Relating free-surface flow and discharge in mountain streams

The most accurate way of measuring water discharge in a mountain stream is to use a concrete structure (like a Parshall flume or a weir), so that the bed elevation is known and hyporheic flow is substantially reduced. This technique is costly, provides only a one-point measurement and it may be overtopped or damaged during floods. An alternative is offered by non-intrusive monitoring techniques, which do not come into contact with the flow.

Non-intrusive monitoring techniques do not measure a river's discharge directly, they extrapolate it from observable features of the free surface.

While empirical relations (e.g. rating curves or velocity profiles) for flows over impermeable walls are widely accepted to infer the discharge from the surface conditions, they fall short in mountain streams where the bed is coarse and permeable. As a result, discharge monitoring in mountain streams, both under normal conditions and during floods, remains inaccurate and calls for a new modeling framework.

Given that free-surface velocity measurements can be noisy and flow parameters (depth, eddy viscosity, porosity) are known with poor precision, we suggest using Bayesian inference to estimate the discharge from the surface velocity while explicitly accounting for parameter uncertainty through prior information.

The proposed approach will be tested using a laboratory flume experiment conducted at the bed roughness scale, based on a refractive index matched scanning (RIMS) setup. This experimental configuration enables direct access to bed porosity and the full velocity field by using glass beads as a sediment analogue and matching the refractive indices of the solid and fluid phases to eliminate optical distortion.