Circular Ice Research Articles

Simulation of infrared scattering from ice aggregates by use of a size-shape distribution of circular ice cylinders.

The scalar optical properties (extinction coefficient, mass extinction coefficient, single-scattering albedo, and asymmetry parameter) of a distribution of randomly oriented ice aggregates are simulated generally to well within 4% accuracy by use of a size-shape distribution of randomly oriented circular ice cylinders at wavelengths in the terrestrial window region. The single-scattering properties of the ice aggregates are calculated over the whole size distribution function by the finite-difference time-domain and improved geometric optics methods. The single-scattering properties of the size-shape distribution of circular ice cylinders are calculated by the T-matrix method supplemented by scattering solutions obtained from complex-angular-momentum theory. Moreover, radiative-transfer studies demonstrate that the maximum error in brightness temperature space when the size-shape distribution of circular ice cylinders is used to represent scattering from ice aggregates is only approximately 0.4 K The methodology presented should find wide applicability in remote sensing of ice cloud and parameterization of cirrus cloud scalar optical properties in climate models.

Sea ice formation on a very cold surface

[1] In this study laboratory experiments of sea ice formed on a vertical surface with initial temperature of −30 to −50°C are presented. The ice formation is rapid, and in 300 s >5 mm of sea ice is formed. Ice formation cooled and salinified the water, and induced a vertical down wards flow of ∼5 mm/s with a boundary layer about 5 mm thick. This ice has a structure with columnar crystals that have small circular cross sections (0.2–1.0 mm) and sea ice salinities are between 24 and 32. A simple model approach indicate that the thermal conductivity of such ice is lower than for other types of sea ice.

EXPERIMENTAL STUDY ON SPREADING OF OIL SPILLED AMONG PACK ICE

In the Sea of Okhotsk, crude oil production had started in the summer of 1999, on the northeastern shelf of Sakhalin Island. And crude oil was exported by oil tanker from July to November because of ice foes in the winter season. However, it is planed to continue the production of crude oil through the year by sub sea pipelines. This development increases the risk of oil spill accident in the ice-covered waters.In this paper, experimental study is presented in order to investigate the behavior of crude oil spreading among pack ice. The experiments were carried out including model pack ice consist of the board of circular ice, and some cases of different discharge, volume conditions and ice concentrations.

Scattering by randomly oriented thin ice disks with moderate equivalent-sphere size parameters

We use the T-matrix method to compute the scattering matrix for randomly oriented circular ice cylinders with diameter-to-length ratios 1 and 20 and surface-equivalent-sphere size parameters up to 12. We show that wavelength-sized, sharp-edged ice plates with extreme diameter-to-length ratios possess the same scattering properties as smooth platelike spheroids: their phase functions are similar to those of surface-equivalent compact particles, whereas all other elements of the scattering matrix are typical of Rayleigh scattering.

Results from the EISMINT model intercomparison: the effects of thermomechanical coupling

AbstractThis paper discusses results from the second phase of the European Ice Sheet Modelling Initiative (EISMINT). It reports the intercomparison of ten operational ice-sheet models and uses a series of experiments to examine the implications of thermomechanical coupling for model behaviour. A schematic, circular ice sheet is used in the work which investigates both steady states and the response to stepped changes in climate. The major finding is that the radial symmetry implied in the experimental design can, under certain circumstances, break down with the formation of distinct, regularly spaced spokes of cold ice which extended from the interior of the ice sheet outward to the surrounding zone of basal melt. These features also manifest themselves in the thickness and velocity distributions predicted by the models. They appear to be a common feature to all of the models which took part in the intercomparison, and may stem from interactions between ice temperature, flow and surface form. The exact nature of these features varies between models, and their existence appears to be controlled by the overall thermal regime of the ice sheet. A second result is that there is considerable agreement between the models in their predictions of global-scale response to imposed climate change.

