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

Abstract

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 $\epsilon$ , empirical studies usually interpret this relation at the reach-scale. Here, we investigate how local $k\left(\epsilon \right)$ 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 $\epsilon$ 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.

Keywords: aggregation bias; energy dissipation rate; gas exchange; gas transfer velocity; reaeration; scaling.