Empirical model to predict bedload flux
On the last note, I shared the physics-based models of seismic generated by sediment transport. There are several limitation of applying either the Tsai et al. (2012) or Luong et al. (2024) models to estimate bedload flux, mainly:
Using seismic methods to track bedload transport is an active field of research recently. However, the physics-based model of seismic noise generated by bedload transport is quite complex, and applying this model to invert back to bedload flux is still challenging, largely due to high dimensional space of model parameters and the uncertainty of several model parameters (e.g., seismic velocity, Green’s function related parameters, or bedload particle hop times).
In this work, we derive an empirical equation to simplify the relationship between seismic power spectral density (PSD) and bedload flux based on the physics-based model. We then hypothesize that adding seismic PSD as a new predictor improves hydraulics-based equation in terms of predicting bedload flux. We then test this newly derived empirical equation that combines the PSD and excess shear stress to predict bedload flux in a sandy-gravel-bed alluvial river in New Mexico. The generic form of the seismic-hydraulic equation is:
$$ q_b = a \left(\frac{P}{P_{re}}\right)^b \left(\tau_{\ast} - \tau_{cr\ast}\right)^c $$
where $q_b$ is non-dimensional bedload flux, $P$ is observed seismic power spectral density (PSD), $P_{re}$ is a reference seismic PSD at a given shear stress, $\tau_{\ast}$ is Shield parameter, and $\tau_{cr\ast}$ is critical Shield required to initiate the movement of sediment particles.
After fitting this above equation with our Pinos field data, we obtained the fitted equation as follows:
$$ q_b = 5.2 \left(\frac{P}{P_{re}}\right)^{0.25} \left(\tau_{\ast} - \tau_{cr\ast}\right)^{1.36} $$
This equation predicts bedload flux better than either using PSD or shear stress alone. We validate this with independent flow events and demonstrate that the newly derived empirical equation could potentially improve the predictive capability of bedload flux.
Detail on the derivations as well as results can be accessed here!
Flash floods at the Arroyo de Los Pinos
During the monsoon season, we chased flash floods at the arroyo de los Pinos to study both sediment transport in ephemeral channels and rainfall-runoff across the basin. We set up a bunch of instrumentation network from upstream to downstream, including rain gauges, level loggers, seismometers. These instruments help us to collect a wealth of information about rainfall/runoff, water flow, ground vibration (seismic sensors), and bedload movement. Here is an example of a flood event at the watershed.
References
[1] Tsai, V.C., Minchew, B., Lamb, M.P. and Ampuero, J.P., 2012. A physical model for seismic noise generation from sediment transport in rivers. Geophysical research letters, 39(2).
[2] Luong, L., Cadol, D., Bilek, S., McLaughlin, J.M., Laronne, J.B. and Turowski, J.M., 2024. Seismic modeling of bedload transport in a gravel‐bed alluvial channel. Journal of Geophysical Research: Earth Surface, 129(9), p.e2024JF007761.
[3] Luong, L., Cadol, D., Turowski, J.M., Bilek, S., McLaughlin, J.M., Stark, K. and Laronne, J.B., 2026. An empirical model combining seismic noise and shear stress to predict bedload flux in a gravel‐bed alluvial channel. Water Resources Research, 62(2), p.e2025WR040371.