Modelling ice conditions in the easternmost Gulf of Finland in the Baltic Sea

To model ice conditions in the eastern Gulf of Finland, a high-resolution three-dimensional hydrodynamic model is coupled with the advanced sea-ice model HELMI (Haapala et al., 2005). To test the model in extreme situations, the ice pattern in the eastern Gulf of Finland was simulated for a mild ice winter (2007–2008) and for a moderate one (2003–2004). The reference runs were performed on the assumption that the ice in the model domain is fast ice if the sea depth is less than 10 m. Using this assumption, the ice thickness averaged over the Neva Bay (the easternmost part of the Gulf of Finland) is overestimated by the model for almost the entire wintertime in the mild winter and during the ice formation and melting periods in the moderate winter, as compared with the thickness reported in ice charts.     

The Deformational Response of a Viscoelastic Solid Earth Model Coupled to a Thermomechanical Ice Sheet Model

We apply a coupled thermomechanical ice sheet—self-gravitating viscoelastic solid Earth model (SGVEM), allowing for the dynamic exchange of ice thickness and bedrock deformation, in order to investigate the effect of viscoelastic deformation on ice dynamics and vice versa. In a synthetic glaciation scenario, we investigate the interaction between the ice sheet and the solid Earth deformation, the glacial-isostatic adjustment (GIA), accounting for an atmospheric forcing depending on the ice sheet surface altitude. We compare the results from the coupled model to runs with the common elastic lithosphere/relaxing asthenosphere (ELRA) model, where the lithosphere is represented by a thin plate and the mantle relaxes with one characteristic relaxation time, as well as to a rigid Earth without any deformation. We find that the deformational behaviour of the SGVEM on ice dynamics (i.e. stored ice volume, ice thickness and velocity field) is comparable to the ELRA for an optimal choice of the parameters in steady state, but exhibits differences in the transient behaviour. Beyond the ice sheet, in the region of peripheral forebulge, the differences in the transient surface deformation between ELRA and SGVEM are substantial, demonstrating the inadequacy of the ELRA model for interpreting constraints on GIA in the periphery of the ice sheet, such as sea-level indicators and GPS uplift rates.     

Ice‐cover variability on shallow lakes at high latitudes: model simulations and observations

A one‐dimensional thermodynamic model for simulating lake‐ice phenology is presented and evaluated. The model can be driven with observed daily or hourly atmospheric forcing of air temperature, relative humidity, wind speed, cloud amount and snowfall. In addition to computing the energy balance components, key model output includes the temperature profile at an arbitrary number of levels within the ice/snow (or the water temperature if there is no ice) and ice thickness (clear ice and snow‐ice) on a daily basis, as well as freeze‐up and break‐up dates. The lake‐ice model is used to simulate ice‐growth processes on shallow lakes in arctic, sub‐arctic, and high‐boreal forest environments. Model output is compared with field and remote sensing observations gathered over several ice seasons. Simulated ice thickness, including snow‐ice formation, compares favourably with field measurements. Ice‐on and ice‐off dates are also well simulated when compared with field and satellite observations, with a mean absolute difference of 2 days. Model simulations and observations illustrate the key role that snow cover plays on the seasonal evolution of ice thickness and the timing of spring break‐up. It is also shown that lake morphometry, depth in particular, is a determinant of ice‐off dates for shallow lakes at high latitudes. Copyright © 2003 John Wiley & Sons, Ltd.     

Modelling inter-annual and spatial variability of ice cover in a temperate lake with complex morphology

The formation of ice cover on lakes alters heat and energy transfer with the water column. The fraction of surface area covered by ice and the timing of ice-on and ice-off therefore affects hydrodynamics and the seasonal development of stratification and related ecosystem processes. Multi-year model simulations of temperate lake ecosystems that freeze partially or completely therefore require simulation of the formation and duration of ice cover. Here we present a multi-year hydrodynamic simulation of an alpine lake with complex morphology (Lower Lake Constance, LLC) using the three-dimensional (3D) model Aquatic Ecosystem Model (AEM3D) over a period of 9 years. LLC is subdivided into three basins (Gnadensee, Zeller See and Rheinsee) which differ in depth, morphological features, hydrodynamic conditions and ice cover phenology and thickness. Model results were validated with field observations and additional information on ice cover derived from a citizen science approach using information from social media. The model reproduced the occurrence of thin ice as well as its inter-annual variability and differentiated the frequency and extent of ice cover between the three sub-basins. It captured that full ice cover occurs almost each winter in Gnadensee, but only rarely in Zeller See and Rheinsee. The results indicate that the 3D model AEM3D is suitable for simulating long-term dynamics of thin ice cover in lakes with complex morphology and inter-annual changes in spatially heterogeneous ice cover.     

