Soil production function

A general model suggests that the rate of physical weathering of bedrock (de/dt) can be represented as an exponential decline with soil thickness:

where h is soil thickness [m], P0 [mm/year] is the potential (or maximum) weathering rate of bedrock and k [m−1] is an empirical constant.

Parameters P0 and k are related to the climate and type of parent material.

[3] This model dates back to G.K. Gilbert's Report 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.