Joint Sensing of Bedload Flux and Water Depth by Seismic Data Inversion

Rivers are the fluvial conveyor belts routing sediment across the landscape. While there are proper techniques for continuous estimates of the flux of suspended solids, constraining bedload flux is much more challenging, typically involving extensive measurement infrastructure or labor-intensive manual measurements. Seismometers are potentially valuable alternatives to in-stream devices, delivering continuous data with high temporal resolution on the average behavior of a reach. Two models exist to predict the seismic spectra generated by river turbulence and bedload flux. However, these models require estimating a large number of parameters and the spectra usually overlap significantly, which hinders straightforward inversion. We provide three functions contained in the R package “eseis” that allow generic modeling of hydraulic and bedload transport dynamics from seismic data using these models. The underlying Monte Carlo approach creates lookup tables of potential spectra, which are compared against the empirical spectra to identify the best fitting solutions. The method is validated against synthetic data sets and independently measured metrics from the Nahal Eshtemoa, Israel, a flash flood-dominated ephemeral gravel bed river. Our approach reproduces the synthetic time series with average absolute deviations of 0.01–0.04 m (water depth, ranging between 0 and 1 m) and 0.00–0.04 kg/sm (bedload flux, ranging between 0 and 4 kg/sm). The example flash flood water depths and bedload fluxes are reproduced with respective average deviations of 0.10 m and 0.02 kg/sm. Our approach thus provides generic, testable, and reproducible routines for a quantitative description of key metrics, hard to collect by other techniques in a continuous and representative manner.