measuring the sea ice floe size distribution sea ice is broken into floes whose diameters range from meters to a hundred kilometers this fragmentation affects the resistance of the ice cover to deformation and the melting at floe sidewalls in summer floes are broken by waves and swell near the ice edge and throughout the pack by isostatic imbalances thermal cracking winds and currents in winter they are welded together by freezing floe size can be measured by several properties p for instance area or mean caliper diameter two definitions of floe size distribution seem useful f p the fraction of area covered by floes no smaller than p and n p the number of floes per unit area no smaller than p f p can be measured by sets other than areas such as the fraction of a line or of a point set covered by floes no smaller than p if n behaves like for small where is mean caliper diameter must be greater than 2 so that the small floes occupy finite area if 2 1 the perimeter of small floes is infinite several summertime distributions have been measured on a log log graph their slopes local values of range from 1 7 to 2 5 one distribution follows a power law the others have steeper slopes for larger floes and more gradual slopes for smaller floes another sampling strategy is to measure the lengths of line segments on floes the distribution of these chord lengths is equivalent to the distribution of floe diameters the variance of an estimate of the fraction g of area covered by floes in any size range is g 1 g k 1 where k is the equivalent number of independent samples k can be found from the autocovariance of the indicator function for the chosen size range for line sampling of a narrow range of floe diameters k is the ratio of the sample length to the floe diameter

a random discontinuous model of sea ice motion the rate at which the sea ice pack spreads apart exposing the warm ocean to the cold atmosphere controls the air sea heat exchange in the arctic and the production of ice mass the rate of spreading or opening can be estimated from observations of ice motion using a model of the ice pack which accounts for the random manner in which the ice is broken into rigid pieces in a region intersected by many cracks some cracks will typically be opening while others are closing in this case the total of the openings will exceed the average divergence of the region a few measurements of the ice motion cannot resolve the openings at each crack so that any estimate of opening will be accompanied by estimation errors the random model adopted here imagines the leads to be distributed according to the poisson distribution and the relative displacements at any crack to be gaussian under these assumptions it is determined how the total opening is related to the average deformation and how this relationship depends on the size of the region and on the number of points used to determine the average deformation

observing the yield curve of compacted pack ice 1 a method for observing the yield curve of compacted pack ice is developed based on the characteristic analysis of the stress field within the pack ice the analysis shows that the slope of the yield curve is associated with the angle between intersecting linear kinematic features thus by measuring the intersection angles we can inversely estimate the yield curve applying this method to the observed angles generates a curved diamond yield curve which possesses almost all the advantages identified by the other methods however due to the limited data available more observations are favored to refine this yield curve

relating arctic pack ice stress and deformation under winter conditions 1 together thermodynamic and dynamic processes determine the thickness distribution of the ice cover on polar oceans which governs the exchange of energy between the atmosphere and the ocean key to the dynamic processes is the mechanical behavior of the ice cover during the surface heat budget of the arctic ocean sheba field experiment we deployed sensors to measure the internal ice stress at several locations within a 15 15 km area these measurements are combined with satellite derived ice motion and imagery products the objective is to make a first step toward using these data sources for evaluating sea ice dynamics models by assessing whether the stress signal can be qualitatively linked to the regional scale 10 100 km deformation activity four case studies are presented each with distinguishing characteristics consolidation of the seasonal ice zone against the alaskan coast 5 7 december 1997 advancement of the consolidation zone into the perennial ice pack 11 13 december extreme divergence 14 17 january and consolidation of the pack against wrangel island and the siberian coast 20 23 february the results of this analysis 1 demonstrate that stress measurements are related to the regional deformation behavior of the ice cover 2 confirm that regional scale ice dynamics is primarily a function of coastal geometry and sustained large scale wind direction and magnitude 3 provide continued evidence that the ice pack behaves as a granular hardening plastic and 4 encourage pursuit of efforts to use direct measurements of ice stress and deformation in the formulation and development of sea ice dynamics models

