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Stephen J. Déry and L-B. Tremblay

1. Introduction At high latitudes, the world's oceans are covered by perennial or seasonal ice cover. Since subfreezing temperatures persist throughout most of the year, precipitation generally falls in the form of snow, blanketing the ice pack with a thin layer of highly reflective and insulating material. With its higher albedo, lower thermal conductivity, and higher attenuation for shortwave radiation (when compared with sea ice), snow reflects a large amount of incoming solar radiation

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Albert J. Semtner Jr.

predicted in climate simulations.A basic one-dimensional diffusion process is taken to act in the ice, with modifications due to penetration ofsolar radiation, melting of internal brine pockets, and accumulation of an insulating snow cover. Thisformulation is similar to that of a previous study by Maykut and Untersteiner, but the introduction of astreamlined numerical method makes the model more suitable for use at each grid point of a coupledatmosphere-ocean model. In spite of its simplicity, the ice

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Sebastian H. Mernild, David M. Holland, Denise Holland, Aqqalu Rosing-Asvid, Jacob C. Yde, Glen E. Liston, and Konrad Steffen

source of energy that primarily melts high latitude snow covers ( Liston and Hiemstra 2011 )] and in air temperature. A detailed evaluation of surface air temperature records was done by Hanna et al. (2012) yielding, on average for Ilulissat, a mean summer and winter temperature of 7.4° ± 0.7°C and −10.4° ± 2.5°C (2001–11), respectively. Fig . 4. Mean monthly (a) Jakobshavn Isbrae ice discharge (2009–10) ( Howat et al. 2011 ) and simulated runoff entering the Icefjord from the Jakobshavn Isbrae

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Syukuro Manabe, Kirk Bryan, and Michael J. Spelman

convective adjustment is introduced. The prediction of soil moisture and snow depth is basedupon the budget of water, snow and heat. Snow cover and sea ice are assumed to have much larger albedosthan soil surface or open sea, and have a very significant effect upon the heat balance of the surface of themodel. Starting from the initial conditions of an isothermal and dry atmosphere at rest, the long-term integrationof the joint model is conducted with the economical method adopted by Bryan and Manabe

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Syukuro Manabe, Kirk Bryan, and Michael J. Spelman

, the CO2-induced warming of the lower troposphere increases with increasinglatitudes and is at a maximum near the North Pole due partly to the albedo feedback process involving sea iceand snow cover. The warming of the upper ocean layer also increases with increasing latitudes up to about65 -N where the absorption of solar radiation increases markedly due to the poleward retreat of sea ice. Overthe Arctic Ocean, the warming is very large in the surface layer of the model atmosphere, whereas it is

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R. C. Frew, D. L. Feltham, P. R. Holland, and A. A. Petty

reduction in sea ice concentration (SIC) results in more solar shortwave radiation being absorbed, causing the SIC to reduce further. The albedo feedback has been shown to be a significant contributor to Arctic amplification of global warming ( Pithan and Mauritsen 2014 ). Unlike in the Arctic, in the Southern Ocean there is very little surface melting of the sea ice as it is covered by a thicker layer of snow and surface air temperatures are much colder. The snow acts to insulate the sea ice, slowing

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William D. Hibler III and John E. Walsh

formulation of Parkinson and Washington (1979). The basic surface energy budget (seeHibler, 1980, Appendix A) includes incoming shortwave and longwave radiation terms, an outgoing fluxof longwave radiation, and sensible and latent heatfluxes formulated in terms of bulk transfer coefficients. The two major departures from the formulation of Parkinson and Washington (1979) are that1) snow cover is not explicitly included and 2) noheat storage is allowed in the oceanic boundary layerwhen ice is present

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Jia Wang, L. A. Mysak, and R. G. Ingram

.5 m for the thin ice. Thegoal is to have the open water represented approximately by the combined fraction of both open waterand thin ice up to the cutoff thickness hR. This icethickness model (Hibler 1980, Appendix B), with bothdynamics and thermodynamics considered, is similarto the "zero-layer" thermodynamic ice model ofSemtner (1976). In this study, the snow cover is neglected due to lack of any detailed data. The ice compactness A is defined as the fractional area within agrid cell covered by

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Warren M. Washington, Albert J. Semtner Jr., Claire Parkinson, and Louise Morrison

in ice thickness. They specifiedas a function of time the fluxes of solar radiation,incoming longwave radiation, sensible and latent heatfrom the atmosphere and sensible heat from the ocean,as well as surface albedo changes and the accumulationrate of snow. They also included the effects of icesalinity and internal heating of ice from solar radiation.Semtner (1976) simplified the Maykut and Untersteinermodel so that it used substantially less computer timeand yet yielded essentially the same

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Th Fichefet and Ph Gaspar

thickness are substantiallyless than through open water (Hibler and Ackley, 1983).The new ice thickness is then averaged with the existingice thickness to obtain a single value and the snow isassumed to be uniformly distributed over the ice-covered portion of each grid cell. Internal ice temperaturesare then recomputed by a weighted formula. A minimum lead fraction of 0.5% (Parkinson and Washington, 1979) is assumed, accounting for the fact thatcracks or leads are always present in the ice owing

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