Extended Data Fig. 5: The effect of different correction methods for modeling methane (CH₄) concentration ~ flux relationships.

Uncorrected model estimates result in a large number of flux observations which are larger than observations reported in the empirical dataset. Plots in the left column provide a comparison between modelled and actual (observed) flux-concentration relationships. Red contours represent the density of modelled fluxes and concentrations, while grey contours represent the density of empirical observations available in GRiMeDB¹³ (n = 4,052), with the lowest contours containing 95% of values. The maps in the right column illustrate modelled fluxes, with mountain areas highlighted as light grey, hollow polygons (from ref. ⁶³); note the different scales for each row. Ideally, the modelled and empirical obervations of the concentration ~ flux relationship should overlap, but do not, as seen in (a), leading us to explore multiple corrections. Capping gas transfer velocity (k) (c, d) at 35 m per day does little to correct this artefact, nor does capping flux estimates above 2 standard deviations of the global population (e,f). In contrast, the river reach footprint correction avoids particularly the high fluxes at low concentrations and better represents the distribution of empirical observations (g, h). See methods section “Uncertainty and refinement of the estimate” for a detailed discussion of this issue and the approach selected.