The riparian doctrine is one of two main systems of determining water allocation and ownership of water rights. The other main scheme is prior appropriation. This is the subject of a separate blog post.
The riparian doctrine evolved in the green countrysides of England and the eastern United States. Riparian law typically deals with abundant water supplies. In short, rights are based on access to water through ownership of banks and land surrounding a water supply. Users restrict demands based on those that constitute reasonable uses.
The riparian doctrine has been critiqued as really not offering much of a system of water allocation. Instead, it is viewed as a fire fighting device to settle the few disputes that arise over plentiful supplies.