Large-time response of ice cover to a load moving along a frozen channel

Unsteady response of an ice cover in a channel with vertical walls is studied for large times. The ice deflection is caused by a load moving along the frozen channel at a constant speed. The ice cover is modelled as a thin elastic plate clamped to the walls of the channel. The time-dependent problem is solved by using the Fourier transform along the channel and the method of separating variables. In the system moving along the channel together with the load, the large-time deflection of the ice cover consists of steady deflection and standing waves in front and behind the load. The number of waves, their frequencies and wavenumbers depend on the speed of the load and the values of the critical speeds for the channel. The number of the waves and their amplitudes are calculated for a given load and its speed. The maximum stress in the ice as a function of the load speed is estimated.     

The attenuation of bending-gravity waves

The influence of the internal friction of snow covering solid elastic floating ice on the waves in a basin with density shear is considered. Dispersion dependences and spatial-temporal attenuation of surface and internal waves are investigated. The role of snow in the formation of the structure of ice bending deformations and fluid disturbances is determined.Translated by Mikhail M. Trufanov.     

基于中国北极考察布放浮标观测和数值模拟的海冰和积雪厚度变化分析

Sea ice and the snow pack on top of it were investigated using Chinese National Arctic Research Expedition(CHINARE) buoy data.Two polar hydrometeorological drifters,known as Zeno? ice stations,were deployed during CHINARE 2003.A new type of high-resolution Snow and Ice Mass Balance Arrays,known as SIMBA buoys,were deployed during CHINARE 2014.Data from those buoys were applied to investigate the thickness of sea ice and snow in the CHINARE domain.A simple approach was applied to estimate the average snow thickness on the basis of Zeno~ temperature data.Snow and ice thicknesses were also derived from vertical temperature profile data based on the SIMBA buoys.A one-dimensional snow and ice thermodynamic model(HIGHTSI) was applied to calculate the snow and ice thickness along the buoy drift trajectories.The model forcing was based on forecasts and analyses of the European Centre for Medium-Range Weather Forecasts(ECMWF).The Zeno~ buoys drifted in a confined area during 2003–2004.The snow thickness modelled applying HIGHTSI was consistent with results based on Zeno~ buoy data.The SIMBA buoys drifted from 81.1°N,157.4°W to 73.5°N,134.9°W in 15 months during2014–2015.The total ice thickness increased from an initial August 2014 value of 1.97 m to a maximum value of2.45 m before the onset of snow melt in May 2015;the last observation was approximately 1 m in late November2015.The ice thickness based on HIGHTSI agreed with SIMBA measurements,in particular when the seasonal variation of oceanic heat flux was taken into account,but the modelled snow thickness differed from the observed one.Sea ice thickness derived from SIMBA data was reasonably good in cold conditions,but challenges remain in both snow and ice thickness in summer.     

适用于Ku波段雷达高度计海冰干舷高度反演的积雪校正方法

工作在Ku波段的Cryo Sat-2和Sentinel-3A合成孔径雷达高度计是当前最先进的高度计。由于雷达回波信号的实际时间跟踪点较预设的时间跟踪点总发生偏移,而且Ku波段波长短,进行海冰探测时易受雪层干扰,造成雷达信号主散射面由海冰表面上移至雪层内,这两个因素都影响着海冰干舷高度的反演精度。针对这些问题,本文首先确定了Cryo Sat-2与Sentinel-3A雷达高度计反演北极海冰干舷高度的最优波形重跟踪阈值组合,然后分析了这两个Ku波段雷达信号的雪层穿透系数,发现Ku波段高度计的主散射面受雪层的影响显著,会高估海冰干舷高度。基于此,文中提出了一种改进的积雪校正方法,并以机载Operation Ice Bridge(OIB)为验证数据,将本文提出的方法与通用积雪校正法和欧洲空间局(European Space Agency,ESA)海冰干舷高度产品进行了对比验证。实验结果表明,本文提出的方法能够有效估计Ku波段电磁波穿透海冰表面积雪深度的比例系数,显著校正了通用积雪校正方法存在的高估海冰干舷高度的问题,提高了海冰干舷高度的估算精度。     

Interaction of uniform current with a circular cylinder submerged below an ice sheet

The problem of a uniform current passing through a circular cylinder submerged below an ice sheet is considered. The fluid flow is described by the linearized velocity potential theory, while the ice sheet is modelled through a thin elastic plate floating on the water surface. The Green function due to a source is first derived, which satisfies all the boundary conditions apart from that on the body surface. Through differentiating the Green function with respect to the source position, the multipoles are obtained. This allows the disturbed velocity potential to be constructed in the form of an infinite series with unknown coefficients which are obtained from the boundary condition. The result shows that there is a critical Froude number which depends on the physical properties of the ice sheet. Below this number there will be no flexural waves propagating to infinity and above this number there will be two waves, one on each side of the body. When the depth based Froude number is larger than 1, there will always be a wave at far upstream of the body. This is similar to those noticed in the related problem and is different from that in the free surface problem without ice sheet. Various results are provided, including the properties of the dispersion equation, resistance and lift, ice sheet deflection, and their physical features are discussed.     

