Abstract
For a wide range of values of the intensity of the incoming solar radiation, the Earth features at least two attracting states, which correspond to competing climates. The warm climate is analogous to the present one; the snowball climate features global glaciation and conditions that can hardly support life forms. Paleoclimatic evidences suggest that in the past our planet flipped between these two states. The main physical mechanism responsible for such an instability is the ice-albedo feedback. In a previous work, we defined the Melancholia states that sit between the two climates. Such states are embedded in the boundaries between the two basins of attraction and feature extensive glaciation down to relatively low latitudes. Here, we explore the global stability properties of the system by introducing random perturbations as modulations to the intensity of the incoming solar radiation. We observe noise-induced transitions between the competing basins of attraction. In the weak-noise limit, large deviation laws define the invariant measure, the statistics of escape times, and typical escape paths called instantons. By constructing the instantons empirically, we show that the Melancholia states are the gateways for the noise-induced transitions. In the region of multistability, in the zero-noise limit, the measure is supported only on one of the competing attractors. For low (high) values of the solar irradiance, the limit measure is the snowball (warm) climate. The changeover between the two regimes corresponds to a first-order phase transition in the system. The framework we propose seems of general relevance for the study of complex multistable systems. Finally, we put forward a new method for constructing Melancholia states from direct numerical simulations, which provides a possible alternative with respect to the edge-tracking algorithm.
Highlights
In the late 1960s and in the 1970s, Budyko, Selllers, and Ghil [1–3] proposed the idea that the Earth, in the current astrophysical and astronomical configuration, supports two co-existing attractors, the warm (W) state we live in, and the so-called snowball (SB) state, which is characterised by global glaciation and globally averaged surface temperature of about 200-220 K
We put forward a new method for constructing Melancholia states from direct numerical simulations, which provides a possible alternative with respect to the edge-tracking algorithm
The stochastic forcing is introduced here as a random modulation for the incoming solar radiation, and leads to a nontrivial multiplicative noise law, because the radiative forcing is affected by the albedo of the surface, which, in turn, depends on the surface temperature
Summary
In the late 1960s and in the 1970s, Budyko, Selllers, and Ghil [1–3] proposed the idea that the Earth, in the current astrophysical and astronomical configuration, supports two co-existing attractors, the warm (W) state we live in, and the so-called snowball (SB) state, which is characterised by global glaciation and globally averaged surface temperature of about 200-220 K. Models of different levels of complexity ranging up to the state-of-the-art Earth System Models currently used for climate projections agree on predicting the existence of multistability in the climate system and point to the fundamental mechanisms described above as responsible for it, as well as providing values for SW∗ →SB that are in broad agreement with those obtained using simple models [7–9]. We remark that both the concentration of greenhouse gases and the position of the continents have an impact on the values of SW∗ →SB and SS∗B→W and on the properties of the W and SB states [10]. One expects that tidally locked planets with an active carbon cycle can never be found in a SB state [17]
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