A Bottom-up Control on Fresh-Bedrock Topography under Landscapes. Rempe, D. M. & Dietrich, W. E. Proceedings of the National Academy of Sciences, 111(18):6576–6581, May, 2014.
doi  abstract   bibtex   
[Significance] Hilly landscapes are typically mantled with soil and underlain by a weathered bedrock zone that may extend tens of meters beneath the surface before reaching fresh bedrock. The weathered bedrock zone influences water runoff to channels, the chemistry of that water, the rates and processes of erosion, and atmospheric processes due to plant uptake of moisture and return to the atmosphere. However, the spatial pattern of the underlying fresh-bedrock surface is essentially unknown. We present a testable model that predicts hillslope form and the depth to fresh bedrock. The depth increases upslope and depends strongly on the porosity and permeability of the bedrock and the rate of channel incision at the base of the hillslope. [Abstract] The depth to unweathered bedrock beneath landscapes influences subsurface runoff paths, erosional processes, moisture availability to biota, and water flux to the atmosphere. Here we propose a quantitative model to predict the vertical extent of weathered rock underlying soil-mantled hillslopes. We hypothesize that once fresh bedrock, saturated with nearly stagnant fluid, is advected into the near surface through uplift and erosion, channel incision produces a lateral head gradient within the fresh bedrock inducing drainage toward the channel. Drainage of the fresh bedrock causes weathering through drying and permits the introduction of atmospheric and biotically controlled acids and oxidants such that the boundary between weathered and unweathered bedrock is set by the uppermost elevation of undrained fresh bedrock, Zb. The slow drainage of fresh bedrock exerts a '' bottom up'' control on the advance of the weathering front. The thickness of the weathered zone is calculated as the difference between the predicted topographic surface profile (driven by erosion) and the predicted groundwater profile (driven by drainage of fresh bedrock). For the steady-state, soil-mantled case, a coupled analytical solution arises in which both profiles are driven by channel incision. The model predicts a thickening of the weathered zone upslope and, consequently, a progressive upslope increase in the residence time of bedrock in the weathered zone. Two nondimensional numbers corresponding to the mean hillslope gradient and mean groundwater-table gradient emerge and their ratio defines the proportion of the hillslope relief that is unweathered. Field data from three field sites are consistent with model predictions.
@article{rempeBottomupControlFreshbedrock2014,
  title = {A Bottom-up Control on Fresh-Bedrock Topography under Landscapes},
  author = {Rempe, Daniella M. and Dietrich, William E.},
  year = {2014},
  month = may,
  volume = {111},
  pages = {6576--6581},
  issn = {1091-6490},
  doi = {10.1073/pnas.1404763111},
  abstract = {[Significance] 

Hilly landscapes are typically mantled with soil and underlain by a weathered bedrock zone that may extend tens of meters beneath the surface before reaching fresh bedrock. The weathered bedrock zone influences water runoff to channels, the chemistry of that water, the rates and processes of erosion, and atmospheric processes due to plant uptake of moisture and return to the atmosphere. However, the spatial pattern of the underlying fresh-bedrock surface is essentially unknown. We present a testable model that predicts hillslope form and the depth to fresh bedrock. The depth increases upslope and depends strongly on the porosity and permeability of the bedrock and the rate of channel incision at the base of the hillslope. [Abstract] 

The depth to unweathered bedrock beneath landscapes influences subsurface runoff paths, erosional processes, moisture availability to biota, and water flux to the atmosphere. Here we propose a quantitative model to predict the vertical extent of weathered rock underlying soil-mantled hillslopes. We hypothesize that once fresh bedrock, saturated with nearly stagnant fluid, is advected into the near surface through uplift and erosion, channel incision produces a lateral head gradient within the fresh bedrock inducing drainage toward the channel. Drainage of the fresh bedrock causes weathering through drying and permits the introduction of atmospheric and biotically controlled acids and oxidants such that the boundary between weathered and unweathered bedrock is set by the uppermost elevation of undrained fresh bedrock, Zb. The slow drainage of fresh bedrock exerts a '' bottom up'' control on the advance of the weathering front. The thickness of the weathered zone is calculated as the difference between the predicted topographic surface profile (driven by erosion) and the predicted groundwater profile (driven by drainage of fresh bedrock). For the steady-state, soil-mantled case, a coupled analytical solution arises in which both profiles are driven by channel incision. The model predicts a thickening of the weathered zone upslope and, consequently, a progressive upslope increase in the residence time of bedrock in the weathered zone. Two nondimensional numbers corresponding to the mean hillslope gradient and mean groundwater-table gradient emerge and their ratio defines the proportion of the hillslope relief that is unweathered. Field data from three field sites are consistent with model predictions.},
  journal = {Proceedings of the National Academy of Sciences},
  keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-13161423,bedrock,climate,erosion,geomorphology,landscape-modelling,mathematical-reasoning,modelling,soil-resources,topography},
  lccn = {INRMM-MiD:c-13161423},
  number = {18}
}
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