A data-based regional scale autoregressive rainfall-runoff model: a study from the Odra River

This paper aims to compare the performances of multivariate autoregressive (MAR) techniques and univariate autoregressive (AR) methods applied to regional scale rainfall-runoff modelling. We focus on the case study from the upper and middle reaches of the Odra River with its main tributaries in SW Poland. The rivers drain both the mountains (the Sudetes) and the lowland (Nizina Śląska). The region is exposed to extreme hydrologic and meteorological events, especially rain-induced and snow-melt floods. For the analysis, four hydrologic and meteorological variables are chosen, i.e., discharge (17 locations), precipitation (7 locations), thickness of snow cover (7 locations) and groundwater level (1 location). The time period is November 1971–December 1981 and the temporal resolution of the time series is of 1 day. Both MAR and AR models of the same orders are fitted to various subsets of the data and subsequently forecasts of discharge are derived. In order to evaluate the predictions the stepwise procedure is applied to make the validation independent of the specific sample path of the stochastic process. It is shown that the model forecasts peak discharges even 2–4 days in advance in the case of both rain-induced and snow-melt peak flows. Furthermore, the accuracy of discharge predictions increases if one analyses the combined data on discharge, precipitation, snow cover, and groundwater level instead of the pure discharge multivariate time series. MAR-based discharge forecasts based on multivariate data on discharges are more accurate than AR-based univariate predictions for a year with a flood, however, this relation is reverse in the case of the free-of-flooding year. In contrast, independently of the occurrence of floods within a year, MAR-based discharge forecasts based on discharges, precipitation, snow cover, and groundwater level are more precise than AR-based predictions.