The influence of snow viscosity on forced flexuralgravity waves in a basin with a density jump

The effect of the internal friction of snow covering floating ice on small-amplitude waves generated by a periodic-in-time source in a basin with a density jump is considered. The dependences of amplitude-phase characteristics of the wave disturbances induced by surface and internal waves on the snow viscosity coefficient, the oscillation frequency, and the depth of the source are studied.Translated by V. Puchkin.     

A global coupled sea ice–ocean model

A new sea ice model, GELATO, was developed at Centre National de Recherches Météorologiques (CNRM) and coupled with OPA global ocean model. The sea ice model includes elastic–viscous–plastic rheology, redistribution of ice floes of different thicknesses, and it also takes into account leads, snow cover and snow ice formation. Climatologies of atmospheric surface parameters are used to perform a 20-year global ocean–sea ice simulation, in order to compute surface heat fluxes from diagnosed sea ice or ocean surface temperature. A surface salinity restoring term is applied only to ocean grid cells with no sea ice to avoid significant surface salinity drifts, but no correction of sea surface temperature is introduced. In the Arctic the use of an ocean model substantially improves the representation of sea ice, and particularly of the ice edge in all seasons, as advection of heat and salt can be more accurately accounted for than in the case of, for example, a sea ice–ocean mixed layer model. In contrast, in the Antarctic, a region where ocean convective processes bear a much stronger influence in shaping sea ice characteristics, a better representation of convection and probably of sea ice (for example, of frazil sea ice, brine rejection) would be needed to improve the simulation of the annual cycle of the sea ice cover. The effect of the inclusion of several ice categories in the sea ice model is assessed by running a sensitivity experiment in which only one category of sea ice is considered, along with leads. In the Arctic, such an experiment clearly shows that a multicategory sea ice model better captures the position of the sea ice edge and yields much more realistic sea ice concentrations in most of the region, which is in agreement with results from Bitz et al. [J. Geophys. Res. 106 (C2) (2001) 2441–2463].     

The influence of the bottom contour on the deformed state of the ice cover due to the motion of the submarine

The authors have previously determined that the effectiveness and failure pattern of the ice cover caused by flexural-gravity waves generated by a submerged body motion near the bottom ice can greatly depend on the depth of the water area. In its turn, the presence of a ledge on the ice surface may affect a wave propagation pattern. This paper presents an experimental study of the bottom contour influence on the deflection and length of flexural-gravity waves. The authors describe a numerical model for the analysis of the deformed state of ice caused by hydrodynamic loads due to a submarine motion, taking into account the bottom contour. The experiments are carried out in the ice tank. The results of calculations and experiments are compared.     

Ice response to an underwater body moving in a frozen channel

Strains in the ice cover of a frozen channel, which are caused by a body moving under the ice at a constant speed along the channel, are studied. The channel is of rectangular cross section, the fluid in the channel is inviscid and incompressible. The ice cover is modeled by a thin viscoelastic plate clamped to the channel walls. The underwater body is modeled by a three-dimensional dipole. The intensity of the dipole is related to the speed and size of the underwater body. The problem is considered within the linear theory of hydroelasticity. For small deflections of the ice cover the velocity potential of the dipole in the channel is obtained by the method of images without account for ice deflection in the leading order. The problem of a dipole moving in the channel with rigid walls provides the hydrodynamic pressure on the upper boundary of the channel, which corresponds to the ice cover. This pressure distribution does not depend on the deflection of the ice cover in the leading approximation. The deflections of ice and the strains in the ice cover are independent of time in the coordinate system moving together with the dipole. The problem is solved numerically using the Fourier transform along the channel, the method of normal modes across the channel, and the truncation method for resulting infinite systems of linear equations. It was revealed that the strains in the ice strongly depend on the speed of the dipole with respect to the critical speeds of the hydroelastic waves propagating along the frozen channel. The width of the channel matters even it is much larger than the characteristic length of the ice cover.     

