Discrete-element sea ice modeling – development of theoretical and numerical methods

Polish National Science Centre project No. 2015/19/B/ST10/01568 ("OPUS 10" Programme)

BASIC INFORMATION

• Project leader: Agnieszka Herman
• Participants: Marta Wenta (PhD student), Natalia strojna (MSc student)
• Project length: 36 months, starting from August 2016

PROJECT OBJECTIVES

The subject of the project is sea ice dynamics, especially dynamics of strongly fragmented sea ice and processes leading to ice fragmentation, as well as sub-mesoscale interactions of the sea ice cover with the ocean and the atmosphere. The main project objectives are:

1. To improve existing and to develop new mathematical models of sea ice–waves interactions suitable for further implementation in discrete-element models, i.e., consistent with underlying concepts of these models.
2. To formulate, based on the theoretical results, numerical ice–waves interaction algorithms, and to implement these algorithms in the code of the Discrete-Element bonded-particle Sea Ice model (DESIgn; see model homepage).
3. To verify a hypothesis that: (i) wave-induced breaking tends to produce narrow floe-size distributions (FSD) and polygonal floe shapes and (ii) that further “grinding” of ice floes by shearing deformation in the inner parts of the marginal ice zone is responsible for the observed heavy-tailed FSDs and rounded floe shapes.
4. To extend the range of applicability of the DESIgn model by developing and implementing parametrization schemes for selected physical processes (e.g., pressure ridging; freezing and melting). Also, to add new functionalities that will facilitate further development and novel applications of the model.
5. To improve our understanding of factors that may lead to rapid fragmentation of the sea ice cover over large domains, similar to the dramatic break-up event that took place in the Beaufort Sea in winter 2013.
6. To use high-resolution numerical modeling to improve our understanding of the atmosphere–sea ice–ocean interactions in situations with fragmented sea ice and/or close to the ice edge. To analyze the influence of FSD on heat and momentum fluxes at the sea surface, turbulence, mixing and vertical stability in the tropospheric and oceanic boundary layers. Also, to verify existing hypotheses of ice-band formation close to the ice edge.
7. To develop parameterizations of the above-mentioned effects, taking into account the floe-size distribution, suitable for future implementation in continuum sea ice models.

A full description of the project can be found here.
A short popular-science summary is here.

PROJECT OUTCOMES

Scientific papers:

Herman, A., Cheng, S., Shen, H.H., 2019. Wave energy attenuation in fields of colliding ice floes – Part 1: Discrete-element modelling of dissipation due to ice–water drag. The Cryosphere, 13, 2887-2900, doi: 10.5194/tc-13-2887-2019 (paper).
Abstract: The energy of water waves propagating through sea ice is attenuated due to non-dissipative (scattering) and dissipative processes. The nature of those processes and their contribution to attenuation depends on wave characteristics and ice properties and is usually difficult (or impossible) to determine from limited observations available. Therefore, many aspects of relevant dissipation mechanisms remain poorly understood. In this work, a discrete-element model (DEM) is used to study one of those mechanisms: dissipation due to ice–water drag. The model consists of two coupled parts, a DEM simulating the surge motion and collisions of ice floes driven by waves and a wave module solving the wave energy transport equation with source terms computed based on phase-averaged DEM results. The wave energy attenuation is analysed analytically for a limiting case of a compact, horizontally confined ice cover. It is shown that the usage of a quadratic drag law leads to non-exponential attenuation of wave amplitude a with distance x, of the form a(x)=1/(αx+1/a₀), with the attenuation rate α linearly proportional to the drag coefficient. The dependence of α on wave frequency ω varies with the dispersion relation used. For the open-water (OW) dispersion relation, α~ω⁴. For the mass loading dispersion relation, suitable for ice covers composed of small floes, the increase in α with ω is much faster than in the OW case, leading to very fast elimination of high-frequency components from the wave energy spectrum. For elastic-plate dispersion relation, suitable for large floes or continuous ice, α~ω^m within the high-frequency tail, with m close to 2.0–2.5; i.e. dissipation is much slower than in the OW case. The coupled DEM–wave model predicts the existence of two zones: a relatively narrow area of very strong attenuation close to the ice edge, with energetic floe collisions and therefore high instantaneous ice–water velocities, and an inner zone where ice floes are in permanent or semi-permanent contact with each other, with attenuation rates close to those analysed theoretically. Dissipation in the collisional zone increases with an increasing restitution coefficient of the ice and with decreasing floe size. In effect, two factors contribute to strong attenuation in fields of small ice floes: lower wave energy propagation speeds and higher relative ice–water velocities due to larger accelerations of floes with smaller mass and more collisions per unit surface area.