A box model of circulation and melting in ice shelf caverns

A simple box model of the circulation into and inside the ocean cavern beneath an ice shelf is used to estimate the melt rates of Antarctic glaciers and ice shelves. The model uses simplified cavern geometries and includes a coarse parameterization of the overturning circulation and vertical mixing. The melting/freezing physics at the ice shelf/ocean interface are those usually implemented in high-resolution circulation models of ice shelf caverns. The model is driven by the thermohaline inflow conditions and coupling to the heat and freshwater exchanges at the sea surface in front of the cavern. We tune the model for Pine Island Glacier and then apply it to six other major caverns. The dependence of the melting rate on thermohaline conditions at the ice shelf front is investigated for this set of caverns, including sensitivity studies, alternative parameterizations, and warming scenarios. An analytical relation between the melting rate and the inflow temperature is derived for a particular model version, showing a quadratic dependence of basal melting on small values of the temperature of the inflow, which changes to a linear dependence for larger values. The model predicts melting at all ice shelf bases in agreement with observations, ranging from below a meter per year for Ronne Ice Shelf to about 25 m/year for the Pine Island Glacier. In a warming scenario with a one-degree increase of the inflow temperature, the latter glacier responds with a 1.4-fold increase of the melting rate. Other caverns respond by more than a tenfold increase, as, e.g., Ronne Ice Shelf. The model is suitable for use as a simple fast module izn coarse large-scale ocean models.     

Assimilation of ice concentration in a coupled ice–ocean model,using the Ensemble Kalman filter

An implementation of the Ensemble Kalman filter (EnKF) with a coupled ice–ocean model is presented. The model system consists of a dynamic–thermodynamic ice model using the elastic-viscous-plastic (EVP) rheology coupled with the HYbrid Coordinate Ocean Model (HYCOM). The observed variable is ice concentration from passive microwave sensor data (SSM/I). The assimilation of ice concentration has the desired effect of reducing the difference between observations and model. Comparison of the assimilation experiment with a free-run experiment shows that there are large differences, especially in summer. In winter the differences are relatively small, partly because the atmospheric forcing used to run the model depends upon SSM/I data. The assimilation has the strongest impact close to the ice edge, where it ensures a correct location of the ice edge throughout the simulation. An inspection of the model ensemble statistics reveals that the error estimates of the model are too small in winter, partly a result of too low model ice-concentration variance in the central ice pack. It is found that the ensemble covariance between ice concentration and sea-surface temperature in the same grid cell is of the same sign (negative) throughout the year. The ensemble covariance between ice concentration and salinity is more dependent upon the physical mechanisms involved, with ice transport and freeze/melt giving different signs of the covariances. The ice-transport and ice-melt mechanisms also impact the ice-concentration variance and the covariance between ice concentration and ice thickness. The ensemble statistics show a high degree of complexity, which to some extent merits the use of computationally expensive assimilation methods, such as the Ensemble Kalman filter. The present study focuses on the assimilation of ice concentration, but it is understood that assimilation of other datasets, such as sea-surface temperature, would be beneficial.Responsible Editor: Jin-Song von Storch     

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.     

Tidal ice drift and ice-generated changes in the tidal dynamics/energetics on the Siberian continental shelf

Tidal ice drift is regarded as an element of the 3D tidal dynamics on the Siberian continental shelf. Two cases are considered: (1) when sea ice is immobile (in a horizontal plane), so that ice-induced changes of tidal characteristics may be treated as if they are limiting, and (2) when sea ice is moveable and internal stresses in the ice cover are described by a viscous-elastic rheology. It is shown that sea ice does not lead to radical changes of the tidal and energetic regimes, although their quantitative changes may be quite significant. In general, the ice-induced influence on the tidal dynamics is less than that on the tidal energetics. Therefore, the commonly accepted assumption that this influence may be viewed as being negligible is justified only partially. We present model results for tidal ice drift parameters—its magnitude, direction, the amplitude of tidal variations of ice concentration and the pressure of ice compression—as well as for ice-induced changes of tidal characteristics and the residual tidal ice drift. Partial attention is given to revealing the zones of ice compression–rarefaction, that is of importance in Arctic navigation.     

E) Organisations Nationales

Abstract

Sudden rapid advances or surges of glaciers and sections of smail ice caps are well known. After remaining dormant or in retreat over long periods of time these ice masses suddenly move forward rapidly with speeds about 2 orders of magnitude greater than usual. If such surges were to occur in large sections of the Antarctic ice sheet serious consequences could result. These include a significant rise of sea level, a substantial increase in the high-albedo ice cover around the continent especially in summer, and a cooling of the Antarctic ocean by the additional ice melting.

