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Abstract:

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Abstract:

&lt;p&gt;Arctic sea ice forms a thin but significant layer at the ocean surface, mediating key climate feedbacks. During summer, surface melting produces considerable volumes of water, which collect on the ice surface in ponds. These ponds have long been suggested as a contributing factor to the discrepancy between observed and predicted sea ice extent. When viewed at large scales ponds have a complicated, approximately fractal geometry and vary in area from tens to thousands of square meters. Increases in pond depth and area lead to further increases in heat absorption and overall melting, contributing to the ice-albedo feedback.&lt;/p&gt;&lt;p&gt;Previous modelling work has focussed either on the physics of individual ponds or on the statistical behaviour of systems of ponds. We present a physically-based network model for systems of ponds which accounts for both the individual and collective behaviour of ponds. Each pond initially occupies a distinct catchment basin and evolves according to a mass-conserving differential equation representing the melting dynamics for bare and water-covered ice. Ponds can later connect together to form a network with fluxes of water between catchment areas, constrained by the ice topography and pond water levels.&lt;/p&gt;&lt;p&gt;We use the model to explore how the evolution of pond area and hence melting depends on the governing parameters, and to explore how the connections between ponds develop over the melt season. Comparisons with observations are made to demonstrate the ways in which the model qualitatively replicates properties of pond systems, including fractal dimension of pond areas and two distinct regimes of pond complexity that are observed during their development cycle. Different perimeter-area relationships exist for ponds in the two regimes. The model replicates these relationships and exhibits a percolation transition around the transition between these regimes, a facet of pond behaviour suggested by previous studies. Our results reinforce the findings of these studies on percolation thresholds in pond systems and further allow us to constrain pond coverage at this threshold - an important quantity in measuring the scale and effects of the ice-albedo feedback.&lt;/p&gt;

Abstract:

Arctic sea ice is one of the most sensitive components of the Earth’s climate system. The underlying ocean plays an important role in the evolution of the ice cover through its heat flux at the ice-ocean interface which moderates ice growth and melt. Despite its importance, the spatio-temporal variations of this heat flux are not well understood. In this work, we combine direct numerical simulations of turbulent convection over fractal surfaces and analysis of time-series data from the Surface Heat Budget of the Arctic Ocean (SHEBA) program using Multifractal Detrended Fluctuation Analysis (MFDFA) to understand the nature of fluctuations in this heat flux. We identify key physical processes associated with the observed Hurst exponents calculated by the MFDFA, and how these evolve over time. We also discuss ongoing work on constructing simple stochastic models of the ocean heat flux to the ice, and potential use as a parameterisation.

Abstract:

Freshwater flux from the melting of Greenland’s Ice Sheet is thought to account for 25% of the observed rise in global mean sea level between 1992 and 2011, with a significant proportion of this associated with increased freshwater flux from marine terminating glaciers within coastal fjords. It has been suggested that increased ocean temperatures have triggered the retreat of Greenland’s outlet glaciers, with the melting of submarine glacier termini leading to an acceleration of inland regions of the ice sheet. Global climate  models  currently  operate  at  resolutions  too  coarse  to resolve  ice-ocean  interaction  on  the length  scales  typical  of  coastal  fjords. Therefore, a parameterization scheme is required to incorporate the relevant physics into such models.

As a first step towards such a parameterisation scheme, we develop theoretical understanding of the first order controls on heat and freshwater exchanges in Greenland’s proglacial fjords, guided by computational simulations in MITgcm. Fjords are modelled with idealised geometries, considering cases with and without bathymetric sills. The model parameterises melting at the glacier terminus, and non-hydrostatic flow in one or more buoyant plumes that form from fresh subglacial discharge at the glacier grounding line. We systematically explore how the overturning circulation and heat transport through a fjord respond to varying subglacial discharge.

In a subglacial-discharge dominated regime with flat bathymetry, we find that the horizontally integrated vertical flow structure set by buoyant plumes at the ice face remains unmodified along the length of the fjord, and is independent of the fjord width. For cases with either single or multiple subglacial-discharge plumes, we derive scaling laws for the heat and freshwater exchanges using buoyant plume theory, finding that the water in contact with the ice face mirrors that outside the fjord. This picture is complicated in the presence of a bathymetric sill, which can inhibit the transportation of deep coastal waters into the fjord. We conclude by discussing how our scaling laws might be used as a simple parameterisation of proglacial fjord dynamics in regimes where subglacial discharge controls the flow strength. We discuss how these results might be extended to incorporate the competing effects of circulation driven by along-fjord and along-shelf winds.

Abstract:

© 2019 The solidification of a binary alloy results in the formation of a porous mushy layer, within which spontaneous localisation of fluid flow can lead to the emergence of features over a range of spatial scales. We describe a finite volume method for simulating binary alloy solidification in two dimensions with local mesh refinement in space and time. The coupled heat, solute, and mass transport is described using an enthalpy method with flow described by a Darcy-Brinkman equation for flow across porous and liquid regions. The resulting equations are solved on a hierarchy of block-structured adaptive grids. A projection method is used to compute the fluid velocity, whilst the viscous and nonlinear diffusive terms are calculated using a semi-implicit scheme. A series of synchronization steps ensure that the scheme is flux-conservative and correct for errors that arise at the boundaries between different levels of refinement. We also develop a corresponding method using Darcy's law for flow in a porous medium/narrow Hele-Shaw cell. We demonstrate the accuracy and efficiency of our method using established benchmarks for solidification without flow and convection in a fixed porous medium, along with convergence tests for the fully coupled code. Finally, we demonstrate the ability of our method to simulate transient mushy layer growth with narrow liquid channels which evolve over time.