Herman, A., Cheng, S., Shen, H.H., 2019. Wave energy attenuation in fields of colliding ice floes – Part 2: A laboratory case study. The Cryosphere, 13, 2901-2914, doi: 10.5194/tc-13-2901-2019 (paper).
Abstract: This work analyses laboratory observations of wave energy attenuation in fragmented sea ice cover composed of interacting, colliding floes. The experiment, performed in a large (72-m long) ice tank, includes several groups of tests in which regular, unidirectional, small-amplitude waves of different periods were run through floating ice with different floe sizes. The vertical deflection of the ice was measured at several locations along the tank, and video recording was used to document the overall ice behaviour, including the presence of collisions and overwash of the ice surface. The observational data are analysed in combination with the results of two types of models: a model of wave scattering by a series of floating elastic plates, based on the matched eigenfunction expansion method (MEEM), and a coupled wave–ice model, based on discrete-element model (DEM) of sea ice and a wave model solving the stationary energy transport equation with two source terms, describing dissipation due to ice–water drag and due to overwash. The observed attenuation rates are significantly larger than those predicted by the MEEM model, indicating substantial contribution from dissipative processes. Moreover, the dissipation is frequency dependent, although, as we demonstrate in the example of two alternative theoretical attenuation curves, the quantitative nature of that dependence is difficult to determine and very sensitive to assumptions underlying the analysis. Similarly, more than one combination of the parameters of the coupled DEM–wave model (restitution coefficient, drag coefficient and overwash criteria) produce spatial attenuation patterns in good agreement with observed ones over a range of wave periods and floe sizes, making selection of “optimal” model settings difficult. The results demonstrate that experiments aimed at identifying dissipative processes accompanying wave propagation in sea ice and quantifying the contribution of those processes to the overall attenuation require simultaneous measurements of many processes over possibly large spatial domains.

Wenta, M., Herman, A., 2019. Area-averaged surface moisture flux over fragmented sea ice: floe size distribution effects and the associated convection structure within the atmospheric boundary layer. Atmosphere, 10, 654, doi: 10.3390/atmos10110654 (paper).
Abstract: Sea ice fragmentation results in the transformation of the surface from relatively homogeneous to highly heterogeneous. Atmospheric boundary layer (ABL) rapidly responds to those changes through a range of processes which are poorly understood and not parametrized in numerical weather prediction (NWP) models. The aim of this work is to increase our understanding and develop parametrization of the ABL response to different floe size distributions (FSD). The analysis is based on the results of simulations with the Weather Research and Forecasting model. Results show that FSD determines the distribution and intensity of convection within the ABL through its influence on the atmospheric circulation. Substantial differences between various FSDs are found in the analysis of spatial arrangement and strength of ABL convection. To incorporate those sub-grid effects in the NWP models, a correction factor for the calculation of surface moisture heat flux is developed. It is expressed as a function of floe size, sea ice concentration and wind speed, and enables a correction of the flux computed from area-averaged quantities, as is typically done in NWP models. In general, the presented study sheds some more light on the sea ice–atmosphere interactions and provides the first attempt to parametrize the influence of FSD on the ABL.

Herman, A., 2018. Wave-induced surge motion and collisions of sea ice floes: finite-floe-fize effects. J. Geophys. Res., 123, 7472-7494, doi: 10.1029/2018JC014500 (paper).
Abstract: Among many mechanisms potentially contributing to wave energy attenuation in sea ice are wave-induced ice floe collisions. At present, little is known about collision patterns and their phase-averaged effects under different combinations of sea ice properties (ice thickness, floe size, etc.) and wave forcing (wavelength and steepness). The existing parameterizations of collision-related effects are therefore based on several simplifying, unverified assumptions. In this work, wave-induced motion and collisions of ice floes are analyzed numerically with a model based on momentum equations for an arbitrary number of floes, with source terms computed by integrating local forcing (wave-induced dynamic pressure, surface drag, etc.) over the surface area/volume of each floe. It is shown that this simple model, with prescribed wave forcing (i.e., no wave-ice interactions), is capable of reproducing observed surge amplitudes up to floe sizes comparable with wavelength. A full Hertzian contact model is used instead of a simple hard-disk algorithm, which makes the model suitable for simulating both rapid collisions and prolonged contact between floes. The model equations are used to formulate heuristic collision criteria based on relative floe size, ice concentration, and wave steepness. The model is then run for different combinations of those three parameters, together with different restitution and drag coefficients, in order to analyze possible motion/collision patterns within the multidimensional parameter space, and phase-averaged effects of collisions: kinetic and contact stress, granular temperature, and work done by forces acting on the ice.