A numerical model has now been developed which simulates surging in certain glaciers and ice sheets in an apparently realistic manner. This model has been found to give close representations to a number of existing real surging temperate ice masses from small mountain glaciers to large sectors of ice caps. The model reproduces realistically many features of these ice masses such as the period of the surge, the duration, the velocity of advance, the magnitude of the advance, and the changes in ice thickness.

The application of the model to the Antarctic ice sheet is made more difficult by the problem caused by the temperature dependence of the flow properties of ice. This means that for a complete study the interaction with the environment needs to be considered. However, at this stage preliminary calculations indicate a number of features that are relevant to the effect of Antarctic ice surges on the global climate. These include the period between surges, the duration of the surge, the amount of ice advanced and the changes in thickness of the ice sheet.     

A uniform stress,multi-grain model for migration recrystallization in polar ice

A multi-grain model for a migration recrystallization process in polar ice is presented. The model is based on the Sachs-Reuss approximation of the stress homogeneity in a polycrystalline aggregate. An individual crystal of ice is treated as a transversely isotropic and incompressible medium which deforms by viscous creep. The highly anisotropic viscous behaviour of the ice crystal is described by a constitutive law expressing microscopic strain-rate in terms of the deviatoric stress and three fluidity parameters that define different viscous resistances of the crystal in different glide directions. It is assumed that the recrystallization occurs in those crystals in the aggregate which are most slowly deforming, and new crystals are nucleated at orientations which favour the crystal deformation by basal glide. The model predictions are illustrated by results of numerical simulations of simple flows, showing the evolution of the microscopic structure of ice and the variation of macroscopic viscosities with increasing deformations.     

Shelf-basin exchange in the Laptev Sea in the warming climate: a model study

GCM-based forecast simulations predict continuously increasing seasonality of the sea ice cover and an almost ice-free, summer-time, Arctic Ocean within several decades from the present. In this study we use a primitive equation ocean model: NEMO, coupled with the sea ice model LIM2, to test the hypothesis that under such an increased range in seasonal ice cover the intensity of shelf-basin water exchange will significantly increase. We use the simulated results for the Laptev Sea from a global model run 1958–2007 and compare results for two years with anomalously high and low summer sea ice extents: 1986–1987 and 2006–2007. The shelf–basin fluxes of volume, heat and salt during specific seasons are evaluated and attributed to plausible driving processes, with particular attention to dense water cascading. Analyses of the model temperature distribution at the depth of the intermediate maximum, associated with Atlantic Water, have shown a marked increase of the amount of the local origin cold water in late winter 2007 in the region, where dense water typically appears as a result of its formation on the shelf and subsequent downslope leakage. Calculation of the shelf-basin exchange during March-May in both years confirmed a substantial increase (a factor of two) of fluxes in “ice-free” 2007 compared to the “icy” 1987. According to several past model studies, dense water production on Arctic shelves in winter driven by ice freezing and brine rejection is not likely to cease in a warmer climate, but rather to increase. There is also observational evidence that cascading in the seasonally ice covered seas (e.g. the Barents Sea) is much more efficient than it is in the permanently ice covered Arctic Ocean, which supports these model results.     

Numerical Modeling of Ice Fog in Interior Alaska Using the Weather Research and Forecasting Model

An ice microphysics parameterization scheme has been modified to better describe and understand ice fog formation. The modeling effort is based on observations in the Sub-Arctic Region of Interior Alaska, where ice fog occurs frequently during the cold season due to abundant water vapor sources and strong inversions existing near the surface at extremely low air temperatures. The microphysical characteristics of ice fog are different from those of other ice clouds, implying that the microphysical processes of ice should be changed in order to generate ice fog particles. Ice fog microphysical characteristics were derived with the NCAR Video Ice Particle Sampler during strong ice fog cases in the vicinity of Fairbanks, Alaska, in January and February 2012. To improve the prediction of ice fog in the Weather Research and Forecasting model, observational data were used to change particle size distribution properties and gravitational settling rates, as well as to implement a homogeneous freezing process. The newly implemented homogeneous freezing process compliments the existing heterogeneous freezing scheme and generates a higher number concentration of ice crystals than the original Thompson scheme. The size distribution of ice crystals is changed into a Gamma distribution with the shape factor of 2.0, using the observed size distribution. Furthermore, gravitational settling rates are reduced for the ice crystals since the crystals in ice fog do not precipitate in a similar manner when compared to the ice crystals of cirrus clouds. The slow terminal velocity plays a role in increasing the time scale for the ice crystals to settle to the surface. Sensitivity tests contribute to understanding the effects of water vapor emissions as an anthropogenic source on the formation of ice fog.     

