Assessing storm surge model performance: what error indicators can measure the model's skill?

Abstract. A well-validated storm surge numerical model is crucial, offering precise coastal hazard information and serving as a basis for extensive databases and advanced data-driven algorithms. However, selecting the best model setup based solely on common error indicators like the root-mean-square error (RMSE) or Pearson correlation does not always yield optimal results. To illustrate this, we conducted 34-year high-resolution simulations for storm surge under barotropic (BT) and baroclinic (BC) configurations using atmospheric data from ERA5 and a high-resolution downscaling of the Climate Forecast System Reanalysis (CFSR) developed by the University of Genoa (UniGe). We combined forcing and configurations to produce three datasets: (1) BT-ERA5, (2) BC-ERA5, and (3) BC-UniGe. The model performance was assessed against nearshore station data using various statistical metrics. While RMSE and Pearson correlation suggest BT-ERA5, i.e., the coarsest and simplest setup, is the best model (followed by BC-ERA5), we demonstrate that these indicators are not always reliable for performance assessment. The most sophisticated model (BC-UniGe) shows worse values of RMSE or Pearson correlation due to the so-called “double penalty” effect. Here we propose new skill indicators that assess the ability of the model to reproduce the distribution of the observations. This, combined with an analysis of values above the 99th percentile, identifies BC-UniGe as the best model, while ERA5 simulations tend to underestimate the extremes. Although the study focuses on the accurate representation of storm surge by the numerical model, the analysis and proposed metrics can be applied to any problem involving the comparison between time series of simulation and observation.