# Timetable (SIPW01)

## Multi-scale modelling of ice characteristics and behaviour

Monday 11th September 2017 to Friday 15th September 2017

 09:00 to 09:35 Registration 09:35 to 09:45 Welcome from David Abrahams (INI Director) 09:45 to 10:30 Donald K. Perovich (Dartmouth College)Small to big, quick to slow: The many scales of sea ice properties and processes Sea ice properties and processes exhibit tremendous variability over spatial scales from millimeters to megameters. Sea ice also evolves over temporal scales of hours to days to seasons to decades. To understand sea ice properties, it is critical to examine and connect the processes that occur on these different scales. For example, sea ice microstructure impacts the partitioning of sunlight. Melt ponds are governed by meter-scale topography and millimeter-scale brine channels. There are similarities in the size distributions of brine pockets, melt ponds, and floes; features that span spatial scales of several orders of magnitude. The timing of short term events, such as snowfall or lead openings, has a large impact on the seasonal evolution of the ice cover. Sea ice scale issues are also important when considering the interactions of the atmosphere-sea ice-ocean-biogeochemical system. INI 1 10:30 to 11:00 Morning Coffee 11:00 to 11:45 Ken Golden (University of Utah)Linking scales in the sea ice system Sea ice exhibits complex structure ranging from the sub-millimeter scale brine inclusions to ice floes and coherent​ ​dynamics on the scale of hundreds of kilometers. I will give an overview of how we are using​ ​ theories of composite​ materials and statistical physics to link behavior on various scales in the sea ice system. In particular, we address key questions in sea ice homogenization, where information on smaller scales is incorporated into rigorous representations of effective large scale behavior. We also consider the inverse problem where small scale structure is inferred from larger scale effective properties. INI 1 11:45 to 12:30 Agnieszka Herman (University of Gdansk)Discrete-element models of sea ice dynamics and fracture At geophysical scales, continuum models provide established and computationally efficient tools for simulating sea ice dynamics and thermodynamics. In recent years, rapidly increasing computational power and availability of high-resolution (esp. remote-sensing) data have contributed to a revival of discrete-element methods (DEM), enabling the analysis of sea ice at smaller spatial and temporal scales. Treating sea ice as a collection of individual, interacting floes, and thus recognizing it as an example of a granular material, opens a wide range of new tools and analysis possibilities for sea ice research. Bonded-particle DEM models enable to simulate brittle fragmentation of sea ice – a process that, in spite of substantial progress in recent years, still poses problems for continuum models. Moreover, there is growing evidence that the size distribution of sea ice floes has a substantial influence on a wide range of processes in the upper ocean, lower atmosphere and within sea ice itself, and it is in turn shaped by those processes. By directly taking into account fragmentation (i.e., floe formation) and dynamics of individual floes, DEMs provide tools to better understand complex interactions between sea ice, ocean and atmosphere acting at the floe-level.In this talk, I will present and discuss selected examples of the application of DEM models to sea ice dynamics and fragmentation problems. The examples will include: wind- and current-induced drift of fragmented (granular’’) sea ice, and the influence of ice concentration and floe-size distribution on the sea ice response to forcing; jamming phase transition under compressive and shear strain, and force transmission in ice subject to different strain fields; sea ice breaking by waves analyzed with a coupled DEM–hydrodynamic model. Unsolved problems and challenges (both computational and theoretical) related to the application of DEMs to sea ice will be presented as well.Most results presented in this talk were obtained with a Discrete-Element bonded-particle Sea Ice model DESIgn, implemented as a toolbox for the open-source numerical library LIGGGHTS (http://www.cfdem.com/). The code and documentation of DESIgn are freely available at http://herman.ocean.ug.edu.pl/LIGGGHTSseaice.html. INI 1 12:30 to 13:30 Lunch @ Wolfson Court 13:30 to 14:00 Break 14:00 to 14:30 Veronique Dansereau (CNRS (Centre national de la recherche scientifique))A new continuum rheological model for the deformation and drift of sea ice Co-authors: Pierre Saramito (CNRS-LJK), Jérôme Weiss (CNRS-ISTerre), Philippe Lattes (Total S.A. E&P)Axel Roy (1) Véronique Dansereau (2)* Jérôme Weiss (2)  Christian Haas (3) Matthieu Chevalier (4) 1 École Nationale de la Météorologie, Météo France, Toulouse, France 2 Institut des Sciences de la Terre, CNRS UMR 5275, Université de