Growth Trajectories of Disk Crystals of Ice Growing from Supercooled Water

The time evolution of a disk crystal of ice with radius R and thickness h growing from supercooled water is studied using a solution of an ordinary differential equation (ODE) for h with respect to R. The growth of thickness, i.e., growth along the c axis of ice, is governed by slow molecular rearrangements on the basal plane and is expressed as a power function of the supercooling at the center of a disk face. Growth of the radius, i.e., growth in the basal plane, is controlled by transport of latent heat and is calculated by solving the diffusion equation for the temperature field surrounding the disk. We combine both functional expressions for growth rate to obtain an ODE for h as a function of R. Our analysis in the (R, h) plane is used to understand the recent results obtained experimentally by Shimada and Furukawa (J. Phys. Chem. 1997, B101, 6171−6173), in which they found two types of growth trajectories for ice disks prior to morphological instability.

How big should hexagonal ice crystals be to produce halos?

It has been hypothesized that the frequent lack of halos in observations of cirrus and contrails and laboratory measurements is caused by small ice crystal sizes that put the particles outside the geometrical optics domain of size parameters. We test this hypothesis by exploiting a strong similarity of ray tracing phase functions for finite hexagonal and circular ice cylinders and using T-matrix computations of electromagnetic scattering by circular cylinders with size parameters up to 180 in the visible. We conclude that well-defined halos should be observable for ice crystal size parameters of the order of 100 and larger and discuss remote-sensing implications of this result.

Particle scattering in the resonance regime: full-wave solution for axisymmetric particles with large aspect ratios

Reliable descriptions of the optical properties of clouds and aerosols are essential for studies of radiative transfer in planetary atmospheres. Mie scattering algorithms provide accurate estimates of these properties for spherical particles with a wide range of sizes and refractive indices, but these methods are not valid for nonspherical particles (e.g., ice crystals, mineral dust, and smoke). Even though a host of methods exist for deriving the optical properties of nonspherical particles that are very small or very large compared with the wavelength, only a few methods are valid in the resonance regime, where the particle dimensions are comparable with the wavelength. Most such methods are not ideal for particles with sharp edges or large axial ratios. We explore the utility of an integral equation approach for deriving the single-scattering optical properties of axisymmetric particles with large axial ratios. The accuracy of this technique is shown for spheres of increasing size parameters and an ensemble of randomly oriented prolate spheroids of size parameter equal to 10.079368. In this last case our results are compared with published results obtained with the T-matrix approach. Next we derive cross sections, single-scattering albedos, and phase functions for cylinders, disks, and spheroids of ice with dimensions extending from the Rayleigh to the geometric optics regime. Compared with those for a standard surface integral equation method, the storage requirement and the computer time needed by this method are reduced, thus making it attractive for generating databases to be used in multiple-scattering calculations. Our results show that water ice disks and cylinders are more strongly absorbing than equivalent volume spheres at most infrared wavelengths. The geometry of these particles also affects the angular dependence of the scattering. Disks and columns with maximum linear dimensions larger than the wavelength scatter much more radiation in the forward and backward directions and much less radiation at intermediate phase angles than equivalent volume spheres.

Growth and Stability of an Ice Disk : Historical Perspective

Growth and Stability of an Ice Disk : Historical Perspective

Climate forcing and thermal feedback of residual lake‐ice covers in the high Arctic

A discontinuous ice coverage and lake temperature record of 36‐yr duration has been compiled for Colour Lake (79°25′N, 90°45′W) on Axel Heiberg Island, Northwest Territories. About once every 6 yr, the ice cover remains through the entire summer, creating a residual ice cover the following winter. Residual ice covers are more frequent in the last 10 yr (1986–1995) than in the 20 yr from 1959 to 1978, indicating a reduction in climate factors controlling ice decay. These factors are identified as the number of thawing degree‐days, suggesting a tendency toward cooler summers over the last decade. We report year‐round meteorology observations that indicate a mean annual temperature of about ‒15.2°C, with ∼500 thawing degree‐days in summer. Following a residual ice year, spring lake‐water temperatures are significantly greater than they are following nonresidual years. The increased temperatures can be attributed to the stabilizing effect of the residual ice pan the previous fall. Without an ice pan, convection cools the entire water column before the surface freezes. When the lake has an ice pan at the start of freezing, the surface freezes over quickly, effectively trapping water heated during summer. The warmer spring water temperatures act as negative feedback, decreasing the potential for a second consecutive residual ice year.

