Refining linear interpolation of water level data with the use of autoregressive models

Although linear interpolation is the simplest method for inputing hydrograph data, there are evidences for its efficiency in hydrology. It works well at edges of no-data gaps because the inputation is limited by bounds. However, it does not reconstruct the hydrologic variability of water levels recorded before and after a no-data gap. 

In this paper, we combine linear interpolation with autoregressive models in order to account for both controlling bounds as well as anticipating irregular variation of hydrograph. We check the performance of this approach using hourly water level time series collected between 2016 and 2022 at 28 gauges located in the Odra/Oder River basin in Poland. For the purpose of validation, we produce missing data gaps artificially, using the moving window approach. By considering root mean square errors (RMSE) of interpolation as a function of gap length and investigating differences between these RMSE values computed using linear interpolation with/without autoregression, we identify cases in which the postulated approach refines purely linear interpolation. Initial studies suggest that the combination of methods reveals slightly better skills than the linear interpolation itself for short no-data gaps, the length of which does not exceed 24 hours.

The research has been conducted in frame of the project no. 2020/38/E/ST10/00295 within the Sonata BIS programme of the National Science Centre, Poland.