A Machine Learning Approach to Predicting Equilibrium Ripple Wavelength

Abstract:

Sand ripples are geomorphic features on the seafloor that are influential in bottom boundary layer dynamics affecting acoustic scattering, sediment resuspension and transport. While equilibrium ripples are not ubiquitous in nature, knowing the geometry that a ripple is being driven to under certain wave conditions is important for time-dependent ripple and sediment transport models (Penko et al., 2017, Traykovski et al., 2007, DuVal et al., 2016). Decades of work focused on studying the equilibrium geometry of ripples generated by constant wave propagation over a sandy bed has resulted in many empirical formulations derived from laboratory and field observations. Typically, the data used to derive these deterministic equilibrium ripple predictors have a large spread and the predictions therefore have high uncertainty. Nelson et al. (2013) compiled over 50 years of laboratory and field observations to produce one of the most recent empirical formulations for the prediction of equilibrium ripple length and height given constant wave forcing. However, instead of using a typical least-squares fit to observations, we present a new equilibrium ripple predictor using a machine learning approach that includes the probability distribution of equilibrium wavelengths to provide a prediction uncertainty. The Bayesian Optimal Model System (BOMS) was created as a specialized machine learning stacked generalizer that combines multiple linear and nonlinear base models with a Bayesian meta-learner to produce probabilistic equilibrium ripple height and length predictions. In addition to modeling uncertainties, BOMS can continuously be re-optimized with new data incorporation to better handle a wide range of environmental conditions. The 50+ year dataset of equilibrium ripple lengths and heights compiled by Nelson et al. (2013) was used for hyper-parameter tuning, model training, and validation. A ten-fold cross validation of the model resulted in an R-squared value of 0.89 and an average RMSE of 10-cm. Additional field observations were used for model prediction testing. When compared with a new set of field observations, BOMS resulted in an average R-squared value of 0.38 and an average RMSE of 14-cm for predicting ripple wavelength.