Response of a circular ice floe to ocean waves

A new model is presented to reproduce the behavior of a solitary, circular, flexible ice floe brought into motion by the action of long‐crested sea waves. The intended application of the work is ultimately a fully three‐dimensional analogue of a marginal ice zone (MIZ) through which ocean waves propagate, allowing the attenuation and directional advance to be forecast and validated against observations. (Existing theory does not treat directional changes correctly.) To enable a check to be made on the model, two independent methods are developed: an expansion in the eigenfunctions of a thin circular plate, and the more general method of eigenfunctions used to construct a Green's function for the floe. Displacement and three‐dimensional scattering patterns in the water surrounding the floe are given for several floe geometries. The model is also used to investigate the strain field generated in the floe, its surge response, and the energy initiated in the water encircling it. Finally, with the aim of understanding how floes herd together to form cohesive structures in the MIZ, the force induced on floes of various thicknesses and diameters is plotted.

A Method to Calculate Pack Ice Driving Forces

Abstract A method is proposed to calculate pack ice driving forces. In order to develop the method, stress distributions in a circular ice floe are calculated for various boundary loading conditions. The analysis is carried out using a special-purpose finite element program in which Sinha’s creep equation is used to model the behavior of ice. Charts relating pack ice driving forces to stresses in the ice floe are produced for both linear elastic and creep equations for ice behavior. The results indicate that, for a short period of loading time and at low stress levels, a linear elastic analysis can be used to calculate the pack ice driving forces. However, when the stress levels in the ice floe are high or the time span of load application is long, linear and nonlinear analyses produce much different values for pack ice driving forces.

Light scattering by hexagonal ice crystals: comparison of finite-difference time domain and geometric optics models

We have developed a finite-difference time domain (FDTD) method and a novel geometric ray-tracing model for the calculation of light scattering by hexagonal ice crystals. In the FDTD method we use a staggered Cartesian grid with the implementation of an efficient absorbing boundary condition for the truncation of the computation domain. We introduce the Maxwell–Garnett rule to compute the mean values of the dielectric constant at grid points to reduce the inaccuracy produced by the staircasing approximation. The phase matrix elements and the scattering efficiencies for the scattering of visible light by two-dimensional long circular ice cylinders match closely those computed from the exact solution for size parameters as large as 60, with maximum differences less than 5%. In the new ray-tracing model we invoke the principle of geometric optics to evaluate the reflection and the refraction of localized waves, from which the electric and magnetic fields at the particle surface (near field) can be computed. Based on the equivalence theorem, the near field can subsequently be transformed to the far field, in which the phase interferences are fully accounted for. The phase functions and the scattering efficiencies for hexagonal ice crystals computed from the new geometric ray-tracing method compare reasonably well with the FDTD results for size parameters larger than approximately 20. When absorption is involved in geometric ray tracing, the adjusted real and imaginary refractive indices and Fresnel formulas are derived for practical applications based on the fundamental wave theory.

Hydrostatic Pressure Loading due to Ice Formation in Manholes

The magnitude of the hydrostatic pressure that results from the growth of an ice layer at the top of a water‐filled manhole is determined using both analytical (for a thin ice layer) and finite‐element methods (for a thick ice layer). The ice‐layer freeze/fracture cycle during the growth of the ice layer is predicted analytically and subsequently verified experimentally. A general expression for the hydrostatic pressure as a function of ice thickness and cross‐sectional area (l2i/a2) for a square cross section is developed. Experimental results for an ice layer of a circular cross section show that up to l2i/r2≃0.5 the trend in pressure versus ice thickness results is predicted by the finite‐element method although in some cases the actual experimental values are approximately twice the predicted values, probably due to thickening of the ice disk around the periphery. For the l2i/r2≃0.5 case, hydrostatic pressures resulting from ice formation at the top of the manhole can be two orders of magnitude greater than the pressure due to the static head in a water‐filled manhole.

Stagnation-line melting of ice cylinders transverse to warm air flow

A model for the melting of ice cylinders transverse to a warm air stream is presented, in which the ice layer is assumed to break at the stagnation line. This work has been conducted in an attempt to model an earlier experimental study and as a first step in modelling warm-air defrosting of heat pump evaporators. It was recognized that the critical circular ice cylinder cross-section would change, as the melting progressed, to an ellipse, resulting in increased heat transfer such that the melting rate remained approximately constant with decrease in cylinder size. The results compared favourably with the experimental values.

