Hydraulic geometry of natural rivers: A review and future directions

The geomorphic relationships known as hydraulic geometry (HG) were first introduced by Leopold and Maddock in 1953, and their application remains critically important for assessing water resources the world over. The practical utility of HG for discharge monitoring, habitat studies, and understanding geomorphic change over time is unquestioned, but its elevation beyond empirically observed relationship to physical principle is not complete, despite universal acceptance of its existence. This review summarizes six decades of HG research while surveying rational, extremal, and empirical attempts to derive HG's underlying physical principles. In addition, so called non-Leopoldian forms of HG are discussed, expanding HG beyond its original construction to examine a range of research that invokes HG in novel ways. The recent discovery of at-many-stations hydraulic geometry (AMHG) is also discussed in the context of previous HG literature. Finally, some common themes linking disparate HG research communities are described in conjunction with suggestions for possible new directions for HG research in the future.