Delivering useful hydrological forecasts is critical for urban and agricultural water management, hydropower generation, flood protection and management, drought mitigation and alleviation, and river basin planning and management, among others. In this work, we present and appraise a new simple and flexible methodology for hydrological time series forecasting. This methodology relies on (a) at least two individual forecasting methods and (b) the median combiner of forecasts. The appraisal is made by using a big dataset consisted of 90-year-long mean annual river flow time series from approximately 600 stations. Covering large parts of North America and Europe, these stations represent various climate and catchment characteristics, and thus can collectively support benchmarking. Five individual forecasting methods and 26 variants of the introduced methodology are applied to each time series. The application is made in one-step ahead forecasting mode. The individual methods are the last-observation benchmark, simple exponential smoothing, complex exponential smoothing, automatic autoregressive fractionally integrated moving average (ARFIMA) and Facebook's Prophet, while the 26 variants are defined by all the possible combinations (per two, three, four or five) of the five afore-mentioned methods. The new methodology is identified as well-performing in the long run, especially when more than two individual forecasting methods are combined within its framework. Moreover, the possibility of case-informed integrations of diverse hydrological forecasting methods within systematic frameworks is algorithmically investigated and discussed. The related investigations encompass linear regression analyses, which aim at finding interpretable relationships between the values of a representative forecasting performance metric and the values of selected river flow statistics...