Floe Distribution Research Articles

Investigation of the effects of managed ice field characteristics on a dynamic positioning AHTS vessel using physical modelling techniques

This paper presents the tools, techniques and outcomes of a model testing program of a dynamically positioned (DP) Ice-1A classed Anchor Handling Tug Supply (AHTS) vessel called the “Magne Viking” in different managed ice environments with ice thickness, concentration, floe size, floe distribution, drift speed, and ice encroachment direction as test variables. A total of 168 test runs were carried out in 7 ice sheets to evaluate the vessel's thruster forces and moment on the horizontal plane and the vessel's 6-DOF motions and accelerations. The time series and probability of exceedance plots of thruster forces and yawing moments are presented, along with the vessel's positioning relative to a set-point in various managed ice conditions. In addition, investigations are carried out to evaluate the influence of various ice field parameters on the time-averaged and time-dependent thruster forces and moment. Both measurements and video recordings confirmed complex and stochastic ice-ship-basin wall interactions and different ice failure modes. Overall, the study demonstrated the capability of the DP-controlled ship to maintain the station for most head-on tests and the oblique ice tests not exceeding 15°. The dataset and video recordings acquired through the testing have improved the understanding of the dynamic ice-vessel interactions.

2D numerical modeling of icebreaker advancing in ice-covered water

This paper presents 2D numerical modeling to calculate ship–ice interactions that occur when an icebreaker advances into ice-covered water. The numerical model calculates repeated icebreaking of an ice plate and removal of small ice floes. The icebreaking of the ice plate is calculated using a ship–ice contact detection technique and fluid–structural interaction of ice plate bending behavior. The ship–ice interactions in small ice floes are calculated using a physically based modeling with 3DOF rigid body equations. The ice plate is broken in crushing, bending, and splitting mode. The ice floes drift by wind or current and by the force induced by the ship–ice interaction. The time history of ice force and ice floe distribution when an icebreaker advances into the ice-covered water are obtained numerically. Numerical results demonstrate that the time history of ice force and distribution of ice floes (ice channel width) depend on the ice floe size, ship motion and ice drifting by wind or current. It is shown that the numerical model of ship maneuvering in realistic ice conditions is necessary to obtain precise information about the ship in ice-covered water. The proposed numerical model can be useful to provide data of a ship operating in ice-covered water.

Winter-to-summer transition of Arctic sea ice breakup and floe size distribution in the Beaufort Sea

Breakup of the near-continuous winter sea ice into discrete summer ice floes is an important transition that dictates the evolution and fate of the marginal ice zone (MIZ) of the Arctic Ocean. During the winter of 2014, more than 50 autonomous drifting buoys were deployed in four separate clusters on the sea ice in the Beaufort Sea, as part of the Office of Naval Research MIZ program. These systems measured the ocean-ice-atmosphere properties at their location whilst the sea ice parameters in the surrounding area of these buoy clusters were continuously monitored by satellite TerraSAR-X Synthetic Aperture Radar. This approach provided a unique Lagrangian view of the winter-to-summer transition of sea ice breakup and floe size distribution at each cluster between March and August. The results show the critical timings of a) temporary breakup of winter sea ice coinciding with strong wind events and b) spring breakup (during surface melt, melt ponding and drainage) leading to distinctive summer ice floes. Importantly our results suggest that summer sea ice floe distribution is potentially affected by the state of winter sea ice, including the composition and fracturing (caused by deformation events) of winter sea ice, and that substantial mid-summer breakup of sea ice floes is likely linked to the timing of thermodynamic melt of sea ice in the area. As the rate of deformation and thermodynamic melt of sea ice has been increasing in the MIZ in the Beaufort Sea, our results suggest that these elevated factors would promote faster and more enhanced breakup of sea ice, leading to a higher melt rate of sea ice and thus a more rapid advance of the summer MIZ.

Power Scaling and Seasonal Changes of Floe Areas in the Arctic East Siberian Sea

The cumulative number versus floe area distribution of seasonal sea floes from six satellite images of the Arctic Ocean during the summer breakup and melting is fit by two scale-invariant power law scaling regimes for floe areas ranging from 30 to 28,400,000 m2. Scaling exponents, β, for larger floe areas range from −0.6 to −1.0 with an average of −0.8. Scaling exponents, β, for smaller floe areas range from −0.3 to −0.6 with an average of −0.5. The inflection point between the two scaling regimes ranges from 283 × 102 to 4850 × 102 m2 and generally moves from larger to smaller floe areas through the summer melting season. The stability of the power scaling results is demonstrated for two of the images by dividing each in half and analyzing each half separately, with the result that the scaling exponents and the size of the inflection points are nearly the same for each half as for the whole image. We propose that the two scaling regimes and the inflection between them are established during the initial breakup of sea ice solely by the process of fracture. The distributions of floe size regimes retain their scaling exponents as the floe pack evolves from larger to smaller floe areas from the initial breakup through the summer season, due to grinding, crushing, fracture, and melting. The scaling exponents for floe area distribution are in the same range as those reported in previous studies of Arctic floes and for the single scaling exponents found for crushed and ground geologic materials including streambed gravel, lunar debris, and artificially crushed quartz. The single scaling exponent found for fault gouge falls below the range for floes possibly because the fracturing and grinding process in fault gouge takes place under high confining pressure. A probabilistic model of fragmentation is proposed that generates a single power law scaling distribution of fragment size.

