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The soil production function and landscape equilibrium

Nature volume 388, pages 358–361 (1997)Cite this article

Abstract

Hilly and mountainous landscapes are partially to completely covered with soil under a wide range of erosion and uplift rates, bedrock type and climate. For soil to persist it must be replenished at a rate equal to or greater than that of erosion. Although it has been assumed for over 100 years that bedrock disintegration into erodable soil declines with increasing soil mantle thickness1,2,3,4,5,6,7,8,9, no field data have shown this relationship. Here we apply two independent field methods for determining soil production rates to hillslopes in northern California. First, we show that hillslope curvature (a surrogate for soil production7) varies inversely with soil depth. Second, we calculate an exponential decline of soil production rates with increasing soil depth from measurements of the in situ produced cosmogenic 10Be and 26Al concentrations in bedrock sampled under soils of different depths. Results from both methods agree well and yield the first empirical soil production function. We also illustrate how our methods can determine whether a landscape is in morphological equilibrium or not.

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Figure 1: The conservation of mass equation for soil thickness h (equation (1)) states that the change in soil mass with time, t, is equal to the conversion of bedrock to soil due to lowering of the bedrock–soil interface less the divergence of transported soil mass.
Figure 2: Plot of negative hillslope curvature, −∇2z, against local soil depth for four distinct small ridges (insetmaps drawn with 2-m contour intervals) in Tennessee Valley, Marin County, California (37.9° N, 122.6° W).
Figure 3: Main figure shows soil production rates (−∂e/∂t) (calculated from in situ produced cosmogenic 10Be and 26Al in bedrock samples) versus measured soil depths h.

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Acknowledgements

We thank K. Heimsath and L. Cossey for field and laboratory assistance; D. DePaolo for laboratory space; D. Lal for suggestions; and the Golden Gate National Recreation Area for access to our study site. We thank P. Bierman and A. Howard for comments on the manuscript. This work was supported by Cal Space, IGPP-LLNL, NSF, NASA, DOE and a Switzer Environmental fellowship.

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Authors and Affiliations

  1. *Department of Geology and Geophysics, University of California, 301 McCone Hall, Berkeley, 94720-4767, California, USA

    Arjun M. Heimsath & William E. Dietrich

  2. †Space Sciences Laboratory, University of California, Berkeley, 94720-7450, California, USA

    Kunihiko Nishiizumi

  3. ‡Center for Accelerator Mass Spectrometry, Lawrence Livermore National Laboratory, Livermore, 94550, California, USA

    Robert C. Finkel

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  1. Arjun M. Heimsath
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Correspondence to Arjun M. Heimsath.

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Heimsath, A., Dietrich, W., Nishiizumi, K. et al. The soil production function and landscape equilibrium. Nature 388, 358–361 (1997). https://doi.org/10.1038/41056

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