A generalized Exner equation for sediment mass balance

Authors

  • C. Paola,

    1. St. Anthony Falls Laboratory, Minneapolis, Minnesota, USA
    2. Also at Department of Geology and Geophysics, University of Minnesota Twin Cities, Minneapolis, Minnesota, USA.
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  • V. R. Voller

    1. St. Anthony Falls Laboratory, Minneapolis, Minnesota, USA
    2. Also at Department of Civil Engineering, University of Minnesota Twin Cities, Minneapolis, Minnesota, USA.
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Abstract

[1] The advance of morphodynamics research into new areas has led to a proliferation of forms of sediment mass balance equation. Without a general equation it is often difficult to know what these problem-specific versions of sediment mass balance leave out. To address this, we derive a general form of the standard Exner equation for sediment mass balance that includes effects of tectonic uplift and subsidence, soil formation and creep, compaction, and chemical precipitation and dissolution. The complete equation, (17), allows for independent evolution of two critical interfaces: that between bedrock and sediment or soil and that between sediment and flow. By eliminating terms from the general equation it is straightforward to derive mass balance equations applicable to a wide range of problems such as short-term bed evolution, basin evolution, bedrock uplift and soil formation, and carbonate precipitation and transport. Dropping terms makes explicit what is not being considered in a given problem and can be done by inspection or by a formal scaling analysis of the terms. Scaling analysis leads directly to dimensionless numbers that measure the relative importance of terms in the equation, for example, the relative influence of spatial versus temporal changes in sediment load on bed evolution. Combining scaling analysis with time averaging shows how the relative importance of terms in the equation can change with timescale; for example, the term representing bed evolution due to temporal change in sediment load tends to zero as timescale increases.

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