Grenoble, Grenoble, France 3 Alfred Wegener Institute, Bremerhaven, Germany 4 CNRM/GMGEC/IOGA Météo France, Toulouse, France Sea ice models are most often compared to each other and to observations in terms of the spatial distribution of the simulated ice thickness. An equally important, and perhaps more appropriate, metric to investigate the mechanical behaviour of the sea ice cover is the ice thickness distribution, i.e., the probability density function, of which some valuable information have been available for some time from drill-hole, upward looking submarine-mounted sonar (USL) and airborne electromagnetic (EM) sounding measurements. An important issue naturally arises when comparing sea ice thickness distributions based on measurements made at the meter scale with that estimated from regional and global sea ice model simulations, with a typical resolution of a few kilometres; the issue of scale dependance. Using USL sea ice draft profiles and EM thickness measurements, we investigate the scaling properties of the sea ice thickness over the Arctic to address the following question: how does the sea ice thickness distribution evolve with the scale of observation? The autocorrelation calculations performed here allow extending previous analyses based on single USL transects (up to 50 km-long) and point to long-range correlations in the thickness of the sea ice cover reaching as far as a few hundreds of kilometres. Multi-fractal analyses are conducted to investigate the variability of the the ice thickness distribution with the spatial scale of observation up to these scales. INI 1 14:30 to 15:00 Christopher Horvat (Harvard University); (Brown University)Floe size and ice thickness distributions INI 1 15:00 to 15:30 Afternoon Tea 15:30 to 16:00 Courtenay Strong (University of Utah)Filling the polar data gap with harmonic functions Coauthors: Elena Cherkaev and Kenneth M. Golden The “polar data gap” is a region around the North Pole where satellite orbits do not provide sufficient coverage for estimating sea ice concentrations. This gap is conventionally made circular and assumed to be ice-covered for the purpose of sea ice extent calculations, but recent conditions around the perimeter of the gap indicate that this assumption may already be invalid. We present partial differential equation-based models for estimating sea ice concentrations within the area of the data gap. In particular, the sea ice concentration field is assumed to satisfy Laplace’s equation with boundary conditions determined by observed sea ice concentrations on the perimeter of the gap region. This type of idealization in the concentration field has already proved to be quite useful in establishing an objective method for measuring the “width” of the marginal ice zone—a highly irregular, annular-shaped region of the ice pack that interacts with the ocean, and typically surrounds the inner core of most densely packed sea ice. Realistic spatial heterogeneity in the idealized concentration field is achieved by adding a spatially autocorrelated stochastic field with temporally varying standard deviation derived from the variability of observations around the gap. Testing in circular regions around the gap yields observation-model correlation exceeding 0.6 to 0.7, and sea ice concentration mean absolute deviations smaller than 0.01. This approach based on solving an elliptic partial differential equation with given boundary conditions has sufficient generality to also provide more sophisticated models which could be more accurate than the Laplace equation version, and such potential generalizations are explored. INI 1 16:00 to 17:00 Elizabeth Hunke (Los Alamos National Laboratory)Rothschild Lecture: Large-scale sea ice modeling: societal needs and community development The CICE sea ice model is used extensively by climate and Earth system research groups, and also by operational centers for applications such as numerical weather prediction and guidance for military operations.  While the research community is energetically improving the models, observationalists are busy taking measurements and operational experts are using all of it to produce predictive products via data assimilation.  In the past, the sea ice research and operational communities have been somewhat distinct with little cross-pollination.  Partly in response to this issue, the CICE Consortium has formed as a formal community effort to to provide a mechanism for accelerating further sea ice model development and its transfer into operational uses.  This colloquium will provide a broad overview of current CICE model capabilities and uses, highlight new analysis techniques for statistically assessing model skill against diverse observations, and discuss our community engagement effort, all toward addressing society's needs in the face of the Earth’s changing polar regions. INI 1 17:00 to 18:00 Rothschild Drinks Reception at INI