Wenta, M., Herman, A., 2018. The influence of the spatial distribution of leads and ice floes on the atmospheric boundary layer over fragmented sea ice. Ann. Glaciol., 59, 213-230, doi: 10.1017/aog.2018.15 (paper)
Abstract: The response of the atmospheric boundary layer (ABL) to subgrid-scale variations of sea ice properties and fracturing is poorly understood and not taken into account in mesoscale Numerical Weather Prediction (NWP) model parametrizations. In this paper we analyze three-dimensional air circulation within the ABL over fragmented sea ice. A series of idealized high-resolution simulations with the Weather Research and Forecasting (WRF) model is performed for several spatial distributions of ice floes and leads for two values of sea ice concentration (0.5 and 0.9) and several ambient wind speed profiles. The results show that the convective circulation within the ABL is sensitive to the subgrid-scale spatial distribution of sea ice. Considerable variability of several domain-averaged quantities – cloud liquid water content, surface turbulent heat flux (THF) – is found for different arrangements of floes. Moreover, the organized structure of air circulation leads to spatial covariance of variables characterizing the ABL. Based on the example of THF, it is demonstrated that this covariance may lead to substantial errors when THF values are estimated from area-averaged quantities, as it is done in mesoscale NWP models. This suggests the need for developing suitable parametrizations of ABL effects related to subgridscale sea ice features for these models.

Herman, A., 2017. Wave-induced stress and breaking of sea ice in a coupled hydrodynamic–discrete-element wave–ice model. The Cryosphere, 11, 2711-2725, doi: 10.5194/tc-11-2711-2017 (paper).
Abstract: In this paper, a coupled sea ice–wave model is developed and used to analyze wave-induced stress and breaking in sea ice for a range of wave and ice conditions. The sea ice module is a discrete-element bonded-particle model, in which ice is represented as cuboid “grains” floating on the water surface that can be connected to their neighbors by elastic joints. The joints may break if instantaneous stresses acting on them exceed their strength. The wave module is based on an open-source version of the Non-Hydrostatic WAVE model (NHWAVE). The two modules are coupled with proper boundary conditions for pressure and velocity, exchanged at every wave model time step. In the present version, the model operates in two dimensions (one vertical and one horizontal) and is suitable for simulating compact ice in which heave and pitch motion dominates over surge. In a series of simulations with varying sea ice properties and incoming wavelength it is shown that wave-induced stress reaches maximum values at a certain distance from the ice edge. The value of maximum stress depends on both ice properties and characteristics of incoming waves, but, crucially for ice breaking, the location at which the maximum occurs does not change with the incoming wavelength. Consequently, both regular and random (Jonswap spectrum) waves break the ice into floes with almost identical sizes. The width of the zone of broken ice depends on ice strength and wave attenuation rates in the ice.

Conference proceedings:

Herman, A., Cheng, S., Shen, H.H., 2019. Discrete-element modeling of wave-induced floe-floe collisions and collision-induced wave attenuation, Proc. IUTAM Symposium on Physics and Mechanics of Sea Ice, Aalto, Finland, 3-7 June 2019.

International conferences:

Herman, A., Cheng, S., Shen, H.H., 2019. Discrete-element modeling of wave-induced floe-floe collisions and collision-induced wave attenuation, IUTAM Symposium on Physics and Mechanics of Sea Ice, Aalto, Finland, 3-7 June 2019 (invited talk).

Wenta M., 2019. Floe size distribution influence on the spatial arrangement and intensity of convection, Polar-CORDEX (Coordinated Regional Downscaling Experiment - Arctic and Antarctic Domains) Meeting 2019, Danish Meteorological Institute, 6-7 Oct 2019, Copenhagen (presentation).

