River flow modelling using nonparametric functional data analysis

Time series and extreme value analyses are two statistical approaches usually applied to study hydrological data. Classical techniques, such as autoregressive integrated moving-average models (in the case of mean flow predictions), and parametric generalised extreme value fits and nonparametric extreme value methods (in the case of extreme value theory) have been usually employed in this context. In this article, nonparametric functional data methods are used to perform mean monthly flow predictions and extreme value analysis, which are important for flood risk management. These are powerful tools that take advantage of both, the functional nature of the data under consideration and the flexibility of nonparametric methods, providing more reliable results. Therefore, they can be useful to prevent damage caused by floods and to reduce the likelihood and/or the impact of floods in a specific location. The nonparametric functional approaches are applied to flow samples of two rivers in the United States. In this way, monthly mean flow is predicted and flow quantiles in the extreme value framework are estimated using the proposed methods. Results show that the nonparametric functional techniques work satisfactorily, generally outperforming the behaviour of classical parametric and nonparametric estimators in both settings.