Prediction of wave runup on beaches using gene-expression programming and empirical relationships

This paper assesses the accuracy of seven empirical models and an explicit Gene-Expression Programming (GEP) model to predict wave runup against a large dataset of runup observations. Observations consist of field and laboratory measurements and include a wide array of beach types with varying sediment sizes (from fine sand to cobbles) and bed roughness (from smooth steel to asphalt). We show that the best performing models in the literature are prone to significant errors (minimum RMSE of 1.05 m and NMSE of 0.23) when used with unseen data, i.e., uncalibrated models; however, overall error values and correlations are significantly reduced when models are optimised for the dataset. The best performing empirical models use a Hunt type scaling with an additional parameter for wave induced setup. The predictive ability of the explicit GEP model, which better captures the complex nonlinear effects of the key factors on the wave runup length, resulted in a statistically significant improvement in predictive capacity in comparison to all other empirical models assessed here, even on unseen data. Wave height, wavelength, and beach slope are shown to be the three primary factors influencing wave runup, with grain size/bed roughness having a smaller, but still significant influence on the runup. The r² of the best optimised existing models (which takes the form of Holman (1986) and Atkinson et al. (2017) their M2 model) was 0.77, with a RMSE of 0.85 m. These were improved to an r² of 0.82 (6% increase) and RMSE of 0.75 m (12% decrease) in the GEP-based model. The sensitivity of the proposed GEP-based model to each input variable is assessed via a partial derivative sensitivity analysis. The results demonstrate a higher sensitivity in the model to small values of each input and that wave steepness and beach slope are the primary factors influencing wave runup.