continuum sea ice rheology determined from subcontinuum mechanics 1 a method is presented to calculate the continuum scale sea ice stress as an imposed continuum scale strain rate is varied the continuum scale stress is calculated as the area average of the stresses within the floes and leads in a region the continuum element the continuum scale stress depends upon the imposed strain rate the subcontinuum scale material rheology of sea ice the chosen configuration of sea ice floes and leads and a prescribed rule for determining the motion of the floes in response to the continuum scale strain rate we calculated plastic yield curves and flow rules associated with subcontinuum scale material sea ice rheologies with elliptic linear and modified coulombic elliptic plastic yield curves and with square diamond and irregular convex polygon shaped floes for the case of a tiling of square floes only for particular orientations of the leads have the principal axes of strain rate and calculated continuum scale sea ice stress aligned and these have been investigated analytically the ensemble average of calculated sea ice stress for square floes with uniform orientation with respect to the principal axes of strain rate yielded alignment of average stress and strain rate principal axes and an isotropic continuum scale sea ice rheology we present a lemon shaped yield curve with normal flow rule derived from ensemble averages of sea ice stress suitable for direct inclusion into the current generation of sea ice models this continuum scale sea ice rheology directly relates the size strength of the continuum scale yield curve to the material compressive strength

the fracture of water ice ih a short overview this paper presents a short overview of the fracture of water ice ih topics include the ductile to brittle transition tensile and compressive strength compressive failure under multiaxial loading compressive failure modes and brittle failure on the geophysical scale arctic sea ice cover europa s icy crust emphasis is placed on the underlying physical mechanisms where appropriate comment is made on the formation of high latitude impact craters on mars

comparison of thin ice thickness distributions derived from radarsat geophysical processor system and advanced very high resolution radiometer data sets 1 thin ice thickness distributions estimated from advanced very high resolution radiometer avhrr and radarsat geophysical processor system rgps data sets were compared over the beaufort sea and the canada basin for the period december 1996 to february 1997 the comparisons show a compelling agreement high correlations were found in cases where thin ice grew in large wide leads extending several hundred kilometers at these large scales estimates from avhrr images and rgps showed similar amounts of thin ice in leads however when major surface deformation occurred on small scales 100 m to 10 km the finer spatial resolution 100 m of radarsat images enabled the rgps algorithm to derive more thin ice than that of avhrr under such conditions the correlation between the two dropped and a small negative bias about 1 was observed in the estimates from avhrr this bias mostly concentrated at the very thin end of the thickness distribution caused a further deficit in the avhrr derived thin ice growth roughly 0 2 cm d although the avhrr and rgps algorithms treat snowfall differently in the ice thickness calculations both snow assumptions appear reasonable however rgps may underestimate the thin ice production because of the 3 day sampling interval with a better understanding of the sources of uncertainty and improved satellite estimates a combination of these two satellite data could offer a wider coverage of thin ice thickness observations in the arctic basin

small scale sea ice deformation in the beaufort sea seasonal ice zone 1 during spring 2003 the deformation of a single lead in the beaufort sea was investigated using four global positioning system recording stations the lead was situated in first year ice in the transition zone between multiyear and seasonal ice packs we discuss the opening rate and shear of this lead in the context of weather system forcing of the beaufort sea sea ice it is found that in an opening mode the lead displays semidiurnal fluctuations in divergence it was also observed that the lead predominately ridged first year ice in closing the volume of ice ridged was the same order of magnitude as ice growth within the study region during the time period studied further work is required to fully understand the implications of the subdiurnal forcing of the ice pack on deformation in the shear zone at the edge of the perennial ice pack in the beaufort sea this study provides information about the temporal and spatial scales that must be resolved in these future investigations

modeling linear kinematic features in sea ice abstract sea ice deformation is localized in narrow zones of high strain rate that extend hundreds of kilometers for example across the arctic basin this paper demonstrates that these failure zones may be modeled with a viscous plastic sea ice model using an isotropic rheology if the ice is assumed to be heterogeneous at the grid scale and allowed to weaken in time intersecting failure zones propagate across the region the direction of failure propagation depends upon the stress applied to the ice wind stress and boundary conditions and the rheological model describing plastic failure of the ice the spacing between failure zones is controlled by the magnitude of the wind stress and the distribution describing spatial variability of ice strength sea ice motion and deformation oscillate at close to a 12 h period throughout the arctic and antarctic pack ice this oscillation is found at all spatial scales from hundreds of kilometers to the lead scale it is shown that with an inertial embedded mo

