Thresholds of catastrophe in the Earth system

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Science Advances  20 Sep 2017:
Vol. 3, no. 9, e1700906
DOI: 10.1126/sciadv.1700906


  • Fig. 1 Parameterization and temporal distribution of carbon isotopic events in the database.

    (A) Schematic diagram illustrating how the parameters δ1(0) and δ1env) are derived from an isotopic time series δ1(t). The time scale τenv represents the duration of time during which the isotopic composition δ1 decreases. (B) Histogram depicting the distribution of events in time.

  • Fig. 2 Depictions of the size and time scale of carbon isotopic events.

    (A) Magnitude of the isotopic shift Δr = δ1env) − δ1(0) as a function of its duration of time, τenv. (B) Dimensionless mass perturbation M = |Δm|/m* as a function of the dimensionless time scale φcτenv/2τ0 for each of the events depicted in (A). The straight (identity) line denotes the equality predicted by Eq. 5 when φ = φc = 0.23 ± 0.07. Event abbreviations are defined in Table 1. Error bars (Materials and Methods) are guides for interpretation.

  • Fig. 3 Evolution of size and time scale.

    (A) Dimensionless mass perturbation M = |Δm|/m* as a function of the geologic age of the event. The relative absence of smaller events in the deeper past likely derives from poor data and a lack of interest. The absence of large events in the more recent past, however, cannot be explained by this bias. (B) Time scale τenv of critical events (events falling within the error bars of the straight line in Fig. 2B) as a function of geologic age. Error bars (Materials and Methods) are guides for interpretation.

  • Fig. 4 Cumulative modern ocean uptake of carbon since 1850, up to the present (green) and projected to 2100 (blue), compared to the predicted critical mass of 310 Pg C (solid red line) and an assumed uncertainty of ±50% (dashed red lines).

    Projections (34) are given for four representative concentration pathway scenarios RCPx, where x represents the radiative forcing, in units of W/m2, deriving from accumulated emissions in the year 2100 (35). At the extreme ends of the projections, RCP2.6 represents the range of lowest-emission scenarios in the scientific literature, and RCP8.5 represents the high range of nonclimate policy scenarios. Of the two intermediate pathways, RCP4.5 corresponds to an emission pathway resulting from many climate policies found in the literature, whereas RCP6.0 is representative of most scenarios without limitations on emissions (35). The present cumulative uptake is obtained by adding 6 years of an annual uptake rate of 2.3 Pg C year−1 (34) to the 2011 total of Ciais et al. (34).


  • Table 1 Event names, event abbreviations, and data used to construct Figs. 2 and 3.

    Values of δ1 and Δr are given in per mil (‰) and derive from the formula δ1 = 1000 × (RRstd)/Rstd, where abundance ratios R = 13C/12C are obtained from samples of inorganic (carbonate) carbon and Rstd is a standard ratio. The variables Δr, τenv, φ, and M are defined in the text. In Fig. 2, the six Eocene and four Miocene events are denoted by Eo and Mio, respectively.

    Event nameAbbreviationDate[Ma]δ1(0)δ1env)Δrτenv[My]φM
    Cambrian SpiceSpice497.004.301.30−3.001.0000.120.443
    Silurian MuldeMul428.204.001.00−3.000.2600.190.181
    Silurian LauLau423.507.001.00−6.000.5000.300.538
    Early TriassicTr251.222.00−1.50−3.500.2500.260.228
    Early late PaleoceneELPE58.903.483.07−0.420.0390.110.015
    Paleocene-Eocene Thermal MaximumPETM55.501.90−0.80−2.700.0830.410.121
    Eocene Thermal Maximum 2ETM253.701.400.27−1.120.0450.280.045
    Eocene Hyperthermal H2H253.601.400.80−0.600.0330.190.023
    Eocene Hyperthermal I2I253.201.560.95−0.610.0400.160.023
    Eocene Hyperthermal I1I153.101.560.84−0.720.0400.190.028
    Eocene Thermal Maximum 3ETM352.500.20−0.60−0.800.0370.240.032
    Eocene-Oligocene boundaryOi133.501.601.00−0.600.4300.030.047
    Miocene Climatic Optimum 1MCO116.901.941.44−0.500.0280.180.018
    Miocene Climatic Optimum 2MCO216.401.801.04−0.760.0220.350.028
    Miocene Climatic Optimum 3MCO316.002.331.67−0.660.0320.210.024
    Miocene Climatic Optimum 4MCO415.602.171.57−0.600.0290.210.022
    Last Glacial Maximum–to–HoloceneLGMH0.020.110.450.340.018−0.20−0.013