Heterogeneity Matters: Aggregation Bias of Gas Transfer Velocity Versus Energy Dissipation Rate Relations in Streams.

The gas transfer velocity, k, modulates gas fluxes across air‐water interfaces in rivers. While the theory postulates a local scaling law between k and the turbulent kinetic energy dissipation rate ε, empirical studies usually interpret this relation at the reach‐scale. Here, we investigate how local k(ε) laws can be integrated along heterogeneous reaches exploiting a simple hydrodynamic model, which links stage and velocity to the local slope. The model is used to quantify the relative difference between the gas transfer velocity of a heterogeneous stream and that of an equivalent homogeneous system. We show that this aggregation bias depends on the exponent of the local scaling law, b, and internal slope variations. In high‐energy streams, where b>1, spatial heterogeneity of ε significantly enhances reach‐scale values of k as compared to homogeneous settings. We conclude that small‐scale hydro‐morphological traits bear a profound impact on gas evasion from inland waters. Plain Language Summary: 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 a local relation between gas transfer rate and energy dissipation can be spatially averaged in presence of heterogeneous flow fields induced by changes in the local slope. Our 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. These results offer a clue for the interpretation of empirical data about stream outgassing in river networks. Key Points: We analyze local and reach‐wise relations between gas transfer velocity (k) and energy dissipation rate (ε)Reach‐scale k(ε) laws depend on the exponent that modulates the local relation between k and ε and the heterogeneity of the reachReach‐scale k(ε) laws in high‐energy heterogeneous streams are affected by a positive aggregation bias [ABSTRACT FROM AUTHOR]