Table 1. Parameter ranges and Bayesian Markov Chain Monte Carlo inversion results.
| Variable | Prior (uniform) |
Nominal model |
Michaelis–Menten law |
|||
|---|---|---|---|---|---|---|
| Median posterior value | 68% Credible interval (1−σ) | 90% Credible interval | Median posterior value | 90% Credible interval | ||
| CO2 dependence, α* | 0.2–0.5 | 0.33 | 0.24–0.44 | 0.21–0.48 | 0.41 | 0.05–0.91 |
| e-folding temp. dep. of cont. weathering, Te (K) | 5–50 | 34 | 22–45 | 17–48 | 31 | 14–48 |
| Relative Cretaceous, weatherability, 1+W | 0.2–1.2 | 0.42 | 0.30–0.58 | 0.24–0.71 | 0.6 | 0.31–0.96 |
| Climate sensitivity, ΔT2x (K) | 1.5–8.0 | 5.6 | 4.4–6.9 | 3.7–7.5 | 5.6 | 3.8–7.6 |
| Relative Cretaceous outgassing, 1+V | 1.2–2.5 | 1.58 | 1.34–1.88 | 1.25–2.1 | 1.56 | 1.24–2.1 |
| Carbonate weatherability modifier, 1+CWF | 0.1–2.5 | 0.36 | 0.18–0.63 | 0.13–0.83 | 0.39 | 0.13–0.88 |
Modern outgassing,  (Tmol C per year) |
4–10 | 6.6 | 4.8–8.8 | 4.2–9.6 | 6.5 | 4.2–9.6 |
Modern carb. weathering,  (Tmol C per year) |
7–14 | 11 | 8.2–12.9 | 7.4–13.7 | 11 | 7.4–13.7 |
Pore-space circulation time,  (kyr) |
20–1,000 | 570 | 239–847 | 100–949 | 555 | 88–945 |
| Carbonate precip. coefficient, n | 1.0–2.5 | 1.66 | 1.22–2.18 | 1.1–2.4 | 1.69 | 1.1–2.4 |
| Modern seafloor dissolution relative to precipitation, x† | 0.5–1.5 | 1.02 | 0.68–1.34 | 0.56–1.45 | 1.01 | 0.56–1.45 |
| Surface-deep temp. gradient, agrad | 0.8–1.4 | 0.99 | 0.88–1.14 | 0.83–1.25 | 0.99 | 0.83–1.25 |
| pH dependence seafloor, γ | 0–0.5 | 0.27 | 0.11–0.43 | 0.04–0.48 | 0.27 | 0.04–0.48 |
| Temp. dependence seafloor, Ebas (kJ mol−1) | 40–110 | 75 | 53–97 | 45–106 | 76 | 45–106 |
| Modern pelagic fraction, fPEL | 0.4–0.6 | 0.49 | 0.43–0.56 | 0.41–0.59 | 0.49 | 0.41–0.59 |
| Spreading rate dep., β | 0.0–1.0 | 0.47 | 0.15–0.82 | 0.05–0.94 | 0.49 | 0.05–0.95 |
| Palaeogeography climate parameter, ΔP (K) | 0.0–5.0 | 2.6 | 0.88–4.2 | 0.28–4.7 | 2.5 | 0.27–4.7 |
Column 1 shows the variables we wish to constrain using proxy data. Column 2 gives the uniform prior for each variable. These intervals also constitute the ranges assumed in the forward model analysis, unless stated otherwise. Columns 3–5 describe the posterior probability distributions for each variable for the nominal model. Columns 6–7 describe the posterior probability distributions for the modified model where the pCO2 dependence of continental weathering is parameterized using the Michaelis–Menten law.
*For the Michaelis–Menten law, the prior for α is 0–1.0 (Supplementary Note 6), and so the posterior distribution is different to that of the nominal model.
†This constant defines the initial seafloor dissolution flux relative to the carbonate precipitation flux in the pore-space (see Table 2 for further details and formal definition).