Alkalinity of sea ice in the high-latitudinal arctic according to the surveys performed at north pole drifting station 34 and characterization of the role of the arctic ice in the CO<Subscript>2</Subscript> exchange

The variability of the total alkalinity in the sea ice of the high-latitudinal Arctic from November 2005 to May 2006 is considered. For the bulk of the one- and two-year sea ice, the alkalinity dependence on the salinity is described as TA = k × Sal, where k is the salinity: alkalinity ratio in the under-ice water. The given relationship is valid within a wide salinity range from 0.1 psu in the desalinated fraction of two-year ice to 36 psu in the snow on the young ice surface. Geochemically significant deviations from the relationship noted were observed exclusively in the snow and the upper layer of one-year ice. In the upper layer of one-year ice, an alkalinity deficiency is observed (ΔTA ～ ?0.07 mequiv/kg, or ?15%). In the snow on the surface of the one-year ice, an alkalinity excess is formed under the desalination (ΔTA is as high as 1.3 mequiv/kg, 380%). The deviations registered are caused by the possibility of carbonate precipitation in the form of CaCO₃ · 6H₂O under the seawater freezing. It is shown that the ice formation and the following melting might cause a loss of the atmospheric CO₂ of up to 3 × 10¹² g C/year.     

雪热传导系数与穿过海冰的热通量研究

雪热传导系数是海冰质量平衡过程中的重要物理参数,决定了穿透海冰的热传导通量。北冰洋海冰质量平衡浮标观测获得多年冰上冬季温度链剖面可以明显地区分冰雪界面。本文考虑到冰雪界面处温度随时间变化,再根据冰雪界面热传导通量连续假定,提出了新的雪热传导系数计算方法。受不同环境因素影响,多年冰上各个浮标的雪热传导系数在0.23~0.41 W/（m·K）之间,均值为（0.32±0.08） W/（m·K）。北冰洋多年冰上冬季穿过海冰的热传导通量最大发生在11月至翌年3月,约14~16 W/m2。结冰季节,来自海冰自身降温的热量对穿过海冰向大气传输的热量贡献逐月减少,从9月100%减小到12月的35%,翌年的1月至3月稳定在10%左右。夏季,短波辐射通能量通过热传导自上而下加热海冰,海冰上层温度高于下层,热量传播方向与冬季反向,往海冰内部传递。直到9月短波辐射完全消失,气温下降,热量再次转变为自下往上传递。从冰底热传导来看,夏季出现海冰向冰水界面传递热量现象。由于雪较好的绝热性,冰上覆雪极大地削弱了海冰上层热传导通量,从而减缓了秋冬季节的结冰速度。尽管受雪厚影响,多年冰上层热传导通量与气温依旧具有很好的线性关系,气温每降低1℃,热传导通量增加约0.59 W/m2。     

The physical structures of snow and sea ice in the Arctic section of 150°-180°W during the summer of 2010

The physical structures of snow and sea ice in the Arctic section of 150°-180°W were observed on the basis of snow-pit, ice-core, and drill-hole measurements from late July to late August 2010. Almost all the investigated floes were first-year ice, except for one located north of Alaska, which was probably multi-year ice transported from north of the Canadian Arctic Archipelago during early summer. The snow covers over all the investigated floes were in the melting phase, with temperatures approaching 0℃ and densities of 295-398 kg/m3 . The snow covers can be divided into two to five layers of different textures, with most cases having a top layer of fresh snow, a round-grain layer in the middle, and slush and/or thin icing layers at the bottom. The first-year sea ice contained about 7%-17% granular ice at the top. There was no granular ice in the lower layers. The interior melting and desalination of sea ice introduced strong stratifications of temperature, salinity, density, and gas and brine volume fractions. The sea ice temperature exhibited linear cooling with depth, while the salinity and the density increased linearly with normalized depth from 0.2 to 0.9 and from 0 to 0.65, respectively. The top layer, especially the freeboard layer, had the lowest salinity and density, and consequently the largest gas content and the smallest brine content. Both the salinity and density in the ice basal layer were highly scattered due to large differences in ice porosity among the samples. The bulk average sea ice temperature, salinity, density, and gas and brine volume fractions were-0.8℃, 1.8, 837 kg/m3 , 9.3% and 10.4%, respectively. The snow cover, sea ice bottom, and sea ice interior show evidences of melting during mid-August in the investigated floe located at about 87°N, 175°W.     

