A new approach for hydrograph data interpolation and outlier removal for vector autoregressive modelling: a case study from the Odra/Oder River

Abstract

This study presents a new approach for predicting water levels of the Odra/Oder river using vector autoregressive models (VAR). We use water level time series from 27 gauging stations, on which we interpolate no-data gaps using the LinAR method and detect outliers with two separate methods: the extreme values (EV) approach and the isolation forest (IFO) algorithm. Before removing potential outliers, we propose a hydrological evaluation based on multivariate data analysis. Finally, we consider three separate data scenarios, i.e. LinAR (no outlier rejection), EV, and IFO. VAR models for six prediction gauges were built in a moving window manner on the most recent 720 hourly water levels prior to each prediction. The analysis covered the time range from January 2016 to May 2022 and resulted in \(\varvec{\approx }\) 1,000,000 water level forecasts (3 scenarios x 6 gauges x 55,000 hourly time steps) with lead time of 72 h. The analysis of root mean squared error (RMSE) indicates that the VAR model performs well, especially for 24-hour predictions, with RMSE values ranging from 8 to 28 cm. The model was also found to have skills in predicting a rising limb of a hydrograph. Our numerical experiments showed the susceptibility of the VAR predictions to artefacts. The IFO method was found to detect outliers skilfully, which allowed to produce the most accurate VAR-based predictions.