Movatterモバイル変換

[0]ホーム
URL:

Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
Thehttps:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

NIH NLM Logo
Log inShow account info
Access keysNCBI HomepageMyNCBI HomepageMain ContentMain Navigation
pubmed logo
Advanced Clipboard
User Guide

Full text links

Atypon full text link Atypon Free PMC article
Full text links

Actions

Share

.2020 Jul;476(2239):20200303.
doi: 10.1098/rspa.2020.0303. Epub 2020 Jul 29.

Routes to global glaciation

Affiliations

Routes to global glaciation

Constantin W Arnscheidt et al. Proc Math Phys Eng Sci.2020 Jul.

Abstract

Theory and observation suggest that Earth and Earth-like planets can undergo runaway low-latitude glaciation when changes in solar heating or in the carbon cycle exceed a critical threshold. Here, we use a simple dynamical-system representation of the ice-albedo feedback and the carbonate-silicate cycle to show that glaciation is also triggered when solar heating changes faster than a critical rate. Such 'rate-induced glaciations' remain accessible far from the outer edge of the habitable zone, because the warm climate state retains long-term stability. In contrast, glaciations induced by changes in the carbon cycle require the warm climate state to become unstable, constraining the kinds of perturbations that could have caused global glaciation in Earth's past. We show that glaciations can occur when Earth's climate transitions between two warm stable states; this property of the Earth system could help explain why major events in the development of life have been accompanied by glaciations.

Keywords: Earth system; dynamical systems; glaciation; snowball Earth; tipping points.

© 2020 The Author(s).

PubMed Disclaimer

Conflict of interest statement

We declare that we have no competing interests.

Figures

Figure 1.
Figure 1.
The climate states associated with particular values of volcanic outgassing and stellar flux. Volcanic outgassingV has been normalized by the weathering rate at (T0,P0), denoted asW0. The system exhibits the possibility of stable warm and stable glaciated states. Consistent with previous work [–17], it also exhibits the possibility of a limit cycle, in which the system oscillates between warm and glaciated states. (Online version in colour.)
Figure 2.
Figure 2.
The dynamical system operates on two distinct timescales. Here, we plot the curves ofT˙=0 andP˙=0 (nullclines) of the dynamical system for modern Earth parameters (S = 1365 W m−2,V/W0 = 1). Because the radiative adjustment of temperature occurs much faster than the geologic adjustment of CO2, the system spends most of its time near theT˙=0 nullcline (thecritical manifold), greatly simplifying the dynamics. Once the system arrives on the high-temperature branch of the critical manifold, it slowly relaxes towards the stable warm climate state. If the system lands on the low-temperature branch of the critical manifold, CO2 slowly builds up over millions of years and eventually triggers a jump to the high-temperature branch of the critical manifold, with subsequent relaxation to the stable warm climate state. (Online version in colour.)
Figure 3.
Figure 3.
Transient glaciations can occur even though the warm state remains uniquely stable. Here,S = 1280 W m−2 andV/W0 = 1. The critical manifoldT˙=0 is folded (has a local minimum) near the fixed point; the right-hand side branch is stable and the left-hand side branch is unstable (see figure 2). The upper trajectory (green) is able to reach the stable part of the critical manifold (i.e. before the fold), relaxing quickly back to the fixed point. The lowest trajectory (blue) is unable to intersect the stable part of the manifold and passes beneath the fold, heading towards the cold branch of the critical manifold (see figure 2). A transient, million-year glaciation results. There is a special kind of trajectory that separates these two cases: it is known in dynamical systems theory as a ‘canard’ [24]. (Online version in colour.)
Figure 4.
Figure 4.
Demonstration of rate-induced glaciation in our model. In both cases, stellar fluxS is decreased linearly from 1280 to 1275 W m−2, but in the slow case this occurs over 60 kyr and in the fast case this occurs over 40 kyr. Changes inS alter the location of the fixed point, as well as that of theT˙=0 nullcline and its fold (local minimum); this is illustrated in the top graph by includingS as a third dimension. Now, the warm stable climate state (black, solid) and the fold (black, dashed) become curves on the three-dimensional critical manifoldT˙=0 (grey). The pCO2 axis (P) is reversed to better illustrate the dynamics. In the slow case, the trajectory does not pass beyond the fold and is able to quickly relax back to the fixed point once ramping stops. In the faster case, the trajectory passes beyond the fold curve, and transient ‘rate-induced glaciation’ ensues. It takes millions of years for the system to return to the unique stable warm climate state. The fluctuations that occur near the fold crossing are numerical. (Online version in colour.)
Figure 5.
Figure 5.
Schematic illustrating the two dynamical routes to glaciation. The parameter space of generalized volcanic outgassingVg and generalized stellar fluxSg follows the regime plot in figure 1. Changes in carbon cycle fluxes and radiative fluxes can be straightforwardly mapped into this space; for example, an increase in weathering corresponds to a decrease inVg and an increase in albedo corresponds to a decrease inSg. Route A is a crossing of the limit cycle boundary due to decreases inVg and/orSg. Route B is a transient rate-induced glaciation triggered by sufficiently fast decreases inSg; this is accessible anywhere in the parameter space. A decrease inVg which does not cross the limit cycle boundary does not lead to glaciation. (Online version in colour.)
Figure 6.
Figure 6.
Susceptibility to glaciation far from the outer edge of the habitable zone. Here, we plot the critical instantaneous change in stellar flux required to trigger a glaciation in our model (ΔSglaciation) versus the change in stellar flux needed to cross the effective outer edge of the habitable zone (ΔSOHZ). Here,V/W0 = 1. We see that ΔSglaciation is significantly smaller than ΔSOHZ; thus, Earth-like planets can be in stable warm climate states far from the OHZ while remaining quite susceptible to glaciation.
Figure 7.
Figure 7.
Forcing the model with step decreases ofV (volcanic outgassing) that persist for different time periods.S = 1280 W m−2. The dashed line indicates the position of the limit cycle bifurcation. Recall that anomalous increases in weathering are functionally equivalent to decreases inV. Since changes in carbon fluxes can only initiate glaciation via passage into the limit cycle regime (figure 5), the only perturbation that can create a single transient glaciation event is one that decays before one period of the limit cycle has elapsed (a). Otherwise, multiple iterations of the limit cycle result: after a short-lived post-deglaciation hothouse, glaciation ensues again (b).
See this image and copyright information in PMC

