Scaling relationships for soil formation and edaphic controls on vegetation growth

Abstract:

Critical path analysis (CPA) is suited to calculating the hydraulic conductivity, K, of heterogeneous porous media by quantifying of paths of least resistance. Whenever CPA could be used to calculate K, advective transport scaling relationships from percolation theory should describe solute transport. Two solute transport relationships are applied to predict soil development and edaphic constraints on natural vegetation growth. These results use known exponents from percolation theory and known subsurface flow velocities. The typical flow velocity itself constrains optimal growth rates of cultivars. The percolation scaling relationship constraining vegetation growth is shown to be in accord with data over time scales from hours to 100,000 years, including over a dozen studies (and two models) of tree growth. The scaling function for soil development explains time scales for formation of soils from years to hundreds of millions of years. Data on soil development comes from 23 different studies. The key unification is the common origin of the time and space coordinates for all three relationships in the time of transport through a single pore of roughly micron size at a typical subsurface pore-scale flow velocity. The distinction in evolving time scales is primarily a result of the hierarchical nature of vascular plant root systems, which speed up nutrient access relative to physical transport rates in the soil. The results help explain reduction in forest productivity with age, diminishing soil production with time, and the temporal distinction between the relevance of chemical and biological processes in soils to the global carbon cycle.