Oblique Wave-Induced Responses of A VLFS Edged with A Pair of Inclined Perforated Plates

This paper is concerned with the hydroelastic responses of a mat-like, rectangular very large floating structure (VLFS) edged with a pair of horizontal/inclined perforated anti-motion plates in the context of the direct coupling method. The updated Lagrangian formulae are applied to establish the equilibrium equations of the VLFS and the total potential formula is employed for fluids in the numerical model including the viscous effect of the perforated plates through the Darcy''s law. The hybrid finite element-boundary element (FE-BE) method is implemented to determine the response reduction of VLFS with attached perforated plates under various oblique incident waves. Also, the numerical solutions are validated against a series of experimental tests. The effectiveness of the attached perforated plates in reducing the deflections of the VLFS can be significantly improved by selecting the proper design parameters such as the porous parameter, submergence depth, plate width and inclination angle for the given sea conditions.     

海冰表面和底层形态的特征相关性分析——以2011年早春拉布拉多海海冰实验数据为例

海冰表面和底层形态的特征相关性分析对海冰分类、气候研究以及海冰厚度估计等方面具有重要作用.目前,海冰底层形态的研究较少,且缺乏海冰表面和底层形态的相关性研究.针对这一问题,本文利用加拿大渔业和海洋局提供的积雪表面粗糙度高度(定义为海冰或积雪表面相对于周围平整表面的高度)、海冰底层轮廓、积雪深度以及海冰厚度数据,采用均方...     

Properties of sea ice and overlying snow in the Southern Sea of Okhotsk

The general properties of sea ice and overlying snow in the southern Sea of Okhotsk were examined during early February of 2003 to 2005 with the P/V “Soya”. Thin section analysis of crystal structure revealed that frazil ice (48% of total core length) was more prevalent than columnar ice (39%) and that stratigraphic layering was prominent with a mean layer thickness of 12 cm, indicating that dynamic processes are essential to ice growth. The mean thickness of ice blocks and visual observations suggest that ridging dominates the deformation process above thicknesses of 30 to 40 cm. As for snow, it was found that faceted crystals and depth hoar are dominant (78%), as which is also common in the Antarctic sea ice, and is indicative of the strong vertical temperature gradients within the snow. Stable isotope measurements (δ¹⁸O) indicate that snow ice occupies 9% of total core length and that the mass fraction of meteoric ice accounts for 1 to 2% of total ice volume, which is lower than the Antarctic sea ice. Associated with this, the effective fractionation coefficient during the freezing of seawater was also derived. Snow ice was characterized by lower density, higher salinity, and nearly twice the gas content of ice of seawater origin. In addition, it is shown that the surface brine volume fraction and freeboard are well correlated with ice thickness, indicating some promise for remote sensing approaches to the estimation of ice thickness.     

Modeling the evolution of snow, snow ice and ice in the Baltic Sea

A numerical 1‐dimensional fine grid sea ice thermodynamic model is constructed accounting specially for: (1) slush formation via flooding and percolation of rain‐ and snow meltwater, (2) the consequent snow ice formation via slush freezing, and (3) the effects of snow compaction on heat diffusion in snow cover. The model simulations from ice winter period 1979–90 are viewed against corresponding observations at the Kemi fast ice station (65 °39.8' N, 24° 31.4' E). The 11‐year averaged model results show good overall consistency with corresponding total ice thickness observations. The model slightly overestimates the snow ice thickness and underestimates the snow thickness in February and March, which is mainly addressed to the model assumption of isostatic balance (i.e., slush formation via flooding), which was probably not fully satisfied at the coastal Kemi fast ice station. Supposing that this assumption is nevertheless generally valid away from the very coastal fast ice zone, an estimate for sea ice sensitivity to changes in winter precipitation rate is produced. Increased precipitation leads to an increase only in snow ice thickness with little change in total ice thickness, while a reduction in precipitation of more than {213}50% causes a significant increase in total ice thickness. The difference in modeled total ice thickness for the case of artificially neglecting snow ice physics is about 25%, which indicates the importance of including snow ice physics in a sea ice model dealing with the seasonal sea ice zone.     

