The hillslope-storage Boussinesq model for non-constant bedrock slope

A. G.J. Hilberts, E. E. Van Loon, P. A. Troch, C. Paniconi

Research output: Contribution to journalArticlepeer-review

61 Scopus citations


In this study the recently introduced hillslope-storage Boussinesq (hsB) model is cast in a generalized formulation enabling the model to handle non-constant bedrock slopes (i.e. bedrock profile curvature). This generalization extends the analysis of hydrological behavior to hillslopes of arbitrary geometrical shape, including hillslopes having curved profile shapes. The generalized hsB model performance for a free drainage scenario is evaluated by comparison to a full three-dimensional Richards equation (RE) based model. The model results are presented in the form of dimensionless storage profiles and dimensionless outflow hydrographs. In addition, comparison of both models to a storage based kinematic wave (KW) model enables us to assess the relative importance of diffusion processes for different hillslope shapes, and to analyze the influence of profile curvature on storage and flow patterns specifically. The comparison setup consists of a set of nine gentle (5% bedrock slope) and nine steep (30% bedrock slope) hillslopes of varying plan shape and profile curvature. Interpretation of the results shows that for highly conductive soils the simulated storage profiles and outflow hydrographs of the generalized hsB model and RE model match remarkably for 5% bedrock slope and for all plan and profile curvatures. The match is slightly poorer on average for 30% bedrock slope, in particular, on divergently shaped hillslopes. In the assessment of the influence of hydraulic diffusion, we find good agreement in simulation results for the KW model compared to results from the generalized hsB model and the RE model for steep divergent and uniform hillslopes, due to a relatively low ratio between water table gradient and bedrock slope compared to convergent or gentle hillslopes. Overall, we demonstrate that, in addition to bedrock slope, hillslope shape as represented by plan and profile curvature is an important control on subsurface flow response.

Original languageEnglish (US)
Pages (from-to)160-173
Number of pages14
JournalJournal of Hydrology
Issue number3-4
StatePublished - Jun 1 2004


  • Boussinesq equation
  • Hillslope hydrology
  • Kinematic wave equation
  • Richards equation
  • Subsurface flow

ASJC Scopus subject areas

  • Water Science and Technology


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