Forecasting upstream flow amount based on downstream flow values is a new way of managing flood risk. This kind of prediction of the flow, size, and intensity of rivers in the alluvial aquifers is, in most cases, a challenging task due to climate change, as well as anthropogenic impacts on river flows. The presented methodology allows for organizing and preparing measures for flood protection, the operational work of hydropower plants, and many other usages. The methodology consists of correlation, cross-correlation, and a rescaled adjusted partial sums (RAPS) method. Although all methods are known, they have not been used in a methodology like the one presented. Research is conducted on a real case study of the river Bednja, on five consecutive hydrological measurement stations in the northwestern part of Croatia, for an available time series of the average daily flows from 2007–2018. High correlations were observed between the five stations along the Bednja River, with values of the correlation coefficient between 0.85 and 0.97 for the average daily flows, and between 0.88 and 0.99 for the RAPS values. The presented analysis gives information about similarities and connections between all five hydrological stations, which is significant and can be used to predict flow intensity.