Diverse regassing history shapes are generated by sampling a limited time interval for a variety of growth rates and inflection times (Fig. 2). To provide a common point of comparison for the evolving conditions within downwellings, we sort results by the time when 130Xed has increased by 10% between its initial and final values (time of 10% rise). a, Times of 10% rise for successful regassing histories. Most successful model realizations have a time of 10% rise later than 2.5 Gyr ago. b, Model realizations with high present-day 130Xed values are uniformly characterized by late 10% rise times, indicating that in these model realizations downwelling Xe concentrations remain very low throughout most of Earth history. c, Variation in sigmoidal growth rates (parameter α) allows testing of near-linear (low α, sampling for a limited time interval) or near-step (high α) functions. Near-linear model realizations have a time of 50% rise that is about five times the time of 10% rise (dashed light-grey line), whereas step functions approach a 1:1 line (solid dark-grey line). Successful regassing histories with late times of 10% rise are characterized by rapid growth, approaching a step function, to a relatively high present-day 130Xed.