Sea-ice floe-size distribution in the context of spontaneous scaling emergence in stochastic systems

Abstract

Sea-ice floe-size distribution (FSD) in ice-pack covered seas influences many aspects of ocean-atmosphere interactions. However, data concerning FSD in the polar oceans are still sparse and processes shaping the observed FSD properties are poorly understood. Typically, power-law FSDs are assumed although no feasible explanation has been provided neither for this one nor for other properties of the observed distributions. Consequently, no model exists capable of predicting FSD parameters in any particular situation. Here I show that the observed FSDs can be well represented by a truncated Pareto distribution P(x)=x(-1-α) exp[(1-α)/x] , which is an emergent property of a certain group of multiplicative stochastic systems, described by the generalized Lotka-Volterra (GLV) equation. Building upon this recognition, a possibility of developing a simple agent-based GLV-type sea-ice model is considered. Contrary to simple power-law FSDs, GLV gives consistent estimates of the total floe perimeter, as well as floe-area distribution in agreement with observations.

Processes controlling surface, bottom and lateral melt of Arctic sea ice in a state of the art sea ice model

“…Example values in this range for the function P 0 are P 0 (2.0) = 0.75, P 0 (1.75) = 0.67, P 0 (1.5) = 0.56, P 0 (1.25) = 0.36, P 0 (1.1) = 0.17 and P 0 (1.0) = 0. Herman [51] introduces a different function P 0 that takes the values P 0 (2.0) = 1, P 0 (1.75) = 0.86, P 0 (1.5) = 0.67, P 0 (1.25) = 0.4, P 0 (1.1) = 0.18 and P 0 (1.0+) = 0.…”

“…Herman [51] and references therein). In our new lateral melt parametrization scheme, the variable L in equation (2.1) represents the average floe size instead of representing a unique floe size as in the default lateral melt scheme.…”

Shear-Jamming in Two-Dimensional Granular Materials with Power-Law Grain-Size Distribution

“…However, in most situations, the geometrical properties of the floes, like, e.g., the aspect ratio, remain within a relatively narrow range independently of the area and conditions of observation [11][12][13]. More importantly, the observed floe-size distributions (FSDs) are very wide and have power-law tails with an exponent α < 2 [11][12][13][14][15][16]. Although it is generally acknowledged that the granular nature of fragmented sea ice influences its dynamics (see, e.g., [17]), most large-scale sea ice models treat ice as a viscous-plastic continuum; our knowledge of how and when the processes taking place at a floe level influence the large-scale behavior of sea ice is very limited.…”

Brief communication: Impacts of ocean-wave-induced breakup of Antarctic sea ice via thermodynamics in a stand-alone version of the CICE sea-ice model

“…Herman, 2010). The probability-density function for the split power law, p(d), where d denotes floe diameter, is defined by…”