The partitioning of water at the Earth’s terrestrial surface is a scientific problem of relevance to the fields of ecology, geomorphology, soil science, and hydrology, among others. The only relationships which prove reasonably useful in predictions are based on Budyko’s phenomenology. In this framework, evaporation and transpiration are combined into ET, while surface and subsurface run-off are put together into Q. Systems in which solar energy exceeds the latent heat required to evaporate the precipitation, P, are termed water-limited; the opposite case is called energy-limited. Here universal characteristics of percolation theory are used to define horizontal optimal flow paths in 2D, and thereby root extension paths in the soil. 3D percolation structures in the vertical direction define chemical weathering and thus soil formation as a function of Q. The resulting predictions for plant height and root radial extent as a function of time and transpiration were previously verified, as were the predictions for soil depth as a function of Q.
Results/Conclusions
Now, using the (verified) relationship that Net Primary Productivity NPP is proportional simultaneously to soil depth and transpiration to the power equal to the mass fractal dimensionality of the root system, df, makes possible a prediction of the fraction of precipitation lost to evapotranspiration, ET = (df/3) P. This prediction was obtained by optimizing NPP with respect to ET. Using the universal percolation value in 2D df = 1.9, predicted from optimality, yields ET = 0.633 P, essentially the global average. Actual values of root fractal dimensionality in an experiment conducted at P = ET0 (potential evapotranspiration), or aridity index 1, generate the observed variability in long-term basin-wide studies of ET. Existing schemes to understand the variability in ET for strongly water-limited and energy-limited systems complete the description of ET (ET0/P) compatible with the Budyko phenomenology and observation.