Percolation transport theory and relevance to soil formation, vegetation growth, and productivity

Scaling laws of percolation theory have been applied to generate the time dependence of vegetation growth rates (both intensively managed and natural) and soil formation rates. The soil depth is thus equal to the solute vertical transport distance, the soil production function, chemical weathering rates, and C and N storage rates are all given by the time derivative of the soil depth. Approximate numerical coefficients based on the maximum flow rates in soils have been proposed, leading to a broad understanding of such processes. What is now required is an accurate understanding of the variability of the coefficients in the scaling relationships. The present abstract focuses on the scaling relationship for solute transport and soil formation. A soil formation rate relates length, x, and time, t, scales, meaning that the missing coefficient must include information about fundamental space and time scales, x0 and t0. x0 is proposed to be a fundamental mineral heterogeneity scale, i.e. a median particle diameter. to is then found from the ratio of x0 and a fundamental flow rate, v0, which is identified with the net infiltration rate. The net infiltration rate is equal to precipitation P less evapotranspiration, ET, plus run-on less run-off. Using this hypothesis, it is possible to predict soil depths and formation rates as functions of time and P - ET, and the formation rate as a function of depth, soil calcic and gypsic horizon depths as functions of P-ET. It is also possible to determine when soils are in equilibrium, and predict relationships of erosion rates and soil formation rates.