Feature importance measures for hydrological applications: insights from a virtual experiment

Discriminating the role of input variables in a hydrological system or in a multivariate hydrological study is particularly useful. Nowadays, emerging tools, called feature importance measures, are increasingly being applied in hydrological applications. In this study, we propose a virtual experiment to fully understand the functionality and, most importantly, the usefulness of these measures. Thirteen importance measures related to four general classes of methods are quantitatively evaluated to reproduce a benchmark importance ranking. This benchmark ranking is designed using a linear combination of ten random variables. Synthetic time series with varying distribution, cross-correlation, autocorrelation and random noise are simulated to mimic hydrological scenarios. The obtained results clearly suggest that a subgroup of three feature importance measures (Shapley-based feature importance, derivative-based measure, and permutation feature importance) generally provide reliable rankings and outperform the remaining importance measures, making them preferable in hydrological applications.