Scale Effect on Evapotranspiration: Predicting the Continental and Global Scale Water Balance Based on Percolation Theory and Optimality Principle

Abstract Moisture recycling over the continents, which is known to increase with increasing spatial scale, increases both precipitation and sensible heat fluxes without increasing the overall latent heat flux, implying a reduction in evapotranspiration (ET) with increasing spatial scale. One may hypothesize that the architecture of plant/ecosystem root systems at the local scale may conform either to two‐dimensional (2D) or 3D fractal structure that is predicted by percolation theory. In this study, we test the hypothesis that only the 2D structure and associated fractal dimensionality are relevant for length scales commensurate with the continents. To test the hypothesis of a scale‐dependent ET, we compare the non‐parametric predictions of our recent theory, derived based on percolation theory and principle of optimality, for ET as a function of precipitation P and potential evapotranspiration potential evapotranspiration (PET) with multiple data sets from the literature for continental ET and P, and compatible estimations of PET. Within the limits set by the uncertainty in the data, most particularly in PET but also ET, the hypothesis that the 2D root structure model is relevant at the continental scales is confirmed. Certainly, at smaller length scales, both 2D and 3D results are observed. The resulting predicted and observed scale‐dependence of ET is consistent with the concept, magnitude, and spatial scale dependence of continental moisture recycling.