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Back to basics: On the proper determination of free-surface slope (FSS) in gradually varied open channel flows
Journal article   Open access   Peer reviewed

Back to basics: On the proper determination of free-surface slope (FSS) in gradually varied open channel flows

Emma House, Kyeongdong Kim, Marian Muste, Ehab Meselhe and Ibrahim Demir
Flow measurement and instrumentation, Vol.106, 102979
12/2025
DOI: 10.1016/j.flowmeasinst.2025.102979
url
https://doi.org/10.1016/j.flowmeasinst.2025.102979View
Published (Version of record) Open Access

Abstract

This study is a fundamental evaluation of the fluvial wave propagation in river reaches affected by hysteresis, one of the most complex open-channel topics, materialized in loops and lags among hydraulic variables. Hysteresis processes are still understudied as measurements in natural streams for the whole wave propagation duration are hardly available, while the data from existing gaging sites (almost exclusively relying on stage-discharge relationships) can deviate up to 65 % from the actual flows. A better understanding of hysteresis in general and its impact on streamflow monitoring in unsteady flows can be obtained if the free-surface slope (FSS) is determined and analyzed for its variation during wave propagation. Reliable FSS replication in such flows requires a robust understanding of the spatial-temporal sampling constraints. The study addresses the basic, but still weakly resolved, issue of tracing the FSS for waves of different magnitudes and durations. We do so by translating theoretical concepts on oscillatory waves to fluvial counterparts and observing rules for sampling continuous-time signals with discrete-time measurements. The conceptual understanding is verified with numerical simulations and experimental data represented in Eulerian and Lagrangian observation frameworks. We demonstrate that sampling stream stages with spatial and temporal resolutions (expressed in terms of fractions of the wavelength, dxi/λR, and duration, ΔTi/TR for the flood wave to reach its peak) between approximately0.0075≤dxi/λR≤0.01 and, 0.004 ≤ΔTi/TR≤0.06, respectively, are required to properly trace FSS for subsequent usage in experimental or numerical simulation contexts. Proper selection of the spatial-temporal resolution for the determination of free-surface slope (FSS) is critical for the accurate reconstruction of the flood wave shape (traced by water surface elevations - WSE) as well as for capturing the FSS changes during the fluvial wave propagation. An increase of the distance used for determining the free-surface slope (i.e., decreasing the spatial resolution) and/or of the time interval between the WSE samples (i.e., decreasing the temporal resolution) result in a deterioration of the accurate tracing of these important variables for streamflow estimation. [Display omitted] •Eulerian and Lagrangian views of flood waves reveal patterns in free-surface slope variation.•Free-surface slope estimations deteriorate with increased sampling intervals.•The central slope estimation method is more robust than forward and backward alternatives.•Experimental and observational river data align and corroborate these findings.
 Free-surface slope (FSS) Gradually varied flow Hysteresis Open-channel flow Spatial-temporal sampling Streamflow monitoring Wave propagation

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