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 1 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.
Highlights
Wave runup is important for characterizing the vulnerability of beach and dune systems and coastal infrastructure to wave action
We focus on duneimpact models, which are simple, commonly used models that typically rely on a parameterization of wave runup to model time-dependent dune erosion
This suggests that the Gaussian processes (GPs) approach efficiently captures scatter in runup predictions and subsequently dune erosion predictions, requiring on the order of 10 samples, which is significantly less than the 103–106 runs typically used in Monte Carlo simulations to develop probabilistic predictions (e.g., Callaghan et al, 2008; Li et al, 2013; Ranasinghe et al, 2012)
Summary
Wave runup is important for characterizing the vulnerability of beach and dune systems and coastal infrastructure to wave action. Even flexible machine-learning approaches based on extensive runup datasets or consensus-style “model of models” do not resolve prediction scatter in runup datasets (e.g., Atkinson et al, 2017; Passarella et al, 2018b; Power et al, 2019). This suggests that the development of a perfect deterministic parameterization of wave runup, especially
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