@misc{WickertSchildgen2019,
  author    = {Wickert, Andrew D. and Schildgen, Taylor F.},
  title     = {Long-profile evolution of transport-limited gravel-bed rivers},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {680},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-42571},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-425718},
  pages     = {27},
  year      = {2019},
  abstract  = {Alluvial and transport-limited bedrock rivers constitute the majority of fluvial systems on Earth. Their long profiles hold clues to their present state and past evolution. We currently possess first-principles-based governing equations for flow, sediment transport, and channel morphodynamics in these systems, which we lack for detachment-limited bedrock rivers. Here we formally couple these equations for transport-limited gravel-bed river long-profile evolution. The result is a new predictive relationship whose functional form and parameters are grounded in theory and defined through experimental data. From this, we produce a power-law analytical solution and a finite-difference numerical solution to long-profile evolution. Steady-state channel concavity and steepness are diagnostic of external drivers: concavity decreases with increasing uplift rate, and steepness increases with an increasing sediment-to-water supply ratio. Constraining free parameters explains common observations of river form: to match observed channel concavities, gravel-sized sediments must weather and fine - typically rapidly - and valleys typically should widen gradually. To match the empirical square-root width-discharge scaling in equilibrium-width gravel-bed rivers, downstream fining must occur. The ability to assign a cause to such observations is the direct result of a deductive approach to developing equations for landscape evolution.},
  language  = {en}
}