 09:00 to 09:45 Vernon Squire (University of Otago)Marginal Ice Zone Evolution due to Wave-Induced Breaking Co-authors: Vernon Squire (University of Otago, NZ), Fabien Montiel (University of Otago, NZ)The influence of ice–albedo temperature feedback arising as a result of global climate change is believed to be enhanced by a contemporaneous intensification of wave climate in the polar seas. Waves break up the sea ice deeper into the ice-covered oceans, accelerating its melting and increasing the area of ice-free ocean, which in turn allows for more energetic waves and swells to develop. Although much attention has been given to the effect of a broken-up ice cover, e.g. the marginal ice zone, on the propagation of ocean waves, less is known about the impact of waves on the morphology of the sea ice. The latter is principally governed by the break-up of flexing sea-ice floes as a result of wave interactions. A sub-grid scale process-based model describing the two-way coupling between the ocean waves and sea ice systems will be discussed, with a particular focus on how to parametrize this coupling in ice/ocean models. INI 1 09:45 to 10:30 Martin Vancoppenolle (CNRS (Centre national de la recherche scientifique)); (Université Pierre & Marie Curie-Paris VI)A compilation of research and thoughts on the future of sea ice models. On the point of view of a model developer, it looks somehow desperating to see how little sensitive climate models seem to be to the representation of sea ice processes. By comparison, atmospheric and oceanic forcing, or mean climate state look much more influential. Is this a good reason to give up sea ice model development ? I will give a few elements of answer to explain why we should maintain our efforts, and illustrate how the European teams involved in NEMO will project themselves into the next generation of sea ice models. INI 1 10:30 to 11:00 Morning Coffee 11:00 to 11:45 Daniel Feltham (University of Reading)Sea ice model physics: in search of fidelity INI 1 11:45 to 12:30 Wieslaw Maslowski (Naval Postgraduate School)Sensitivity of Arctic sea ice state to model parameter space, resolved processes and climate coupling INI 1 12:30 to 13:30 Lunch @ Wolfson Court 13:30 to 14:00 Break 14:00 to 14:30 Sukun Cheng (Clarkson University)A viscoelastic model for wave propagation in the marginal ice zone Co-author: Hayley H. Shen (Clarkson Univerisity) Regional wave forecasts for the Arctic rely on a good understanding of wave propagation through sea ice covers. Disagreements among the models and the lack of field validations cause uncertainty in wave forecasts. A recent viscoelastic ice model has been developed to simulate a wide range of ice covers. This model synthesized several previous models that considered ice covers as a continuum. In this model, a simple parameterization is used to include both energy storage and dissipation mechanisms. However, the model has two parameters, the equivalent elasticity and viscosity, which need to be determined. In this presentation, we will describe the basis of this model, and its calibration using data from a recent field campaign. INI 1 14:30 to 15:00 Christian Samspon (University of Utah); (University of Utah); (UNC Chapel Hill and RIMS)Effective Rheology and Wave Propagation in the Marginal Ice Zone Co-authors: Ken Golden (University of Utah), Ben Murphy (University of Utah), Elena Cherkaev (University of Utah) Wave-ice interactions in the polar oceans comprise a complex but important set of processes influencing sea ice extent, ice pack albedo, and ice thickness. In both the Arctic and Antarctic, the ice floe size distribution in the Marginal Ice Zone (MIZ) plays a central role in the properties of wave propagation. Ocean waves break up and shape the ice floes which, in turn, attenuate various wave characteristics. Recently, continuum models have been developed which treat the MIZ as a two-component composite of ice and slushy water. The top layer has been taken to be purely elastic, purely viscous or viscoelastic. At the heart of these models are effective parameters, namely, the effective elasticity, viscosity, and complex viscoelasticity. In practice, these effective parameters, which depend on the composite geometry and the physical properties of the constituents, are quite difficult to determine. To help overcome this limitation, we employ the methods of homogenization theory, in a quasistatic, fixed frequency regime, to find a Stieltjes integral representation for the complex viscoelasticity. This integral representation involves the spectral measure of a self adjoint operator and provides what we believe are the first rigorous bounds on the effective viscoelasticity of the sea ice pack. The bounds themselves depend on the moments of the measure which in turn depend on the geometry of the ice floe configurations. This work has the potential to provide simple parameterizations of wave properties which take into account floe concentration and