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Paul R. Holland

Abstract

Idealized modeling studies have shown that the melting of ice shelves varies as a quadratic function of ocean temperature. However, this result is the equilibrium response, derived from steady ice–ocean simulations subjected to a fixed ocean forcing. This study considers instead the transient response of melting, using unsteady simulations subjected to forcing conditions that are oscillated with a range of periods. The results show that the residence time of water in the subice cavity offers a critical time scale. When the forcing varies slowly (period of oscillation ≫ residence time), the cavity is fully flushed with forcing anomalies at all stages of the cycle and melting follows the equilibrium response. When the forcing varies rapidly (period ≤ residence time), multiple cold and warm anomalies coexist in the cavity, cancelling each other in the spatial mean and thus inducing a relatively steady melt rate. This implies that all ice shelves have a maximum frequency of ocean variability that can be manifested in melting. Between these two extremes, an intermediate regime occurs in which melting follows the equilibrium response during the cooling phase of the forcing cycle, but deviates during warming. The results show that ice shelves forced by warm water have high melt rates, high equilibrium sensitivity, and short residence times and hence a short time scale over which the equilibrium sensitivity is manifest. The most rapid melting adjustment is induced by warm anomalies that are also saline. Thus, ice shelves in the Amundsen and Bellingshausen Seas, Antarctica, are highly sensitive to ocean change.

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Paul R. Holland and Noriaki Kimura

Abstract

In recent decades, Antarctic sea ice has expanded slightly while Arctic sea ice has contracted dramatically. The anthropogenic contribution to these changes cannot be fully assessed unless climate models are able to reproduce them. Process-based evaluation is needed to provide a clear view of the capabilities and limitations of such models. In this study, ice concentration and drift derived from AMSR-E data during 2003–10 are combined to derive a climatology of the ice concentration budget at both poles. This enables an observational decomposition of the seasonal dynamic and thermodynamic changes in ice cover. In both hemispheres, the results show spring ice loss dominated by ice melting. In other seasons ice divergence maintains freezing in the inner pack while advection causes melting at the ice edge, as ice is transported beyond the region where it is thermodynamically sustainable. Mechanical redistribution provides an important sink of ice concentration in the central Arctic and around the Antarctic coastline. This insight builds upon existing understanding of the sea ice cycle gained from ice and climate models, and the datasets may provide a valuable tool in validating such models in the future.

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Paul R. Holland, Adrian Jenkins, and David M. Holland

Abstract

A three-dimensional ocean general circulation model is used to study the response of idealized ice shelves to a series of ocean-warming scenarios. The model predicts that the total ice shelf basal melt increases quadratically as the ocean offshore of the ice front warms. This occurs because the melt rate is proportional to the product of ocean flow speed and temperature in the mixed layer directly beneath the ice shelf, both of which are found to increase linearly with ocean warming. The behavior of this complex primitive equation model can be described surprisingly well with recourse to an idealized reduced system of equations, and it is shown that this system supports a melt rate response to warming that is generally quadratic in nature. This study confirms and unifies several previous examinations of the relation between melt rate and ocean temperature but disagrees with other results, particularly the claim that a single melt rate sensitivity to warming is universally valid. The hypothesized warming does not necessarily require a heat input to the ocean, as warmer waters (or larger volumes of “warm” water) may reach ice shelves purely through a shift in ocean circulation. Since ice shelves link the Antarctic Ice Sheet to the climate of the Southern Ocean, this finding of an above-linear rise in ice shelf mass loss as the ocean steadily warms is of significant importance to understanding ice sheet evolution and sea level rise.

