Fig. 1: Geological map of the study area overlaid with sampling locations, the contributions of weathering pathways to the solute production, the net DIC production, and the transient CO₂ gas emission.

The relative fractions of cations from silicate and carbonate weathering were calculated from the data set corrected for precipitation and hot spring inputs using a Bayesian algorithm based on the modeled compositions of silicate and carbonate minerals. The fractions of the solute loads from individual pathways were further deconvoluted to constrain the acid contribution and bulk CO₂ production considering the charge balance for reactions that produce both DIC and gaseous CO₂ (Supplementary Methods). The fraction of each pathway (“F” value) represents an average for the high-water or low-water periods (sample names attached with “-H” and “-L”, respectively). The net DIC production represents the production of DIC from carbonate dissolution. For comparison, the transient CO₂ emission is derived from the subtraction of the gaseous CO₂ produced from carbonate dissolution from the dissolution of atmospheric CO₂. The red and green arrows mark the net transient emission and sink of gaseous CO₂, respectively. The error bars represent one standard deviation. Detailed computation approaches can be found in Supplementary Methods.