Hillslopes, Streams, and the Soil Production Function.

It is said that the geomorphic world is one of hillslopes and streams, with streams setting the beat of the landscape. The combination of stream incision and hillslope response is the stream-hillslope couple. Importantly, the harmonization of the stream-hillslope couple requires freely mobile material, soil. Thus understanding how soil is produced (aka mobilized) is key to understanding the responses of hillslopes to stream incision or aggradation. The concept of soil production functions are not new, and are currently experiencing a revived interest due in part, to the widespread usage of Cosmogenic Radionuclides for surface exposure dating. Moreover, recent modeling exercises indicate that bioturbation associated with vegetation dynamics can reproduce a humped soil production function (HSPF) as well. Thus, soil production and vegetation are integrally linked, and where conditions for plant growth are limiting, there is undoubtedly an effect on soil production.  Here we present a mathematical analysis of the HSPF to determine what controls the transition between exponential and depth-dependent styles of soil production. Moreover, we propose a working hypothesis that scaling parameters used in the function are proportional to the ratio of precipitation to potential evapotranspiration (AI) and to lithologic properties, namely rock strength.  Global values of the aridity index, EEMT, and rock strength are compared to published values of soil production in an extensive compilation.