Soil production function refers to the rate ofbedrockweathering intosoil as a function of soil thickness. A general model suggests that the rate of physical weathering of bedrock (de/dt) can be represented as an exponential decline with soil thickness:

${\displaystyle de/dt=P_0\exp [-kh]}$

whereh is soil thickness [m],P₀ [mm/year] is the potential (or maximum) weathering rate of bedrock andk [m⁻¹] is an empirical constant.^[1]

The reduction of weathering rate with thickening of soil is related to the exponential decrease of temperature amplitude with increasing depth below the soil surface, and also the exponential decrease in average water penetration (for freely-drained soils). ParametersP₀ andk are related to the climate and type ofparent material. The value ofP₀ was found to range from 0.08 to 2.0 mm/yr for sites innorthern California, and 0.05–0.14 mm/yr for sites in southeasternAustralia.^[2] Meanwhile values ofk do not vary significantly, ranging from 2 to 4 m⁻¹.

Severallandscape evolution models have adopted the so-calledhumped model.^[3] This model dates back toG.K. Gilbert'sReport on the Geology of the Henry Mountains (1877). Gilbert reasoned that the weathering of bedrock was fastest under an intermediate thickness of soil and slower under exposed bedrock or under thick mantled soil. This is because chemical weathering requires the presence of water. Under thin soil or exposed bedrock water tends to run off, reducing the chance of the decomposition of bedrock.

• Biorhexistasy
• Hillslope evolution
• Pedogenesis
• Soil functions

• Ahnert, F. (1977). "Some comments on the quantitative formulation of geomorphological process in a theoretical model".Earth Surface Processes.2 (2–3):191–201.doi:10.1002/esp.3290020211.
• Humphreys, G. S.; Wilkinson, M. T. (2007)."The soil production function: a brief history and its rediscovery"(PDF).Geoderma.139 (1–2):73–78.Bibcode:2007Geode.139...73H.doi:10.1016/j.geoderma.2007.01.004.
• Wilkinson, M. T.; Chappell, J.; Humphreys, G. S.; Fifield, K.; Smith, B.; Hesse, P. P. (2005)."Soil production in heath and forest, Blue Mountains, Australia: influence of lithology and palaeoclimate"(PDF).Earth Surface Processes and Landforms.30 (8):923–934.Bibcode:2005ESPL...30..923W.doi:10.1002/esp.1254.S2CID 128557903.
• Wilkinson, M. T.; Humphreys, G. S. (2005)."Exploring pedogenesis via nuclide-based soil production rates and OSL-based bioturbation rates"(PDF).Australian Journal of Soil Research.43 (6):767–779.Bibcode:2005SoilR..43..767W.doi:10.1071/SR04158.