modeling ice dynamics of coastal seas a coupled sea ice barotropic ocean model with a 1 km resolution and a seaward domain of 200 km quantifies three coastal processes coupling of ice motion to wind driven coastal currents ice thickness redistribution under compaction at the coast and formation of coastal shear zones the model consists of an ice momentum balance mass concentration and two parameter ice thickness distribution and equations for horizontal water motion and continuity using vertical structure functions an appropriate constitutive law appears to be a hardening plastic based on qualitative observations from alaskan continental shelves for first year sea ice strength is taken to be proportional to the square of ice thickness a north wind example of 10 m s with the coastline to the west shows the depth dependence of rotational shear in the sea ice ocean boundary layer and sea surface tilt which contributes an alongshore slope current there is slight convergence of sea ice over the shelf a coastal shear zone of 4 km and an alongshore ice speed seaward of the shear zone of 6 of the wind speed caused by the combination of an under ice shear layer and an alongshore slope current for an onshore wind ice is near free drift at 3 of the wind seaward of a ridging front which propagates seaward a square dependence of ice strength on thickness is required for the rubble field to approach a limiting thickness consistent with observations the hardening plastic interpretation of the rubble field has the stress state at the yield limit in contrast with a rigid plastic of high constant strength that yields only at the coast we conclude that 1 ice thickness motion feedback is important on scales less than 10 km 2 the observational base to discriminate between mesoscale constitutive laws is not yet available and 3 the relation of ice velocity to wind stress is variable because the ocean slope current responds only to the alongshore component of the wind

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

america eurasia plate boundary in eastern asia and the opening of marginal basins abstract the opening of the arctic ocean during the past 55 ma resulted in relative rotation of america with respect to eurasia about a pole located in eastern siberia near the plate boundary the extensional plate boundary enters deep inside the eurasian continent up to the rotation pole on the opposite side of the pole on the pacific side of the plate boundary compressive tectonics are recorded along sakhalin and hokkaido from the oligocene to middle miocene the relative movement was accommodated by strike slip motion along sakhalin and hokkaido although the rotation pole was not located at a significatively different position from now in this paper we explain this by independent motion of the southernmost tip of the american plate towards the pacific margin which behaves as a free boundary this oceanward motion resulted in an extension of the american plate giving rise to the wedge structure of the okhotsk sea the japan sea opened as a pull apart basin along the strike slip boundary finally the increasing extension in the okhotsk sea led to the opening of the oceanic kuril basin

spatial and temporal characterization of sea ice deformation in late march 2007 an array of gps ice drifters was deployed in the beaufort sea as part of the sea ice experiment dynamic nature of the arctic sedna the drifters were deployed in an array designed to resolve four nested spatial scales of sea ice deformation from 10 to 140 km with the arrays maintaining appropriate shape for strain rate calculation until mid june in this paper we test whether sea ice deformation displays fractal properties in the vicinity of sedna we identify that deformation time series have different spectral properties depending on the spatial scale at the scales around 100 km deformation is a red noise process indicating the importance of the ice pack surface forcing in determining the deformation rate of sea ice at this scale at smaller scales the deformation becomes an increasingly whiter process it has pink noise properties which suggests an increasing role of dissipative processes at smaller scales at spatial scales of 10 100 km and sub daily scales there is no deformation coherence across scales coherence only becomes apparent at longer scales greater than 100 km the lack of coherence at small scales aids in understanding previous observations where correlation between 10km regions adjacent to each other varied widely with correlation coefficients between 0 3 and 1 this suggests it is not appropriate to think of sea ice as having a decorrelation length scale for deformation we find that lead scale observations of deformation are required when estimating ice growth in leads and ridging time series for the two sedna arrays we find coherence between 140 and 20 km scale deformation up to periods of 16 days this suggests sea ice deformation displays coherent deformation between 100 km scale and the scale of the beaufort sea of order 1000 km over synoptic time periods daily to weekly timescales organization of leads at synoptic and larger scales is an emergent feature of the deformation field that is caused by the smooth variation of surface forcing wind on the ice pack