Image processing for ice floe analyses in broken-ice model testing

The ice floe shape and size distribution are important ice parameters in ice-structure analyses. Before performing an analysis at full scale, the dynamic positioning (DP) experiments in model ice at the Hamburg Ship Model Basin (HSVA) allow for the testing of relevant image processing algorithms. A complete overview image of the ice floe distribution in the ice tank was generated from the experiments. An image processing method based on a gradient vector flow (GVF) snake and a distance transform is proposed to identify individual ice floes. Ice floe characteristics such as position, area, and size distribution are obtained. A model of the managed ice field's configuration, including identification of overlapping floes, is also proposed for further studies in ice-force numerical simulations. Finally, the proposed algorithm is applied to an ice surveillance video to further illustrate its applicability to ice management.

Floe formation in Arctic sea ice

The ice pack covering northern seas is composed of a mixture of thick ridged and rafted ice, undeformed ice, and open water. Ice motions determined from satellite remote sensing data show that deformation of the pack takes place along the boundary of large floes. Eulerian continuum sea ice models can simulate this behavior to a degree by capturing the localization of gridded ice strength in some average sense. However, using a discontinuous Lagrangian approach that explicitly models ice floes and the interactions between them, it is possible to simulate both the fracture process that creates floe boundaries and the continued deformation along those floe boundaries. We have developed a granular model of the central Arctic ice pack that consists of thousands of individual grains that can freeze together, fracture apart, and interact through ridging. Accelerations produced by passing weather patterns and sustained quasi‐steady deformation cause the model pack to fracture apart into floes composed of one or more grains. When the ice pack is nonuniformly accelerating due to passage of a weather pattern, simulations show that the factors that influence the size of the floes are the tensile strength of the joints between grains, the gradient of the wind field, and the average size of the individual grains. During sustained deformation the pack continues to deform along existing floe boundaries while stresses build and further fracture takes place. In quiet areas of the basin, fractures refreeze. To explore the fracture process during sustained deformation, we run 24‐hour basin scale simulations at resolutions from 2.8 km to 14 km. At the end of each simulation we construct a distribution of floe areas. The cumulative distribution of floes at the large end of the distribution is approximately the same at each resolution. As we increase the resolution from 14 km to 2.8 km, the damage zones between large floes become more localized. A log‐log plot of the cumulative floe size distributions obtained from the simulations appears linear over several orders of magnitude.

Modelling the rheology of sea ice as a collection of diamond-shaped floes

In polar oceans, seawater freezes to form a layer of sea ice of several metres thickness that can cover up to 8% of the Earth’s surface. The modelled sea ice cover state is described by thickness and orientational distribution of interlocking, anisotropic diamond-shaped ice floes delineated by slip lines, as supported by observation. The purpose of this study is to develop a set of equations describing the mean-field sea ice stresses that result from interactions between the ice floes and the evolution of the ice floe orientation, which are simple enough to be incorporated into a climate model. The sea ice stress caused by a deformation of the ice cover is determined by employing an existing kinematic model of ice floe motion, which enables us to calculate the forces acting on the ice floes due to crushing into and sliding past each other, and then by averaging over all possible floe orientations. We describe the orientational floe distribution with a structure tensor and propose an evolution equation for this tensor that accounts for rigid body rotation of the floes, their apparent re-orientation due to new slip line formation, and change of shape of the floes due to freezing and melting. The form of the evolution equation proposed is motivated by laboratory observations of sea ice failure under controlled conditions. Finally, we present simulations of the evolution of sea ice stress and floe orientation for several imposed flow types. Although evidence to test the simulations against is lacking, the simulations seem physically reasonable.

Statistical analysis of ice cover state parameters in the Sea of Japan and mathematical modeling of its evolution

Data of a sample from long-term observations (made with an interval of ten days) of ice cover state parameters in the Sea of Japan are analyzed. The results of analysis are used to formulate a model describing the evolution of ice floe distribution in terms of area and thickness. The obtained model is used to construct a model describing the evolution of ice thickness. Particular cases are studied analytically. A method for parametric identification of the model is considered and its adequacy is assessed against observed distributions. The model can be used to predict the state of the ice cover in the Sea of Japan.

Ice floe distribution in the Sea of Okhotsk in the period when sea‐ice extent is advancing

Ice floe distribution in the Sea of Okhotsk during a cold‐air outbreak was investigated by analyzing several thousand of sea‐ice images obtained by the aircraft observation on 18 February in 2000. The effective floe size became small (from 10 m to 2 m) within the marginal ice zone (MIZ). The scaling properties of floe distribution are demonstrated by a cumulative number frequency which follows a power law scaling with an exponent α. The value of α increased from 1.5 within the internal ice zone to 2.1 within the MIZ, which means that relatively small ice floes dominate in the MIZ. The effective width of the MIZ estimated by a wave attenuation theory agreed with the observed width, suggesting that the flexural stress of waves penetrating into the ice is one of the possible mechanisms which cause the difference in the scaling property.