Sea-ice-thickness variability in the Chukchi Sea,spring and summer 2002–2004

Measurements of sea-ice thickness were obtained from drill holes, an ice-based electromagnetic induction instrument (IEM), and a ship-borne electromagnetic induction instrument (SEM) during the early-melt season in the southern Chukchi Sea in 2002 and 2004, and in late summer 2003 at the time of minimum ice extent in the northern Chukchi Sea. An ice roughness criterion was applied to distinguish between level and rough or ridged ice. Ice-thickness modes in the probability density functions (PDFs) derived from drill-hole and IEM measurements agreed well, with modes at 1.5–1.6 and 1.8–1.9 m for all data from level ice. The PDFs derived from SEM measurements show that the primary modes are at 0.1 and 1.1 m in 2003 and 0.7 m in 2004. In 2002 and 2004, significant fractions (between one-third and one-half) of level ice were found to consist of rafted ice segments. Snow depth varied significantly between years, with 2004 data showing more than half the snow cover on level ice to be at or below 0.05 m depth in late spring. Ice growth simulations and examination of ice drift and deformation history indicate that impacts of atmospheric and oceanic warming on level-ice thickness in the region over the past few decades are masked to a large extent by variability in snow depth and the contribution of deformation processes. In comparison with submarine sonar ice-thickness data from previous decades, a reduction in ice thickness by about 0.5–1 m is in part explained by the replacement of multi-year with first-year ice over the Chukchi and Beaufort shelves.     

A Numerical Study on Water Waves Generated by A Submerged Moving Body in A Two-Layer Fluid System

This is a numerical study on the time development of surface waves generated by a submerged body moving steadily in a two-layer fluid system, in which a layer of water is underlain by a layer of viscous mud. The fully nonlinear Navier-Stokes equations are solved on FLUENT with the Volume-of-Fluid (VOF) multiphase scheme in order to simulate the free surface waves as well as the water-mud interface waves as functions of time. The numerical model is validated by mimicking a reported experiment in a one-layer ...     

Ice Height and Backscattering Coefficient Variability over Greenland Ice Sheets Using SARAL Radar Altimeter

Ice sheets investigation is important with regard to climate change and contribution to the sea level rise or fall. Radar altimetry in complement with laser altimetry can serve as a suitable candidate for precise monitoring of ice sheet evaluations. SARAL due to higher observation into the polar region (up to 82.5°N) can cover nearly 100% of the Greenland ice sheet. Continuous ice tracking mode retracker can provide useful information about ice surfaces, that is, determining the snow coverage, ice sheet transaction margin, and the evolution of snow depth during winter more accurately. This study present the results obtained with SARAL satellite Altika radar altimeter over the Greenland ice sheet region. The altimeter high rate waveforms products are used for utilizing the full capability of the instrument. High resolution DEM (1 km) generated using ICESAT/GLAS altimeter has been used for selecting the good quality data over the study region. Four different retrackers—Ocean, ICE-1, ICE-2, and Sea-Ice—were tested on the SARAL altimeter data set and compared with the DEM extracted ice sheet elevations. Three different data analysis—region of interest (ROI), track analysis, and cross-over analysis—were performed for in-depth analysis of the ice height changes and back scattering coefficient variability. ROI's (1° × 0.5°) were selected based on accumulation dry snow zone, percolation zone, wet snow zone, and ablation zone. Finally to observe the effect of Ka band, SARAL results has been compared with the Envisat altimeter in terms of back scatter and error in the height retrieval due to penetration problem within the ice sheet layer. The new SARAL data set confirms the potential of ice altimetry and provides a new opportunity to monitor the ice sheet surface topography evolution.     

积雪密度演变对北极积雪深度模拟的影响

积雪具有复杂的时空分布,在高纬度地区的气−冰−海耦合系统中扮演了重要的角色。准确的积雪质量平衡计算可以帮助我们更好地理解海冰演变过程以及极区冰雪与大气之间的相互作用。雪密度是影响积雪质量平衡众多因素中的重要因子。现有的一维高分辨率冰雪热力学模型（如HIGHTSI）中,使用常数块体雪密度均值将降雪雪水当量转化为积雪深度。本文参考拉格朗日冰上积雪模型（SnowModel-LG）模式对积雪分层压实的处理,简化为新、旧两个雪层,并在质量守恒条件下同时考虑新、旧雪层深度对压实增密的响应,将该物理过程加入HIGHTSI模式中。利用ERA-Interim再分析数据作为大气强迫,针对北极15个冰质量平衡浮标沿其漂移轨迹模拟了降雪积累期海冰表面雪密度变化对积雪深度变化的影响,在原HIGHTSI设置下分别采用定常块体雪密度均值330 kg/m³（T1试验）、接近实际的常数新雪密度200 kg/m³（T2试验）以及改进后框架下新、旧雪层随时间压实增密的雪密度（T3试验）计算积雪深度,并将模拟结果与浮标观测进行对比。结果表明,本文改进的算法对雪密度变化的处理更为合理,且能较好地再现积雪深度的变化;考虑新、旧雪层深度对压实增密的响应能较好地避免以较低的降雪密度持续过度积累,以浮标观测为标准,分层积雪密度压实计算得到的平均绝对误差相对T2减小了5 cm。