Stream hydraulic geometry

We established hydraulic geometry scaling relationships from mountain streams in the Swiss Alps (Supplementary Fig. ¹), where we derived annual mean stream channel width (w), depth (z) and flow velocity (v) from annual mean discharge (Q) as follows (Supplementary Fig. ³).

We performed a total of 141 slug releases where we added sodium chloride (NaCl) at the top of each reach (in average 12 slugs per site) and measured the change in specific conductivity at the bottom of the reaches. By measuring the change in specific conductivity, which we converted to mass by applying a pre-established relationship between specific conductivity and the conductivity potential of the added NaCl, we estimated discharge. We also estimated the travel time as the time for the NaCl to reach the bottom of the reach (i.e., the peak in the specific conductivity). To obtain average flow velocity we divided reach length by the travel time. We also measured stream width and stream depth.

In comparison to previous scaling relationships⁵⁹, our relationships are more representative for mountain streams, where steeper slopes induce higher flow velocities and narrower channels. Annual mean discharges ranged from 0.02 to 2.26 m³ s⁻¹ in our study streams (n = 12) in the Swiss Alps. The maximum annual mean discharge was used as an upper boundary within which we consider our hydraulic geometry scaling valid, and we, therefore, restricted our data for all further analyses to streams with maximal annual mean discharge of 2.26 m³ s⁻¹. Hence we restrained our definition of mountain streams further and consider our estimates of CO₂ fluxes from mountain streams as conservative as we discarded streams with Q > 2.26 m³ s⁻¹.