Ensemble models from machine learning: an example of wave runup and coastal dune erosion

Abstract

Abstract. After decades of study and significant data collection of time-varying swash on sandy beaches, there is no single deterministic prediction scheme for wave runup that eliminates prediction error – even bespoke, locally tuned predictors present scatter when compared to observations. Scatter in runup prediction is meaningful and can be used to create probabilistic predictions of runup for a given wave climate and beach slope. This contribution demonstrates this using a data-driven Gaussian process predictor; a probabilistic machine learning technique. The runup predictor is developed using one year of hourly wave runup data (8328 observations) collected by a fixed LIDAR at Narrabeen Beach, Sydney, Australia. The Gaussian process predictor accurately predicts hourly wave runup elevation when tested on unseen data with a root mean-squared-error of 0.18 m and bias of 0.02 m. The uncertainty estimates output from the probabilistic GP predictor are then used practically in a deterministic numerical model of coastal dune erosion, which relies on a parameterization of wave runup, to generate ensemble predictions. When applied to a dataset of dune erosion caused by a storm event that impacted Narrabeen Beach in 2011, the ensemble approach reproduced ~ 85 % of the observed variability in dune erosion along the 3.5 km beach and provided clear uncertainty estimates around these predictions. This work demonstrates how data-driven methods can be used with traditional deterministic models to develop ensemble predictions that provide more information and greater forecasting skill when compared to a single model using a deterministic parameterization; an idea that could be applied more generally to other numerical models of geomorphic systems.

Bayesian geomorphology

“…How do we choose a meaningful covariance function and how do we specify its hyperparameters? The standard way to do this is to maximize the marginal likelihood to obtain the optimal hyperparameter values (Rasmussen and Williams, 2006;Beuzen et al 2019). In many geostatistical studies, this procedure is part of what is known as ordinary kriging and built around a semivariogram, which is closely related to the covariance function ( Figure 8B).…”

“…Regardless, we can use Gaussian processes as highly flexible components of models that also handle physical formulations. For example, Beuzen et al (2019) coupled a Gaussian process predictor of wave runup with a morphodynamic model of coastal dune erosion in New South Wales, Australia. Fully Bayesian implementations of Gaussian processes like our example on channel width, however, are still rare in geomorphology.…”