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/content/aip/journal/chaos/21/1/10.1063/1.3555835
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27.
27. Physical constants and fixed system parameters used in this paper: size of ice-ocean layer: N = 16, M = 100; dimension of cubic cell h = 0.3 m; sharpness factor ; density of water ; density of ice ; latent heat of fusion ; volumetric heat capacity of water ; volumetric heat capacity of ice ; coupling constant ; thermal conductivity of water ; thermal conductivity of ice , atmospheric transmittance , albedo of open water , latitude .
28.
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34.
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35.
35. A qualitative argument for the stable state in the liquid phase is presented. If solar radiation is assumed to be constant in time (e.g. replaced with its yearly average), the total drive is given by a shift in RLW [Fig. 3(b)] such that it vanishes at three discrete energies. In the spatially homogeneous case a zero drive yields in Eq. (3). The fixed point with is stable due to the negative slope of the shifted RLW-curve in this E-regime. Simulations of Eq. (3) confirm a stable asymptotic cycle for OW in the “ vs E” phase space ( day). An analogous argument and simulation holds for the stable state in the solid phase.
36.
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37.
37. The spectral albedo for a given wave length is defined as the ratio of reflected to incoming shortwave solar radiation, . The albedo used throughout the paper is defined as the integral of the spectral albedo over the solar shortwave radiation spectrum.
38.
38. Diffuse solar radiation received during twilight () and corresponding corrections to the formula for the extraterrestrial solar flux density 0 are neglected. In addition, the error in omitting the eccentricity e in the extraterrestrial solar flux density, , is considered small since .
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/content/aip/journal/chaos/21/1/10.1063/1.3555835

/content/aip/journal/chaos/21/1/10.1063/1.3555835
2011-03-28
2016-10-26

### Abstract

The Arctic Ocean and sea ice form a feedback system that plays an important role in the global climate. The complexity of highly parameterized global circulation (climate) models makes it very difficult to assess feedback processes in climate without the concurrent use of simple models where the physics is understood. We introduce a two-dimensional energy-based regular network model to investigate feedback processes in an Arctic ice-ocean layer. The model includes the nonlinear aspect of the ice-water phase transition, a nonlinear diffusive energy transport within a heterogeneous ice-ocean lattice, and spatiotemporal atmospheric and oceanic forcing at the surfaces. First results for a horizontally homogeneous ice-ocean layer show bistability and related hysteresis between perennial ice and perennial open water for varying atmospheric heat influx. Seasonal ice cover exists as a transient phenomenon. We also find that ocean heat fluxes are more efficient than atmospheric heat fluxes to melt Arctic sea ice.

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