Melting Heat Transfer From a Horizontal Ice Cylinder Immersed in Quiescent Saline Water

The melting characteristics of a horizontal circular ice cylinder immersed in quiescent saline water were determined experimentally. The experiments were carried out in 3.5 wt% saline water for ambient liquid temperatures ranging from 2.8 to 20.3°C. It was observed that the flow consisted of a laminar bidirectional flow at the lower portion of the melting ice cylinder, and an upward turbulent flow at the upper portion of the cylinder, and that the melting ice surface was characterized variously by secondary flow caused by instabilities based on buoyancy forces in the boundary layer flow. It was also found that the melting heat transfer behavior was markedly affected by the character of the flow in the boundary layer.

Estimation of sublimation rate from ice disk on heating plate at low pressures

The sublimation rate from ice disk resting on a heated plate under low pressures was determined by measuring the decrease of weight of the ice disk. The observed sublimation rates varied with the thickness and the radius of the ice disk. The system was modelled by application of the pumping speed and of the basic differential equations for transient flow with appropriate boundary conditions. The calculated sublimation rates agreed reasonably well with the experimental results.

A bistatic, high‐frequency, under‐ice, acoustic scattering model. II: Applications

A model that has been developed to calculate the scatter produced by a high‐frequency acoustic pulse that originates from a stationary and arbitrarily located source; is incident on and scattered from an under‐ice surface characteristic of pack ice regions of the interior Arctic; and is detected by a stationary and arbitrarily located receiver is used to calculate a variety of acoustic data. Scattering from small‐scale surface roughness produced by ice blocks as well as from large‐scale surface roughness produced by ice keels is calculated and discussed. The effects of physical parameters on the scatter of a high‐frequency plane wave from an ice block whose physical and geometric parameters are characteristic of those found in the Arctic are calculated and discussed briefly. The ice block scattering model is modified to calculate the near field target strength of a circular ice piston as a function of incidence angle. When measured and modeled facet target strength data are compared, it is shown that, near normal incidence, measured and modeled target strength levels agree reasonably well, but that the details of their dependence on incidence angle are different and that differences between the measured and modeled target strength data increase as frequency increases. Monostatic reverberation time series, facet target strength distributions, and correlation data are calculated and compared with measured data for three Arctic sites, and it is shown that measured and modeled data agree reasonably well. For the Chukchi Sea site, a variety of monostatic and bistatic time series, distribution, and correlation data are calculated and discussed for ice keels and flat ice features as well as for the entire under‐ice surface. It is shown that the predominant large‐scale, under‐ice scatterers are ice keels; that ice keels increase reverberation levels; that the facets of ice blocks from which ice keels are composed produce high‐level echos or glints; that generally the spatial location of these high‐level echoes depends on source–receiver location, although some may persist from one location to the next; and that high‐level echos from ice facets are one of the principal means by which ice keels increase high‐frequency, under‐ice reverberation.

On the elasticity of ice plates

The rigidity modulus is determined for simply supported, circular ice plates 0.5 and 1.22 m in diameter. Measurements for the 0.5 m diameter plates were made at −10 °C and for the 1.22 m plates in the range of −7 to −37 °C. The elastic moduli and Poisson's ratio, calculated from the rigidity modulus, are in the range of 6.0–12.0 GPa and 0.29–0.60 respectively, depending on ice type, temperature, and grain size. The plate characteristic lengths calculated from the measured values of the elastic moduli are compared with characteristic lengths determined from field measurements of the deflection of ice covers under load. Key words: ice, ice cover, rigidity modulus, elastic modulus, Poisson's ratio.

Chemistry of Deicing Roads: Penetrating Ice

Experimental measurements of the rates at which sodium chloride, calcium chloride, urea, and calcium magnesium acetate (CMA) penetrate ice are consistent with a theory developed to predict this rate. These measurements and theory complement earlier studies of the rate at which ice can be debonded from road pavement. The mass transfer coefficients found from the penetration measurements are similar to those found from spinning ice disks, but are much less than those found for debonding. Possible reasons for this discrepancy and the steps that limit road deicing are discussed.