Stochastic Snowball States in Planetary Climate
Abstract
Motivated by the recent finding of Ji and Abbot (2025) that at moderate eccentricity (0.2--0.3) the planetary Snowball bistability vanishes, we have introduced stochasticity of the orbital eccentricity into a simplified version of the energy balance model of Eisenman and Wettlaufer (2009) to study a general Earth-like planet. The stochastic eccentricity is approximated by two dominant time scales, annual and daily, and is introduced through an analysis of the Kepler equation. We find that, apart from mean eccentricities less than 0.1, the stochastic dynamics are quantitatively and qualitatively different than the deterministic dynamics. For a fixed mean eccentricity, fluctuations in eccentricity amplify the asymmetry and intermittency in radiative flux forcing, thereby increasing the time it takes to reach a stable seasonal cycle. As the mean eccentricity increases above 0.1, the stochastic transition from the Snowball to non-Snowball state occurs over a range of mean stellar flux ΔS* rather that at a particular stellar flux S* for the deterministic case. Moreover, as the mean eccentricity increases from 0.1 and the variance of the annual eccentricity fluctuations increases, ΔS* increases and the probability of the system reaching a steady state and experiencing a Snowball to non-Snowball bifurcation decreases. This implies that there may be many high eccentricity planetary systems in a perpetually transient state.
Related
- Gen-EBM: An energy balance model for terrestrial planets. Climate multistability from snowball to post-runaway greenhouse climates
- Gen-EBM: an energy balance model for terrestrial planets. Climate multistability from snowball to post-runaway greenhouse climates
- Collisionless stationary states of a stratified plasma in an expanding magnetic tube with stochastic heating
- Diversity of planetary origins and compositions traced by stellar abundance differences among co-natal star systems
- X-Shooter view of planetary nebulae microstructures. I. The case of NGC 7009 knots
BibTeX
@misc{vu2026stochastic,
title = {{Stochastic Snowball States in Planetary Climate}},
author = {Duc Thach Son Vu and John S. Wettlaufer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10922},
eprint = {2610.10922},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10922},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stochastic Snowball States in Planetary Climate
AU - Duc Thach Son Vu
AU - John S. Wettlaufer
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10922
UR - https://arxiv.org/abs/2610.10922
AB - Motivated by the recent finding of Ji and Abbot (2025) that at moderate eccentricity (0.2--0.3) the planetary Snowball bistability vanishes, we have introduced stochasticity of the orbital eccentricity into a simplified version of the energy balance model of Eisenman and Wettlaufer (2009) to study a general Earth-like planet. The stochastic eccentricity is approximated by two dominant time scales, annual and daily, and is introduced through an analysis of the Kepler equation. We find that, apart from mean eccentricities less than 0.1, the stochastic dynamics are quantitatively and qualitatively different than the deterministic dynamics. For a fixed mean eccentricity, fluctuations in eccentricity amplify the asymmetry and intermittency in radiative flux forcing, thereby increasing the time it takes to reach a stable seasonal cycle. As the mean eccentricity increases above 0.1, the stochastic transition from the Snowball to non-Snowball state occurs over a range of mean stellar flux ΔS^* rather that at a particular stellar flux S^* for the deterministic case. Moreover, as the mean eccentricity increases from 0.1 and the variance of the annual eccentricity fluctuations increases, ΔS^* increases and the probability of the system reaching a steady state and experiencing a Snowball to non-Snowball bifurcation decreases. This implies that there may be many high eccentricity planetary systems in a perpetually transient state.
ER -