Table 1 Parameter ranges for our numerical model.

\({F}_{{\rm{out}}}^{{\rm{mod}}}\)

Modern CO₂ outgassing flux

6–10

Tmol C yr⁻¹

n

Carbonate precipitation coefficient

1–2.5

\(\propto {\left[{{\rm{CO}}}_{3}^{2-}\right]}^{n}\)

x

Modern seafloor dissolution relative to precipitation

0.5–1.5

\(\propto x{F}_{{\rm{out}}}^{{\rm{mod}}}\)

T_e

E-folding temperature factor for continental weathering

10–40

K

α

Power law exponent for CO₂ dependence of continental silicate weathering

0.1–0.5

\(\propto {\left({{\rm{pCO}}}_{2}\right)}^{\alpha }\)

ξ

Power law exponent for CO₂ dependence of continental carbonate weathering

0.1–0.5

\(\propto {\left({{\rm{pCO}}}_{2}\right)}^{\xi }\)

f_land

Land fraction compared to modern Earth

0–1

S_thick

Ocean sediment thickness relative to modern Earth

0.2–1

\({F}_{{\rm{carb}}}^{{\rm{mod}}}\)

Modern continental carbonate weathering

7–14

Tmol C yr⁻¹

f_bio

Biological weathering compared to modern Earth

0–1

\({a}_{{\rm{grad}}}\)

Surface to deep ocean temperature gradient scaling

0.8–1.4

\(\propto {a}_{{\rm{grad}}}{T}_{{\rm{s}}}\)

γ

Power law exponent for pH dependence of seafloor dissolution

0–0.5

\(\propto {\left(\left[{{\rm{H}}}^{+}\right]\right)}^{\gamma }\)

β

Power law exponent for seafloor spreading rate

0–0.2

∝ Q^β

m

Exponent for outgassing dependence on crustal production

1–2

∝ Q^m

E_bas

Seafloor dissolution activation energy

60–100

kJ mol⁻¹

n_out

Exponent for internal heat with time

0–0.73

see Eq. (10)

τ

Planet age (see Eq. (10))*

0–10

Gyr

S

Incident flux relative to modern Earth*

0.35–1.05