Wenta M., 2019. The influence of sea-ice floe-size distribution on the area-averaged values of surface fluxes, IGS (International Glaciological Society) 2019 Sea Ice Symposium, 19-23.08.2019, Winnipeg (presentation).

Herman, A., Cheng, S., Shen, H.H., 2019. Wave-induced floe–floe collisions and wave attenuation in the marginal ice zone, International Glaciological Society Sea Ice Symposium, Winnipeg, 19–23 Aug 2019 (poster).

Wenta. M., 2019. The sea ice floes size distribution influence on the turbulent and moisture fluxes in the atmospheric boundary layers, 15th Conference on Polar Meteorology and Oceanography, American Meteorological Society, 19-23 May 2019, Boulder (poster).

Wenta. M., 2019. The influence of ice fragmentation on the atmospheric boundary layer processes, Year of Polar Prediction (YOPP) Arctic Science Workshop, Finnish Meteorological Institute, 14-16 Jan 2019, Helsinki (presentation).

Herman, A., 2018. Wave-induced stress and breaking of sea ice in a coupled hydrodynamic discrete-element wave–ice model, SIAM COnference on Nonlinear Waves and Coherent Structures, Anaheim, California, USA, 11-14 June 2018 (invited talk).

Wenta. M., 2018. The influence of sea ice floes size and distribution on the area averaged turbulent fluxes, Polar-CORDEX (Coordinated Regional Downscaling Experiment - Arctic and Antarctic Domains) Meeting 2018, Instytut Geofizyki Polskiej Akademii Nauk, 17-19 Oct 2018, Warsaw (presentation).

Wenta M., 2018. The atmospheric boundary layer response to sea ice fragmentation, POLAR 2018, 19-23 June 2018, Davos (presentation).

Herman, A., 2018. Wave-induced floe-floe collisions and ocean-sea ice momentum transfer, POLAR-2018, Davos, Szwajcaria, 19-23 June 2018 (presentation).

Herman, A., 2017. DEM modelling of wave-induced floe-floe (and floe-structure) collisions, Ice–Structure Interaction Workshop, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 6-10 Nov 2017 (invited talk).

Herman, A., 2017. Discrete-element models of sea ice dynamics and fracture, Multi-scale Modelling of Ice Characteristics and Behaviour Workshop, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 11-15 Sep 2017 (invited talk).

Herman, A., 2017. Coupled hydrodynamic–discrete-element modeling of wave–sea ice interactions and ice breaking on waves, IGS Symposium on Polar Ice, Polar Climate, Polar Change, Boulder, Colorado, USA, 14-19 Aug 2017 (presentation).

Wenta M., Herman A., 2017. The influence of ice fragmentation on the atmospheric boundary layer processes, International Glaciological Society Symposium 2017 - Polar Ice, Polar Climate, Polar Change, 14–19 Jul 2017, Boulder, DOI: 10.13140/RG.2.2.28348.54408 (poster).

Wenta, M., Herman, A., 2017. Submesoscale atmospheric boundary layer processes over fragmented sea ice, 97th AMS Annual Meeting, 14th Conference on Polar Meteorology and Oceanography, Seattle, USA, 22-26 Jan 2017 (poster).

Polish conferences:

Wenta. M., 2019. Wpływ wielkości i rozmieszczenia kier lodowych na procesy fizyczne w warstwie granicznej atmosfery, XXIX Seminarium Meteorologii i Klimatologii Polarnej, Zakład Klimatologii i Ochrony Atmosfery Instytutu Geografii i Rozwoju Regionalnego Uniwersytetu Wrocławskiego, 9-10 May 2019, Wrocław (presentation).

Wenta M., 2017. Struktury konwekcyjne nad pofragmentowanym lodem morskim, XVI Sympozjum Młodych Oceanografów, Instytut Oceanografii, Uniwersytet Gdański, 24 Nov 2017, Gdynia (presentation).

Wenta M., 2017. Submesoscale Atmospheric Boundary Layer Processes over Fragmented Sea Ice, International Sopot Youth Conference 2017: Where the World is Heading, Instytut Oceanologii Polskiej Akademii Nauk, 26 May 2017 (presentation).