Similar articles

See all similar articles

Cited by

References

    1. Kirschvink JL. 1992. Late Proterozoic low-latitude global glaciation: the snowball earth. In The Proterozoic biosphere: a multidisciplinary study (eds JW Schopf, C Klein, D Des Marais), pp. 51–52. Cambridge, UK: Cambridge University Press.
    1. Evans D, Beukes NJ, Kirschvink JL. 1997. Low-latitude glaciation in the Palaeoproterozoic era. Nature 386, 262–266. (10.1038/386262a0) - DOI
    1. Hoffman PF, Kaufman AJ, Halverson GP, Schrag DP. 1998. A Neoproterozoic snowball earth. Science 281, 1342–1346. (10.1126/science.281.5381.1342) - DOI - PubMed
    1. Hoffman PF. et al. 2017. Snowball Earth climate dynamics and Cryogenian geology-geobiology. Sci. Adv. 3, e1600983 (10.1126/sciadv.1600983) - DOI - PMC - PubMed
    1. Pierrehumbert R, Abbot D, Voigt A, Koll D. 2011. Climate of the neoproterozoic. Annu. Rev. Earth Planet. Sci. 39, 417–460. (10.1146/annurev-earth-040809-152447) - DOI

Associated data

LinkOut - more resources

Full text links
Atypon full text link Atypon Free PMC article
Cite
Send To

NCBI Literature Resources

MeSHPMCBookshelfDisclaimer

The PubMed wordmark and PubMed logo are registered trademarks of the U.S. Department of Health and Human Services (HHS). Unauthorized use of these marks is strictly prohibited.

[8]ページ先頭
©2009-2025 Movatter.jp