A Multiplicative-Noise Mechanism for Variability Amplification under Radiative Forcing in an Arctic Energy-Balance Model
We propose and analyse a mechanism by which $\mathrm{CO}_2$-driven radiative forcing can increase Arctic temperature variability in a stochastic Sellers-type energy-balance model. Starting from a fast-slow formulation in which insolation is modelled by a rapidly mean-reverting Ornstein-Uhlenbeck process while temperature evolves on a slow macroweather timescale, a Wong-Zakai reduction leads to a stochastic energy-balance equation with \emph{multiplicative} noise. After linearising around the stable equilibrium $T^{*,\lambda}$, we derive an explicit expression for the stationary variance of the temperature anomaly and prove that it increases monotonically with the forcing parameter $\lambda$ whenever $T^{*,\lambda}$ lies in the ice-sensitive regime of the co-albedo. We then consider a spatial anomaly model and its finite-difference semi-discretisation, obtaining a finite-dimensional SDE. Under natural stability conditions and nonnegative noise correlations, we establish a component-wise monotone increase of the stationary covariance matrix with respect to $\lambda$, including its off-diagonal entries. In particular, radiative forcing amplifies not only local variances but also the covariance between temperature anomalies at distinct spatial locations, indicating increased similarity in the variability of the anomaly field across space.