Pacific Institute helps to answer these questions. Shown are rivers, merging into rivers, displayed as increasing width of blue branches leading to their trunk exit at the ocean. In the East Central US the flow is primarily into the Gulf of Mexico and appears in this graphic as a great branching tree of water with some branches stretching across the country, nearly to Canada. Many dimensions (i.e. variables) are shown in this graphic: Longitude, Latitude, (and the associated nominal variable of State Name), Direction, Water Flow (with river width drawn proportional to the square root of its estimated average annual flow volume), across forested regions (in green) of the US. Perhaps another (seventh) variable indicating transit time from the tip of a branch to the ocean could also be color coded. Is such information easily available? I don't know.
The map is reminiscent of Minard's acclaimed map of Napoleon's march. Via Scientific Illustration and joerojasburke.