An Empirical Model Combining Seismic Noise and Shear Stress to Predict Bedload Flux in a Gravel‐Bed Alluvial Channel

Abstract Bedload flux estimation from reach‐averaged hydraulic conditions, while tractable and generally reliable over long integration periods, struggles to capture the intrinsic variability of transport in turbulent flow and the strong influence of local sediment size and morphological heterogeneity. Here we suggest an empirical equation to simplify the relationship between seismic power spectral density (PSD) and bedload flux relative to a full physics‐based seismic model. We posit that adding seismic PSD as a predictor to hydraulics‐based bedload equations improves bedload flux predictions by accounting for short‐ and medium‐term flux variations independent of flow conditions. We present a new calibrated empirical equation combining seismic PSD and excess shear stress to predict bedload flux at high temporal resolution (minute‐scale). The calibrated coefficients for the shear contribution are consistent with existing hydraulics‐based equations (e.g., Meyer‐Peter and Müller) that have been calibrated across a broad range of channels, suggesting that the values for the seismic parameter might also be broadly applicable across channels. In comparison to field data from a sandy‐gravel‐bed alluvial river in New Mexico, USA, the locally‐trained equation reduces scatter in bedload flux predictions relative to methods solely using either seismic PSD or shear stress. We further validate the equation with independent flow events from the same river and from a separate gravel bed channel, the Nahal Eshtemoa in Israel. Notably, the seismic‐hydraulic equation was able to be calibrated on low‐transport data and reliably predict high‐transport data. Likewise, the seismic‐hydraulic equation reduced apparent overestimations of bedload flux by the hydraulics‐based equation during high‐shear conditions.