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Abstract

The Cryogenian period (720–635 million years ago) in the Neoproterozoic era featured two phases of global or near-global ice cover, termed ‘Snowball Earth’. Climate models of all kinds indicate that the inception of these phases must have occurred in the course of a self-amplifying ice–albedo feedback that forced the climate from a partially ice-covered to a Snowball state within a few years or decades. The maximum concentration of atmospheric carbon dioxide (CO₂) allowing such a drastic shift depends on the choice of model, the boundary conditions prescribed in the model, and the amount of climatic variability. Many previous studies report values or ranges for this CO₂ threshold but typically test only very few different boundary conditions or exclude variability due to volcanism. Here we present a comprehensive sensitivity study determining the CO₂ threshold in different scenarios for the Cryogenian continental configuration, orbital geometry, and short-term volcanic cooling effects in a consistent model framework, using the climate model of intermediate complexity CLIMBER-3α. The continental configurations comprise two palaeogeographic reconstructions for each of both Snowball-Earth onsets, as well as two idealised configurations with either uniformly dispersed continents or a single polar supercontinent. Orbital geometries are sampled as multiple different combinations of the parameters obliquity, eccentricity, and argument of perihelion. For volcanic eruptions, we differentiate between single globally-homogeneous perturbations, single zonally-resolved perturbations, and random sequences of globally-homogeneous perturbations with realistic statistics. The CO₂ threshold lies between 10 and 250 ppm for all simulations. While the idealised continental configurations span a difference of around 200 ppm for the threshold, the CO₂ thresholds for the continental reconstructions differ by only 20–40 ppm. Changes in orbital geometry account for variations in the CO₂ threshold by up to 32 ppm. The effects of volcanic perturbations largely depend on the orbital geometry and the corresponding structure of coexisting stable states. A very large peak reduction of net solar radiation by around 20 W m⁻² can shift the CO₂ threshold by the same order of magnitude as or less than the orbital geometry. Exceptionally large eruptions of up to −40 W m⁻² shift the threshold by up to 50 ppm for one orbital configuration. Eruptions near the equator tend to, but do not always, cause larger shifts than eruptions at high latitudes. The effect of realistic eruption sequences is mostly determined by their largest events. In the presence of particularly intense small-magnitude volcanism, this effect can go beyond the ranges expected from single eruptions.