geometry. INI 1 15:00 to 15:30 Afternoon Tea 15:30 to 16:00 Konrad Simon (Universität Hamburg)Flow-induced Coordinates for Transient Advection-Diffusion Equations with Multiple Scales Co-author: Jörn Behrens (University of Hamburg, Germany) Simulation over a long time scale in climate sciences as done, e.g., in paleo climate simulations require coarse grids due to computational constraints. Unresolved scales, however, significantly influence the coarse grid variables. Such processes include (slowly) moving land-sea interfaces or ice shields as well as flow over urbanic areas. Neglecting these scales amounts to unreliable simulation results. State-of-the-art dynamical cores represent the influence of subscale processes typically via subscale parametrizations and often employ heuristic coupling of scales. Our aim is to improve the mathematical consistency of the upscaling process that transfers information from the subgrid to the coarse prognostic scale (and vice-versa). We investigate a new bottom-up techniques for advection dominated problems arising in climate simulations [Lauritzen et al. (2011)]. Our tools are based on ideas for multiscale finite element methods for elliptic problems that play a role in oil reservoir modeling and porous media in general [Efendiev and Hou (2009), Graham et al. (2012)]. Modifying these ideas is in necessary in order to account for the transient and advection dominated character which is typical for flows encountered in climate models. We present a new Garlerkin based idea to account for the typical difficulties in climate simulations. Our modified ideas employ a change of coordinates based on a coarse grid characteristic transform induced by the advection term in order to account for appropriate subgrid boundary conditions for the multiscale basis functions which are essential for such approaches. We present results from sample runs for a simple advection-diffusion equation with rapidly varying coefficients on several scales. INI 1 16:00 to 16:30 Noa Kraitzman (University of Utah)Advection enhanced diffusion processes We investigate thermal conduction in sea ice in the presence of fluid flow, as an important example of an advection diffusion process in the polar marine environment. Using new Stieltjes integral representations for the effective diffusivity in turbulent transport, we present a series of rigorous bounds on the effective diffusivity, obtained using Padé approximates in terms of the Péclet number. We first analyze the effective thermal conductivity of sea ice in the presence of an averaged convective velocity field, neglecting the two phase microstructure of sea ice, and then present a homogenization analysis of the full two component system composed of brine and ice. INI 1 16:30 to 18:00 Poster Session with Wine Reception at INI
 09:00 to 09:45 Ian Eisenman (University of California, San Diego)Sea ice stability and rapid retreat Changes in the Arctic sea ice cover involve an amplifying feedback associated with the surface albedo, which suggests the possibility of unstable climate states and bifurcations, or "tipping points". The first part of this talk will focus on the stability of the sea ice cover. Previous studies have identified sea ice bifurcations due to the ice-albedo feedback occurring in a range of idealized models but not in comprehensive global climate models (GCMs). We will propose a physical explanation for this discrepancy, drawing on a model that we developed to bridge the gap between low-order models and GCMs. The results support the finding from GCMs, suggesting that such bifurcations should not be expected in nature. Nonetheless, Arctic sea ice has been observed to retreat abruptly during recent decades. The second part of the talk will address how well the observed rate of Arctic sea ice retreat is simulated in the suite of current GCMs. Although the majority of these GCMs simulate less sea ice retreat than observed, a substantial minority of the simulations do capture the observed rate of retreat. Hence a number of recent studies have suggested that the GCMs and the observations are consistent. We will show that the observed rate of Arctic sea ice retreat actually occurs only in GCM simulations with substantially more global warming than observed. We will suggest an alternative metric for evaluating the GCMs that takes this factor into consideration. The results suggest that the GCMs may be getting the right Arctic sea ice trends for the wrong reasons. INI 1 09:45 to 10:30 Andrew Roberts (Naval Postgraduate School)Modeling macro-porosity of ridged sea ice in basin-scale models Co-authors: Elizabeth Hunke (Los Alamos National Laboratory), William Lipscomb (National Center for Atmospheric Research), Samy Kamal (Naval Postgraduate School), Wieslaw Maslowski (Naval Postgraduate School) One of the largest limitations of current-generation sea ice models is that they characterize sea ice morphology using a thickness