline causes a flow convergence below the mixed layer that continues to spin down the deeper flow and flatten the dome. The erosion of the dome, however, occurs over a much longer time scale of (γN)−1T, where γ and N are dimensionless parameters characterizing the entrainment rate and the deep stratification. Using realistic parameter values for the polar eddies, this time scale is of the order of a year or longer. The pycnocline dome observed over the Antarctic warm cells is thus likely to survive into the following freezing season and provide a preconditioning for the deep convection in the Weddell Sea.

Environmental correlates of pack ice noise

Low-frequency ambient noise under pack ice of the central Arctic Ocean has long-term variations (periods greater than 1 h) which correlate highly with composite measures of stress applied to the ice by wind, current, and drift. These composites are the horizontal ice stress and the stress moment, and are derived from meteorological and oceanographic data observed simultaneously with the noise. Atmospheric cooling, a known high correlate of midfrequency noise under the ice, is not important at low frequencies.

Ice banding as a response of the coupled ice‐ocean system to temporally varying winds

In this study we model formation of ice bands in the marginal ice zones. A one‐dimensional coupled ice‐ocean model is used in which the ice model is coupled to a reduced gravity ocean model through interfacial stresses. The internal ice stresses are important only at high ice concentrations (90%–100%); otherwise, the main balance for the ice motion is between the air‐ice stress and the ice‐water stress, i.e., free drift. The drag coefficients were chosen so that the air‐ice momentum flux is 3 times greater than the air‐ocean momentum flux. Thus the Ekman transport is larger under the ice than in the open water, so that winds parallel to the ice edge, with the ice on the right, produce upwelling. The upwelling simulation was extended to include temporally varying forcing, which was chosen to vary sinusoidally with a 4‐day period. This forcing resembles successive cyclone passings perpendicular to the ice edge. When the oceanic upper layer was thin, which means that the dynamics are strongly nonlinear, the ice bands were formed. The up/downwelling signals do not disappear in wind reversals because of nonlinear advection. This leads to convergences and divergences in oceanic and ice velocities that manifest themselves as ice banding. At least one wind reversal is needed to produce one ice band.

In-Ice Calibration Tests for an Elongated, Uniaxial Brass Ice Stress Sensor

An elongated, uniaxial brass ice stress sensor has been developed by the University of Alaska and used in several field experiments. Laboratory calibration tests have been conducted, in a 60 × 29.5 × 8.5 in. (1524 × 750 × 216 mm) ice block into which the sensor was frozen, to determine the sensor’s response characteristics. Test results indicate that the sensor acts as a stress concentrator with a stress concentration factor of 2.4 and transverse sensitivity of −1.3 at stresses below 30 lbf/in2 (207 kPa). At stresses greater than 30 lbf/in2 (207 kPa) the stress concentration factor increased and the sensor exhibited a time delay response to load. Differences of 22 percent were measured between the measured sensor stress immediately after a constant ice load was applied and the asymptotic stress limit. Interpretation of measured sensor stresses can be considered reliable at ambient ice stress levels below 30 lbf/in2 (207 kPa).