The role of stream heterogeneity in gas emissions from headwater streams.

Headwater streams represent a key component of the global carbon cycle, as they are hotspots for the evasion of carbon dioxide from surface waters. Gas emissions from rivers and streams are modulated by the gas transfer velocity at the water-air interface, k, which is physically related to the energy dissipated by the flow field, ε. Here we study how local relations between gas transfer rate and energy dissipation can be spatially averaged in presence of heterogeneous flow fields, e.g. as induced by changes in the local slope. Furthermore, we develop mathematical tools for the quantification of the fraction of gas emission that is related to localized energy losses (e.g. sudden drops and step-pool formations). The study complements numerical simulations and direct measures of stream CO2 outgassing in an Italian headwater catchment. Our theoretical results indicate that reach-scale relations between k and ε in general differ from the corresponding local scaling laws. In particular, we show that high energy heterogeneous streams are characterized by a gas transfer velocity significantly higher than that of an equivalent homogeneous stream. The empirical data suggest that the outgassing is highly heterogeneous along a river network, with the outgassing generated by localized gas emissions in correspondence of hydraulic discontinuities that might be a dominant contribution to the total gas evasion in many settings. These results offer a clue for the interpretation of empirical data about stream outgassing in heterogeneous reaches and complex river networks.