Fig. 3: Temperature estimate of the snowball ocean according to the CIF δ⁵⁶Fe anomaly.

a Rayleigh distillation model of Fe isotope evolution during the genesis of IF and relative frequency distribution of δ⁵⁶Fe values for pre-GOE IF and CIF (excluding data from the Fulu Fm). Orange dashed lines are theoretical δ⁵⁶Fe distribution curves of instantaneous Fe (oxyhydr)oxide precipitation by progressive oxidation (distillation) at two different temperatures, assuming an initial source of δ⁵⁶Fe = 0 (Methods). Median δ⁵⁶Fe values for pre-GOE IF (–0.03, n = 783) and CIF (0.91, n = 148) are the red and blue dashed lines, respectively. A Mood test for equal medians yields a p value of 8.5 × 10^–9, which is «<0.05, indicating that the null hypothesis can be rejected and that the two medians are strongly statistically distinct. b The temperature-dependent equilibrium fractionation between aqueous Fe³⁺ and aqueous Fe²⁺ (Methods). Dashed portion of the line is extrapolated to predict the snowball temperature based on the observed +0.94‰ δ⁵⁶Fe anomaly (a). Experimental data⁷⁰ are consistent with the theoretical curve⁵⁹ used for extrapolation, and both are provided in Table 1. Bell curves indicate the 25 ± 10˚C Archaean seawater temperature used for the Gaussian-distributed Monte Carlo simulations spanning that range used to estimate uncertainty of the calculated snowball temperature (Methods). GOE, Great Oxidation Event. IF, iron formation. CIF, Cryogenian iron formation.