distribution, g(h), over an area A(x). This inherently introduces a scale limitation to sea ice models, because g(h) only represents the relative quantity of ice of thickness, h, over a region, rather than describe how thickness is locally organized. Moreover, the approach assumes that sea ice deformed into rafts, folds, buckles, ridges and hummocks is equally as porous as undeformed ice, despite strong evidence to the contrary. This problem may be addressed by expanding the state space of the thickness distribution to become a multivariate distribution g(h,phi) where phi is the macro-porosity of sea ice rubble. Then, sea ice ridging may be described using a Euler-Lagrange equation for ridge cross-sections that mimic many of the characteristics of existing ridge-scale simulations. The approach requires careful consideration of non-conservative components of ridging, and, in the most basic approach, can use a Coulombic failure criteria applied vertically within ridges to predict their angle of repose, macro-porosity, extent and seperation in large scale models. This talk presents the theoretical basis for this new method of simulating sea ice thickness. INI 1 10:30 to 11:00 Morning Coffee 11:00 to 11:45 Dirk Notz (Max-Planck-Institut für Meteorology)When is all the sea ice gone? Co-author: Julienne Stroeve (University College London) We examine the future evolution of Arctic sea ice, focusing in particular on the allowable carbon dioxide emissions that would prevent sea-ice loss in the various seasons. In this context, the relationship between model simulations and observations is crucial, and we will briefly discuss why it is so difficult to identify models that most reliably simulate the future of Arctic sea ice. Based on this discussion, we will then introduce an observation-based estimate of the future evolution of Arctic sea ice that considers our physical understanding of the main processes that cause the ongoing ice loss. INI 1 11:45 to 12:30 Pat Langhorne (University of Otago)Changes to sea ice thickness distribution due to Ice Shelf Water Co-authors: Inga Smith, Greg Leonard, Andrew Pauling, Pat Wongpan, David Dempsey, Ken Hughes, Craig Purdie, Eamon Frazer (University of Otago), Mike Williams, Natalie Robinson, Craig Stevens (NIWA), Alena Malyarenko, Stefan Jendersie (NIWA & University of Otago), Wolfgang Rack, Gemma Brett, Dan Price (University of Canterbury), Christian Haas (Alfred Wegener Institute), Cecilia Bitz (University of Washington), Andy Mahoney (Geophysical Institute) and Tim Haskell (Callaghan Innovation Ltd) Satellite observations show that the winter maximum sea ice extent around Antarctica has been increasing slowly over the past three decades, a behaviour superficially at odds with “global warming”.  One hypothesis is that an increase in freshwater input from the base of ice shelves has influenced sea ice extent. This process can drive seawater temperatures below the surface freezing point. Ice crystals then persist in the supercooled water and add to the mass of the coastal sea ice cover. The crystals may form a porous, friable layer, called the sub-ice platelet layer, which can be several metres thick beneath the two-metres of sea ice. Consequently platelet ice formation not only causes sea ice to be thicker, but it also alters the hydrostatic relationship between sea ice elevation and thickness, influencing satellite altimeter determination of sea ice thickness.   Here we describe ice shelf–sea ice interaction at a range of scales from parameterization in an Earth System Model, to the sub-metre detail of winter ice-ocean relationships. On a regional scale we have focused on a location affected by an ISW outflow at the surface. Regional ocean modeling and satellite altimeter observations provide context for airborne sea ice thickness surveys using electromagnetic (EM) induction sounding. These regional surveys have been supported over smaller geographic areas by detailed on-ice sea ice and snow thickness measurements, by on-ice EM induction transects of sea ice thickness, and by under-ice oceanographic observations that track the heat deficit and mixing in the upper ocean at selected sites. INI 1 12:30 to 13:30 Lunch @ Wolfson Court 13:30 to 17:00 Free Afternoon 19:30 to 22:00 Formal Dinner at Emmanuel College
