Power laws in the sea ice floe size distribution: a stochastic theory

TL;DR

This paper develops a stochastic fragmentation-coagulation theory to explain the power-law distribution of sea ice floe sizes, supported by numerical simulations and matching observed seasonal variations.

Contribution

It introduces a new theoretical model that derives power-law distributions with variable exponents based on fracture and welding rates in sea ice.

Findings

Exact solutions show power-law distributions for floe sizes.

The exponent varies with fracture and welding rates.

The model explains seasonal changes in floe size distribution.

Abstract

Sea ice is a complex system, and observations have shown that ice segments (i.e., floes) have a wide range of sizes, with a floe size distribution that follows a power law. However, a theory for the power law and its exponent have remained elusive. Here, floe-resolving numerical simulations are investigated with a discrete element model, in order to gain further information by gathering statistics of fracture and welding events. Then, based on the insights from the floe-resolving simulations, a stochastic fragmentation-coagulation theory is proposed. Exact solutions are found with a power law. The power-law exponent can take a variety of values, and it depends on the fracture and welding rates. Such behavior is reminiscent of seasonal changes in the power-law exponent, which have been reported in past analyses of observational data.