arctic sea ice as a granular plastic an important consideration in understanding sea ice mechanics is the integration of observed sea ice behavior on a floe neighborhood scale 1 10 km into ice dynamics on a regional scale o 50 km we investigate sea ice kinematics from october 1993 through april 1994 using relative motions from 13 drifting buoys with global positioning system navigation in a 20 km array centered on the sea ice mechanics initiative ice camp and we compare these motions to synthetic aperture radar sar derived ice velocities over a 100 by 500 km region in the beaufort sea there is excellent correspondence between the deformation of the buoy array and that from the sar inferred ice dynamics from analysis of the two major northerly wind convergence events of the winter are consistent with a granular hardening plastic conceptual model for beaufort sea ice under continued northerly winds the ice from the alaskan shore to the camp failed in shear and convergence in a progressive manner away from the coast the continuum scale o 10 km is an order of magnitude larger than the grain i e floe size o 1 km the ice motion often forms aggregates of 20 200 km separated by narrow 10 km shear zones similar to granular materials at moderate forcing i e wind stress multiplied by fetch the ice appears to fail along slip lines that occur at an acute angle to each other and to the direction of the wind forcing characteristic of a plastic material at critical state with longer fetch the ice appears to fail in compression perpendicular to the wind direction sea ice appeared to harden on a regional scale after the first event during the second northerly wind event there was a sea ice breakout toward the west apparently due to a lack of lateral confining stress our observations suggest that the ice floes advect through relatively stationary stress fields created by the wind forcing and coastal boundaries for example while the sar and advanced very high resolution radiometer images indicated the presence of the shear feature at the same geographic location for nearly a week buoys would show shearing only for several days as they transited across the region of shear there is a high correspondence between the major internal ice deformation events and persistent weather patterns on a 3 to 5 day temporal scale this implies that sar data collection and analysis for regional sea ice dynamics should be consistent with the wind forcing and have a sampling of less than 3 days

mathematical characteristics of sea ice dynamics models mathematical characteristics of plasticity models that describe large scale sea ice behavior are studied in an attempt to understand the models better and to compare the analytical results to observed ice behavior separate stress and velocity characteristics occur when a nonassociated flow rule is used the two sets coincide for associated flow rules the relative orientation of characteristic directions at a point can change depending on the stress state and the direction of plastic stretching two real velocity characteristic directions exist when the magnitude of shearing exceeds the magnitude of dilating one exists when they are equal and none exist when the shearing magnitude is less than the dilating magnitude the system is hyperbolic parabolic or elliptic respectively in these conditions quasi steady elastic plastic and viscous plastic models have identical characteristics so that we cannot use the characteristics to discriminate between these models attention has been focused on the velocity characteristics with the desire to relate these directions directly to leads and other features observed in satellite imagery the velocity characteristic curves cannot stretch so that floes lying along a characteristic line neither approach nor separate from each other therefore the amount of open water will not change between these floes which makes it unlikely that we will be able to observe fields of characteristic directions directly in satellite imagery we have however observed velocity discontinuities across large scale lead systems which are special characteristic curves this result offers a way to use remotely sensed imagery directly to estimate part of the deformation field

two dimensional deformation patterns in sea ice the mechanical behaviour for the geome trical properties of two dimensional def ormation has been investi gated the mohr formulation of failure which is based on the concept of slip at the plane of weakness is used in this study it is shown that alteration of the shear stress t n at the plane of weakn ess requires self similarity of features in deformation patt erns a general relationship between the angle of internal friction and the breaking angle of deformation patterns is derived using imagery data this relat ionship is used to find the angle of internal friction from selected sea ice deforma tion patterns the value obtained for this angle is is 0 20 for deform ation on a scale from 100 m to 100 km

continuous gravity measurements reveal a low density lava lake at kīlauea volcano hawai i abstract on 5 march 2011 the lava lake within the summit eruptive vent at k lauea volcano hawai i began to drain as magma withdrew to feed a dike intrusion and fissure eruption on the volcano s east rift zone the draining was monitored by a variety of continuous geological and geophysical measurements including deformation thermal and visual imagery and gravity over the first 14 hours of the draining the ground near the eruptive vent subsided by about 0 15 m gravity dropped by more than 100 gal and the lava lake retreated by over 120 m we used gps data to correct the gravity signal for the effects of subsurface mass loss and vertical deformation in order to isolate the change in gravity due to draining of the lava lake alone using a model of the eruptive vent geometry based on visual observations and the lava level over time determined from thermal camera data we calculated the best fit lava density to the observed gravity decrease to our knowledge the first geophysical determination of the density of a lava lake anywhere in the world our result 950 300 kg m 3 suggests a lava density less than that of water and indicates that k lauea s lava lake is gas rich which can explain why rockfalls that impact the lake trigger small explosions knowledge of such a fundamental material property as density is also critical to investigations of lava lake convection and degassing and can inform calculations of pressure change in the subsurface magma plumbing system

