Spatiotemporal Scaling of Vegetation Growth and Soil Formation: Explicit Predictions

Abstract

Core Ideas Universal exponents of percolation describe vegetation growth and soil formation. The variability in the coefficient of vegetation growth relates to evapotranspiration. The variability in the coefficient for soil formation relates to net infiltration. The variability in the coefficient of net primary productivity relates to nutrients. In a previous study, vegetation linear extent and soil depth as functions of time were proposed to follow percolation‐based scaling laws of power‐law form. Although the power‐law exponents are specified by theory, the fundamental length, x0, and time, t0, scales must be generated from physical arguments. In principle, these length and time scales can vary widely with climate, soil, and plant variables. In the previous study, approximate values, microns and seconds, were proposed for x0 and t0, based on typical soil flow rates, x0/t0, under saturated conditions, and the concept of a single pore having a diameter measured in microns. But the focus here is on development of predictive relationships for soil depth and vegetation linear extent as functions of time and, thus, on guidance for choosing specific values for x0 and t0. In the present study, it is argued that the relevant flow rate for soil formation is net (deep) infiltration, whereas for vegetation extent, the relevant flux must equate to transpiration. In vegetation, linear extent refers (approximately) equivalently to plant height, or root radial extent. Here root radial extent is taken as half the diameter of the projected root system. Since the root radial extent and the root biomass are by definition related through the root fractal dimensionality, the proposed relevance of transpiration to root radial extent implies a specific relationship between transpiration and root productivity, a measure of the root biomass added in a year. When above‐ground and below‐ground biomass are closely related, one can infer a proportionality of net primary productivity to root biomass changes. The general concepts are tested on large data‐bases for the temporal evolution of plant heights and soil depths, as well as the productivity as a function of evapotranspiration and soil calcic and gypsic horizon depths.