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Paul R. Holland and Daniel L. Feltham

Abstract

A model of the dynamics and thermodynamics of a plume of meltwater at the base of an ice shelf is presented. Such ice shelf water plumes may become supercooled and deposit marine ice if they rise (because of the pressure decrease in the in situ freezing temperature), so the model incorporates both melting and freezing at the ice shelf base and a multiple-size-class model of frazil ice dynamics and deposition. The plume is considered in two horizontal dimensions, so the influence of Coriolis forces is incorporated for the first time. It is found that rotation is extremely influential, with simulated plumes flowing in near-geostrophy because of the low friction at a smooth ice shelf base. As a result, an ice shelf water plume will only rise and become supercooled (and thus deposit marine ice) if it is constrained to flow upslope by topography. This result agrees with the observed distribution of marine ice under Filchner–Ronne Ice Shelf, Antarctica. In addition, it is found that the model only produces reasonable marine ice formation rates when an accurate ice shelf draft is used, implying that the characteristics of real ice shelf water plumes can only be captured using models with both rotation and a realistic topography.

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Alexander V. Wilchinsky, Daniel L. Feltham, and Paul R. Holland

Abstract

A drag law accounting for Ekman rotation adjacent to a flat, horizontal boundary is proposed for use in a plume model that is written in terms of the depth-mean velocity. The drag law contains a variable turning angle between the mean velocity and the drag imposed by the turbulent boundary layer. The effect of the variable turning angle in the drag law is studied for a plume of ice shelf water (ISW) ascending and turning beneath an Antarctic ice shelf with draft decreasing away from the grounding line. As the ISW plume ascends the sloping ice shelf–ocean boundary, it can melt the ice shelf, which alters the buoyancy forcing driving the plume motion. Under these conditions, the typical turning angle is of order −10° over most of the plume area for a range of drag coefficients (the minus sign arises for the Southern Hemisphere). The rotation of the drag with respect to the mean velocity is found to be significant if the drag coefficient exceeds 0.003; in this case the plume body propagates farther along and across the base of the ice shelf than a plume with the standard quadratic drag law with no turning angle.

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Satoshi Kimura, Paul R. Holland, Adrian Jenkins, and Matthew Piggott

Abstract

Freshwater produced by the surface melting of ice sheets is commonly discharged into ocean fjords from the bottom of deep fjord-terminating glaciers. The discharge of the freshwater forms upwelling plumes in front of the glacier calving face. This study simulates the meltwater plumes emanated into an unstratified environment using a nonhydrostatic ocean model with an unstructured mesh and subgrid-scale mixing calibrated by comparison to established plume theory. The presence of an ice face reduces the entrainment of seawater into the meltwater plumes, so the plumes remain attached to the ice front, in contrast to previous simple models. Ice melting increases with height above the discharge, also in contrast to some simple models, and the authors speculate that this “overcutting” may contribute to the tendency of icebergs to topple inwards toward the ice face upon calving. The overall melt rate is found to increase with discharge flux only up to a critical value, which depends on the channel size. The melt rate is not a simple function of the subglacial discharge flux, as assumed by many previous studies. For a given discharge flux, the geometry of the plume source also significantly affects the melting, with higher melt rates obtained for a thinner, wider source. In a wider channel, two plumes are emanated near the source and these plumes eventually coalesce. Such merged meltwater plumes ascend faster and increase the maximum melt rate near the center of the channel. The melt rate per unit discharge decreases as the subglacial system becomes more channelized.

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Alek A. Petty, Daniel L. Feltham, and Paul R. Holland

Abstract

The Antarctic continental shelf seas feature a bimodal distribution of water mass temperature, with the Amundsen and Bellingshausen Seas flooded by Circumpolar Deep Water that is several degrees Celsius warmer than the cold shelf waters prevalent in the Weddell and Ross Seas. This bimodal distribution could be caused by differences in atmospheric forcing, ocean dynamics, ocean and ice feedbacks, or some combination of these factors. In this study, a highly simplified coupled sea ice–mixed layer model is developed to investigate the physical processes controlling this situation. Under regional atmospheric forcings and parameter choices the 10-yr simulations demonstrate a complete destratification of the Weddell Sea water column in winter, forming cold, relatively saline shelf waters, while the Amundsen Sea winter mixed layer remains shallower, allowing a layer of deep warm water to persist. Applying the Weddell atmospheric forcing to the Amundsen Sea model destratifies the water column after two years, and applying the Amundsen forcing to the Weddell Sea model results in a shallower steady-state winter mixed layer that no longer destratifies the water column. This suggests that the regional difference in atmospheric forcings alone is sufficient to account for the bimodal distribution in Antarctic shelf-sea temperatures. The model prediction of mixed layer depth is most sensitive to the air temperature forcing, but a switch in all forcings is required to prevent destratification of the Weddell Sea water column.

