SCALING APPROACHES TO GEOCHEMISTRY AND ECOLOGY LINKED TO THE WATER BALANCE

Geological processes and sciences link enormous time scales with short time scales in the present. Describing this linkage through the principle of uniformitarianism, however, is subject to criticism; evolution of landforms may be dominated by rare, catastrophic events. Ecological elements adapt constantly to each other as well as existing and changing conditions of surface chemistry, climate, and the balance of water and solar energies and, on sufficiently long time scales, atmospheric chemistry. Precipitated water, P, with its mechanical energy and geochemical transport continuously reworks the surface, limiting chemical weathering, biological growth, and physical transport. The evolution of our planet’s surface is thus heavily influenced by the intersection of the rock, water, and carbon cycles at its surface. This intersection is focused at the scale of the intersection of plant roots with the soil pores, where flowing water sets the fundamental process rates, scaling laws describe their temporal evolution, and the network scale the basic unit. In this picture, the vegetation growth rate follows its predicted scaling law over time scales up to at least 100,000 years, with variability governed by the rate of evapotranspiration, ET, and the soil formation rate follows its predicted scaling law over periods to 130 Myr, but with variability governed by infiltration through the top soil (related to subsurface run-off, Q ≈ P - ET). The same theoretical underpinnings work for both threshold and gradual landscape evolution. Finally, vegetation exploits the conditions to the fullest, since an optimization of net primary productivity NPP in terms of the principle hydrologic fluxes yields the observed water partitioning at the terrestrial Earth’s surface. The procedure involves writing NPP as a product of the 2D root growth in the lateral directions (ET to a power near 2) and the soil depth (P-ET) to a power near 1. The result, that ET ≈ 2/(2+1) P, matches the global mean. When theoretical values of the appropriate vegetation scaling exponent are replaced by actual root fractal dimensionalities, the variability in the water balance is mapped out.