Effectiveness and Longevity of Phosphorus Inactivation with Alum

ABSTRACT Effectiveness and longevity of alum treatments were evaluated in 21 lakes (or lake basins) across the United States; 9 were polymictic and 12 were dimictic. Effectiveness was judged from reductions in lake TP (total phosphorus) and internal loading rate, as well as chlorophyll a (chl a), both initially and over periods ranging from 4 to 20 years following treatment. Internal loading rate was reduced in six of nine polymictic lakes/basins by an average of two-thirds, and lake TP was reduced by about one-half, which persisted for 5–11 years. Internal loading rate in dimictic lakes (7 of 7 with adequate data) remained reduced by an average of 80% for 4 to 21 years (average 13 yrs). For the six polymictic lakes, in which treatment was effective, chl a decreased by an average of two-thirds initially, but was about 40% less than die pre-treatment level after 5 to 11 years. Chl a decreased in seven dimictic lakes by an average of 57% initially and 42% after 5–18 years. In some cases, response was independent of alum treatment because the trophogenic zone was affected more by external than internal P loading. At West Twin Lake, OH, nutrient diversion was more important than control of P release from hypolimnetic sediments in improving surface water quality. The significance of vertical P entrainment, as well as external loading, should be considered before treating dimictic lakes. Alum was initially ineffective in two polymictic lakes and was effective only for a few years in a third, apparently due to interference from macrophytes. Dense macrophytes may have caused uneven floe distribution or sediment P was recycled from below the floe layer through plant senescence and decay. Where macrophytes did not interfere, treatments were usually effective for at least 8 years and up to 11 years in polymictic lakes; an expectation of 10 years longevity is considered reasonable for unstratified lakes. Several dimictic lakes showed effectiveness/longevity of internal loading control for at least 13 and up to 18 to 20 years; an expectation of 15 years longevity seems reasonable for dimictic lakes. The decline in treatment effectiveness could have been due to bioturbation, or to sinking and burial of the aluminum floe over time, as evidenced by a distinct Al layer located at about 20 cm after 16 years in West Twin Lake, OH. A direct relation between dose and treatment longevity, as well as an inverse relation between dose and sediment P release rate, was apparent in the dimictic lakes.

Habitat selection by marine mammals in the marginal ice zone

As part of the multi-disciplinary project, Antarctic Marine Ecosystem Research at the Ice Edge Zone (AMERIEZ), habitat selection by marine mammals was investigated within the marginal ice zone in relation to measured ice variables and other environmental factors. Data were collected on three cruises to the southern Scotia and northern Weddell seas during spring 1983, autumn 1986, and winter 1988. During winter, Antarctic fur seals were significantly associated with drift, pancake, brash ice, icebergs, and areas of uneven floe distribution, all characteristic of the marginal ice zone. Fur seals were seen in open water close to the ice edge during autumn, but during spring, as the pack ice began to retreat rapidly, animals were seen more often away from the ice. Minke whales were also associated with pancake and new ice but were seen further into the pack ice during both winter and autumn. The largest groups of minke whales during winter were observed with a large krill swarm in new ice. Crabeater seal was exclusively a species of the deep pack ice during all seasons and was associated with ice cover of 7–8 oktas and evenly distributed ice floes.

Sea ice thickness data: The many vs. the few

During May 1988 a 1230‐m ice thickness profile was drilled across a floe in Fram Strait. The probability density function of this data set corresponds closely to extensive ice draft measurements from submarines and the thickness distribution of floes sampled randomly in the area. The observed similarity is attributed to the topography of the pack ice in Fram Strait where each floe is composed of a spectrum of smaller components. This may imply that mutual independence and representativeness of thickness measurements can be satisfied to some degree even for short profiles.

Multiyear sea ice floe distribution in the Canadian Arctic Ocean

A series of aerial photographic flights, made over the polar pack ice during April 1982, from M'Clure Strait in the south to Ellef Ringnes Island in the north, shows the changes in ice floe type, size, and area as the pack moves southwest under the effect of the Polar Gyre. The area has some of the most heavily ridged and dynamically active ice in the Arctic Ocean. Floe size distributions were found to fit a negative power relationship (y = A xb, where b = −3.7), rather than the expected negative exponential function. A Prony analysis suggests that a single physical parameter controls the distribution: most likely splitting, rather than bending, shear, or crushing. The effect of proximity to the coast was investigated and showed that nearshore floes were about 20% smaller than their offshore counterparts. The ratio of maximum to minimum floe diameter was consistently 1.5–1.6. The mean floe diameter was found to be 700 m; the mean area was 0.38 km 2.Heavily hummocked and ridged floes were found to be a fairly constant fraction (1%) of the multiyear pack.