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Paul R. Holland, Richard E. Hewitt, and Matthew M. Scase

Abstract

Sinking dense plumes are important in many oceanographic settings, notably the polar formation of deep and bottom waters. The dense water sources feeding such plumes are commonly affected by tidal modulation, leading to plume variability on short time scales. In a simple unsteady theory of one-dimensional plumes (based on conservation equations for volume, momentum, and buoyancy), this plume variability is manifested as waves that travel down the resulting current. Using numerical techniques applied to the hyperbolic conservation equations, this study investigates the novel concept that these waves may break as they travel down the plumes, triggering intense local mixing between the dense fluid and surrounding ocean. The results demonstrate that the waves break at geophysically relevant distances from the plume source. The location of wave breaking is very sensitive to plume drag from the seabed, the properties of the dense source, and the amplitude and period of the source modulation. To the extent that the simple model represents the real world, these results suggest that wave breaking originating from the tidal modulation of dense plumes could lead to a strong and previously unexplored source of local deep-ocean mixing.

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Leo Middleton, Catherine A. Vreugdenhil, Paul R. Holland, and John R. Taylor

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The transport of heat and salt through turbulent ice shelf–ocean boundary layers is a large source of uncertainty within ocean models of ice shelf cavities. This study uses small-scale, high-resolution, 3D numerical simulations to model an idealized boundary layer beneath a melting ice shelf to investigate the influence of ambient turbulence on double-diffusive convection (i.e., convection driven by the difference in diffusivities between salinity and temperature). Isotropic turbulence is forced throughout the simulations and the temperature and salinity are initialized with homogeneous values similar to observations. The initial temperature and the strength of forced turbulence are varied as controlling parameters within an oceanographically relevant parameter space. Two contrasting regimes are identified. In one regime double-diffusive convection dominates, and in the other convection is inhibited by the forced turbulence. The convective regime occurs for high temperatures and low turbulence levels, where it is long lived and affects the flow, melt rate, and melt pattern. A criterion for identifying convection in terms of the temperature and salinity profiles, and the turbulent dissipation rate, is proposed. This criterion may be applied to observations and theoretical models to quantify the effect of double-diffusive convection on ice shelf melt rates.

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James R. Jordan, Satoshi Kimura, Paul R. Holland, Adrian Jenkins, and Matthew D. Piggott

Abstract

It has been suggested that the presence of frazil ice can lead to a conditional instability in seawater. Any frazil forming in the water column reduces the bulk density of a parcel of frazil–seawater mixture, causing it to rise. As a result of the pressure decrease in the freezing point, this causes more frazil to form, causing the parcel to accelerate, and so on. This study uses linear stability analysis and a nonhydrostatic ocean model to study this instability. The authors find that frazil ice growth caused by the rising of supercooled water is indeed able to generate a buoyancy-driven instability. Even in a gravitationally stable water column, the frazil ice mechanism can still generate convection. The instability does not operate in the presence of strong density stratification, high thermal driving (warm water), a small initial perturbation, high background mixing, or the prevalence of large frazil ice crystals. In an unstable water column, the instability is not necessarily expressed in frazil ice at all times; an initial frazil perturbation may melt and refreeze. Given a large enough initial perturbation, this instability can allow significant ice growth. A model shows frazil ice growth in an Ice Shelf Water plume several kilometers from an ice shelf, under similar conditions to observations of frazil ice growth under sea ice. The presence of this instability could be a factor affecting the growth of sea ice near ice shelves, with implications for Antarctic Bottom Water formation.

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