A coupled channel network growth and hillslope evolution model: 2. Nondimensionalization and applications

Authors:
  • GWGarry Willgoose
    Garry Willgoose
  • RBRafael L. Bras
    Rafael L. Bras
  • IRIgnacio Rodriguez‐Iturbe
    Ignacio Rodriguez‐Iturbe
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Abstract
This paper explores the scaling and similitude properties of the system of governing equations for a catchment evolution model that was presented in an accompanying paper (Willgoose et al., this issue). Similitude is an important concept that allows the quantification of the similarities of, and differences between, two catchments. Through the use of a small number of nondimensional numbers the governing physics of the channel network and surrounding hillslopes in a catchment may be summarized. These nondimensional numbers lead to similarity conditions that allow for the quantitative comparison of data between field catchments and between the field scale and the controlled experimental scale. Derived relationships are presented for the drainage density of the channel network and the rate at which the network grows, parameterized using the nondimensional numbers. Drainage density is shown to be mostly a function of the hillslope channel initiation number that relates the slopes and lengths of hillslopes in a very simple fashion. Finally, it is shown that the form of a channel network is very sensitive to initial conditions. Though the exact form of the network and the hillslopes may vary greatly, along with their topological statistics, physical statistics such as drainage density are only slightly affected.

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