Modeling the Development of Ice Phenomena in Rivers as Applied to the Assessment of Probable Changes in Ice Conditions at Various Scenarios of the Future Climate

The results of investigations of the alteration in river ice regime associated with the global climate warming are presented. It is shown that a simple model based on the relationship between the dates of ice phenomena and the average air temperature for the preceding month can be used for the assessment of probable changes in ice phenomena at various scenarios of the future climate. It is found that as a rule, the allowance made for the rate of streamflow in autumn does not improve the assessment of the probable dates of river freeze-up, whereas the model of the process of river breakup allows improving the estimates of the relevant shifts in the dates.     

A mathematical model of polythermal glaciers and ice sheets

Abstract

A mathematical model of the flow and temperature distribution of polythermal glaciers or ice sheets is deduced. Cold ice is treated as a non-linear viscous heat conducting fluid, while temperate ice is regarded as a binary mixture of ice and water. The simplest mixture concept with two balance laws of mass but only one balance law of momentum and energy is proposed. The field equations for the ice and water content and the boundary conditions which must hold at the free surface, at the ice-water interface, at the cold-temperature transition surface and at the rock-bed are deduced. In particular it is shown that an earlier formulation of polythermal ice due to Fowler and Larson (1978) is inconsistent. No boundary value problems are solved as the emphasis is on the physical motivation and justification of the principles.     

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.     

Improved sea ice parcel trajectories in the Arctic via data assimilation

An assimilated sea ice motion product is used to track ice parcels in several regions of the Arctic over time periods of one day to several weeks during 1992-1993. Motions simulated using a two-dimensional, dynamic-thermodynamic sea ice model are combined with motions derived from daily 85 GHz special sensor microwave/imager (SSM/I) imagery using an optimal interpolation method that minimizes error covariance. Assimilation attenuates the tracking error over the stand-alone model in comparison to buoy trajectories with the same starting location and time. The average 14-day assimilated trajectory's displacement error is as much as 34% lower than the model trajectory, while the RMS direction error is decreased by up to 10 degrees (24%). Assimilation can also yield an estimate of dispersion, which is not retrievable by point buoy observations. An assimilation approach improves estimates of ice drift and has the potential to further the understanding of ice mass flux, freshwater flux, and pollutant transport in the polar regions.     

Wind and melt driven circulation in a marginal sea ice edge frontal system: a numerical model

A seasonal ice edge zone is a unique frontal system with an air-ice-sea interface. This paper is a report on the numerical results from a quasi-three dimensional, time dependent, non-linear numerical model of circulation at a continental shelf-seasonal ice edge zone. The purpose of the experiments is to model the hydrography and circulation, including upwelling, baroclinic geostrophic flow, and inertial oscillations, at the ice edge with emphasis on examining the driving forces of wind and melting ice. It is suggested that the non-linear acceleration terms and vertical density diffusion terms are negligible and that the horizontal density diffusion terms are of secondary importance within the time and space scales of the experiments. The vertical eddy viscosity terms are important in a spin-up time scale and for Ekman transport and a bottom Ekman layer. The effects of the horizontal eddy viscosity terms are observable (a long-ice jet is diffused away from the ice edge) by the end (72 h) of the model runs.Model results are compared with available oceanographic and meteorological data for verification. The observed and modeled features of melt water induced water column stability, frontal structure, and ice edge upwelling are briefly discussed relative to observed ice edge primary production. Because the model is relatively general in nature, it is readily applicable to other seasonal or marginal ice edge zones in either hemisphere.     

Stability of supraglacial debris

Rock debris on the surface of ablating glaciers is not static, and is often transported across the ice surface as relief evolves during melt. This supraglacial debris transport has a strong influence on the spatial distribution of melt, and is implicated in the formation of hummocky glacial topography in deglaciated terrain. Furthermore, as ice‐dammed lakes and ice‐cored slopes become increasingly common in deglaciating watersheds, there is rising concern about hazards to humans and infrastructure posed by mass‐wasting of ice‐cored debris. The existing quantitative framework for describing these debris transport processes is limited, making it difficult to account for transport in mass balance, hazard assessment, and landscape development models. This paper develops a theoretical framework for assessing slope stability and gravitational mass transport in a debris‐covered ice setting. Excess water pressure at the interface between ablating ice and lowering debris is computed by combining Darcy's law with a meltwater balance. A limit‐equilibrium slope stability analysis is then applied to hypothetical debris layers with end‐member moisture conditions derived from a downslope meltwater balance that includes production and seepage. The resulting model system constrains maximum stable slope angles and lengths that vary with debris texture, thickness, and the rate of meltwater production. Model predictions are compared with field observations and with digital elevation model (DEM)‐derived terrain metrics from two modern debris‐covered glaciers on Mount Rainier, USA. Copyright © 2017 John Wiley & Sons, Ltd.