Developing a decision tree model to forecast runup and assess uncertainty in empirical formulations

The coastal zone is a dynamic region that can change rapidly and significantly with respect to the morphology of the beach and incoming wave conditions. Runup forecasts may be improved by adapting a dynamic approach that allows for different runup models to be implemented in response to changes in beach state. Accurately forecasting wave runup is critical to characterize exposure to coastal hazards and provide an early warning against potential erosion and inundation. Here, we developed a decision tree model to produce a weighted ensemble of existing runup models to predict 1.25 years of runup at Duck, North Carolina, USA. We then applied the calibrated decision tree model to reproduce observed runup during the DUNEX experiment in Pea Island, North Carolina, USA. We found that the decision tree approach yielded a prediction that was comparable or greater in accuracy (i.e. higher r², lower RMSE) than the individual runup models. We also interrogated the decision tree predictions to determine how the individual models perform relative to each other and why certain models perform better than others under the same observed wave and beach conditions. We found that the decision tree approach drew on the processes represented in the individual models in the ensemble to produce a forecast that is accurate and explainable without relying on prior knowledge of the study site(s) or requiring manual adjustments beyond the initial model training.