 09:00 to 09:45 Andrew Wells (University of Oxford)Models of multi-scale and multi-phase sea ice thermodynamics Sea ice is a multi-phase material, consisting of a mixture of solid ice crystals and liquid brine. The properties of this mixture vary significantly during initial ice growth, from the growth of suspensions of frazil ice crystals in supercooled leads and polynyas through to a reactive porous material during consolidated congelation growth. The resulting mixture is also inherently multi-scale, with the macroscopic scales of interest such as ice depth or mixed layer depth being many order of magnitude larger than the scale of an individual ice crystal. This talk will provide an introduction to key continuum models of the multi-phase and multi-scale thermodynamics of sea ice growth. I will introduce so-called "mushy layer theory" for characterising the evolution of reactive porous sea ice, and also review theories of crystal suspension dynamics derived from a master equation. Selected case studies will be used to illustrate the application of these theories to predict ice accumulation rates, structural properties of ice, and interaction with convective flow. INI 1 09:45 to 10:30 Daniela Flocco (University of Reading)Modeling Arctic melt ponds INI 1 10:30 to 11:00 Morning Coffee 11:00 to 11:45 Robert Bridges (Total E&P UK Limited)Sea ice research - needs and gaps INI 1 11:45 to 12:30 Erik Almkvist (Viking Ice Concultancy)Different ice observation methods in marine operations INI 1 12:30 to 13:30 Lunch @ Wolfson Court 13:30 to 14:00 Break 14:00 to 14:30 Predrag Popovic (University of Chicago)Simple rules govern the patterns of Arctic sea ice melt ponds Co-authors: BB Cael (MIT), Mary Silber (University of Chicago), Dorian Abbot (University of Chicago) Climate change, amplified in the far north, has led to a rapid sea ice decline in recent years. Melt ponds that form on the surface of Arctic sea ice in the summer significantly lower the ice albedo, thereby accelerating ice melt. Pond geometry controls the details of this crucial feedback. However, a question of modeling pond geometry remains unresolved. Here we show that an extremely simple model of voids surrounding randomly sized and placed overlapping circles reproduces the essential features of pond patterns. The model has only two parameters, circle scale and the fraction of the surface covered by voids, which we choose by comparing the model to pond images. Using these parameters the void model robustly reproduces all of the examined pond features such as the ponds' area-perimeter relationship and the area-abundance relationship over nearly 7 orders of magnitude. By analyzing airborne photographs of sea ice, we also find that the pond width distribution is surpris ingly constant across different years, regions, and ice types. These results demonstrate that the geometric and abundance patterns of Arctic melt ponds can be simply described, and can guide future models of Arctic melt ponds to improve predictions of how sea ice will respond to Arctic warming. INI 1 14:30 to 15:00 Yiping Ma (Northumbria University)Ising model for melt ponds on Arctic sea ice Perhaps the most iconic feature of melting Arctic sea ice is the formation of distinctive, complex ponds on its surface during late spring. The evolution of melt ponds and their geometrical characteristics determines the albedo of sea ice, a key parameter in climate modeling. However, a theoretical understanding of this evolution, and predictions of geometrical features, have remained elusive. To address this fundamental problem in polar climate science, here we introduce a two dimensional random field Ising model for melt ponds. The ponds are identified as metastable states of the system, where the binary spin variable corresponds to the presence of melt water or ice on the sea ice surface. With only a minimal set of physical parameters, the model predictions agree very closely with observed power law scaling of the pond size distribution and critical length scale where melt ponds undergo a transition in fractal geometry.This is joint work with Ivan Sudakov, Courtenay Strong, and Kenneth M. Golden. INI 1 15:00 to 15:30 Afternoon Tea 15:30 to 16:00 Woosok Moon (British Antarctic Survey); (NORDITA)Nonlinear stochastic time series analysis for sea ice and climate INI 1 16:00 to 17:00 Grae Worster (University of Cambridge)Brine rejection from sea ice Brine rejection from sea ice provides a significant contribution to the buoyancy flux that drives ocean circulations.  Indeed, it provides the dominant contribution in the case of polynyas but the situation with consolidated sea ice is more complex.  Although salt is rejected completely by the ice crystals that form when the ocean freezes, it can be retained as saturated brine within the interstices of sea ice.  Buoyancy-driven convection driven in the interior of sea ice can cause the dense brine to drain into the underlying ocean via brine channels that form by dissolution of the ice matrix.  These intricate interactions between fluid flow and phase change occur on the scale of millimetres to centimetres within sea ice but their consequences must be captured within the sea-ice components of climate models.  I will describe the fundamental physical processes that govern the occurrence and rates of brine rejection from sea ice, and show how the understanding gained from detailed mathematical models of local, three-dimensional processes can be incorporated into an appropriately parameterised one-dimensional model of convection in sea ice suitable for inclusion in climate models. INI 1