hierarchy and sea ice mechanics a case study from the beaufort sea hierarchy implies that the study of sea ice can be divided into analysis of subsets of processes based on scale and their interaction with adjacent scales we apply these concepts to regional sea ice dynamics the apparent self similar property of ice floes seen in aircraft or satellite images argues for an aggregate nature of sea ice that viscouslike regional behavior arises from discrete floe interactions however for some regions and some times characteristic behavior where lead patterns seen in basin wide advanced very high resolution radiometer images appear to be related to coastal orientation hundreds of kilometers away suggests that small regional scale processes o 10 km and discontinuities in the velocity or stress state along boundaries can affect the larger scale sea ice distribution and dynamics o 500 km thus sea ice displays both aggregate type behavior and discontinuous type behavior based on the history of forcing and shape of the enclosing basin the appropriate matching of atmospheric processes to sea ice processes in air ice interaction is through the sea ice deformation field rather than the response of ice velocity to the local wind this is because atmospheric forcing and sea ice deformation have matching energetic scales at several hundred kilometers and timescales of days an example of northerly winds during the april 1992 arctic leads experiment period suggests discontinuous type behavior upwind of the alaska coast followed by a general opening behavior with easterly winds there appear to be natural scale divisions between climate scale sea ice processes of o 100 300 km which resolve aggregate behavior regional scale o 10 50 km which is necessary to resolve observed shearing behavior and the floe scale o 1 km because the climate scale is two levels removed from the floe scale care must be exercised in using ice properties from the floe scale in climate scale models ice strength is an example of such a scale dependent parameter

atmospheric boundary layer structure and drag coefficients over sea ice this paper estimates the air sea drag coefficient for first year ice from recent aircraft measurements and reconciles the range of observed drag coefficients 103cd 1 2 3 7 referenced to 10 m for all sea ice types based on ice roughness and seasonal meteorology for the purpose of sea ice modeling it is necessary to define an effective drag coefficient which relates regional stress to regional wind because sea ice is heterogeneous on scales less than 20 km regional stress is influenced by the distribution of surface roughness the buoyancy flux from quasi periodic leads and external atmospheric conditions principally the inversion height 103cd is 1 3 1 5 for smooth ice but is much greater for nonflat surfaces for wind speeds greater than 5 m s and air temperatures below freezing the effective 103cd is 2 5 3 0 for nearly continuous pack ice such as first year ice in seasonal ice zones and central arctic basin the range of values of 103cd is 3 0 3 7 for unstable boundary layers typical of off ice winds in the marginal ice zone miz or even greater if the ice has been broken by a recent storm cd values at the lower end of these ranges are associated with low inversion heights these coefficients are confirmed by 103cd of 2 9 2 5 and 3 1 for first year sea ice calculated from gust probe data collected by the noaa p 3 aircraft interior to the inner miz in the bering sea during the marginal ice zone experiment mizex west in february 1983 and 103cd of 2 6 for the arctic calculated from arctic ice dynamics joint experiment aidjex aircraft data for february 1976 the effective drag coefficient with the presence of even a small concentration of sea ice is greater than the oceanic value as shown by a 103cd of 2 2 calculated from noaa p 3 gust probe data over a 40 km track of 0 4 ice concentration in the outer miz of the greenland sea in june 1984 during mizex 84 the relation of surface wind and stress to the geostrophic wind for shallow inversion heights typical of high latitudes is reviewed with a turbulent closure atmospheric boundary layer model the winter arctic is typified by low inversions 100 m low geostrophic drag coefficients and large geostrophic surface wind turning angles with low functional dependence on surface roughness seasonal ice zones are typified by a more modest influence of the inversion on boundary layer characteristics

micromechanics model of ice fields ii monte carlo simulation the graph model presented in part i of this series provides the basis for development of a computer simulation of tightly packed ice fields taken as ensembles of square shaped ice floes with random physical properties a program based on an alternating direction scheme is developed to model the time evolution of a field of ice floes in a rectangular domain the simulation of a field in an arctic channel shows that there is a strong tendency for an earlier onset of microscale plastic flows and formation of irregular clusters of ice floes and openings in a field with spatially random properties versus a field with deterministic spatially homogeneous properties a special study is conducted of an elastic plastic transition in a field of 101 101 floes the transition to macroscopically plastic flow is possible only with a percolation of inelastic regions through the entire domain of the ice field the fact that this percolation is characterized by a noninteger fractal dimension uncovers a possibly principal generation mechanism of ice field morphologies and points to scale dependence in mechanics of ice fields for certain ranges of loads

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