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 e, empirical studies usually interpret this relation at the reach-scale. Here, we investigate how local k(e) 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 e 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.