@misc{Wickert2016,
  author    = {Wickert, Andrew D.},
  title     = {Open-source modular solutions for flexural isostasy},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {498},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-40836},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-408366},
  pages     = {21},
  year      = {2016},
  abstract  = {Isostasy is one of the oldest and most widely applied concepts in the geosciences, but the geoscientific community lacks a coherent, easy-to-use tool to simulate flexure of a realistic (i.e., laterally heterogeneous) lithosphere under an arbitrary set of surface loads. Such a model is needed for studies of mountain building, sedimentary basin formation, glaciation, sea-level change, and other tectonic, geodynamic, and surface processes. Here I present gFlex (for GNU flexure), an open-source model that can produce analytical and finite difference solutions for lithospheric flexure in one (profile) and two (map view) dimensions. To simulate the flexural isostatic response to an imposed load, it can be used by itself or within GRASS GIS for better integration with field data. gFlex is also a component with the Community Surface Dynamics Modeling System (CSDMS) and Landlab modeling frameworks for coupling with a wide range of Earth-surface-related models, and can be coupled to additional models within Python scripts. As an example of this in-script coupling, I simulate the effects of spatially variable lithospheric thickness on a modeled Iceland ice cap. Finite difference solutions in gFlex can use any of five types of boundary conditions: 0-displacement, 0-slope (i.e., clamped); 0-slope, 0-shear; 0-moment, 0-shear (i.e., broken plate); mirror symmetry; and periodic. Typical calculations with gFlex require << 1 s to similar to 1 min on a personal laptop computer. These characteristics - multiple ways to run the model, multiple solution methods, multiple boundary conditions, and short compute time - make gFlex an effective tool for flexural isostatic modeling across the geosciences.},
  language  = {en}
}
@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}
}