Stochastic dynamics of Arctic sea ice Part II: Multiplicative noise

TL;DR

This paper investigates how multiplicative noise influences the stochastic dynamics of Arctic sea ice energy, revealing differences from additive noise effects across various greenhouse gas forcing scenarios.

Contribution

It introduces a detailed analysis of multiplicative noise in a stochastic Arctic sea ice model, contrasting it with additive noise and exploring implications for ice state variability.

Findings

Multiplicative noise significantly alters the statistical moments of ice energy.

Different stochastic calculus interpretations (Itô vs Stratonovich) affect model outcomes.

The stochastic effects vary across the entire range of greenhouse gas forcing scenarios.

Abstract

We analyze the numerical solutions of a stochastic Arctic sea ice model with multiplicative noise over a wide range of external heat-fluxes, $\Delta F_0$, which correspond to greenhouse gas forcing. When the noise is multiplicative, the noise-magnitude depends on the state-variable, and this will influence the statistical moments in a manner that differs from the additive case, which we analyzed in Part I of this study. The state variable describing the deterministic backbone of our model is the energy, $E(t)$, contained in the ice or the ocean and for a thorough comparison and contrast we choose the simplest form of multiplicative noise $\sigma E(t) \xi(t)$, where $\sigma$ is the noise amplitude and $\xi(t)$ is the noise process. The case of constant additive noise (CA) we write as $\sigma\overline{E_S}\xi(t)$, in which $\overline{E_S}$ is the seasonally averaged value of the periodic deterministic steady-state solution $E_S(t)$, or the deterministic seasonal cycle. We then treat the case of seasonally-varying additive noise (SVA), $\sigma E_S(t) \xi(t)$, as well as two types of multiplicative noise that depend on the form of stochastic calculus (It\^{o} or Stratonovich) used to interpret the noise itself. The comparison of these four cases reveals the stochastic anatomy of the system over the entire range of the $\Delta F_0$ from the perennial ice states to near the ice-free state.