Interpreting water demands of forests and grasslands within a new Budyko formulation of evapotranspiration using percolation theory.

The relationship between carbon cycle and water demand is key to understanding global climate change, vegetation productivity, and predicting the future of water resources. The water balance, which enumerates the relative fractions of precipitation P that run off, Q, or are returned to the atmosphere through evapotranspiration, ET, links drawdown of atmospheric carbon with the water cycle through plant transpiration. Our theoretical description based on percolation theory proposes that dominant ecosystems tend to maximize drawdown of atmospheric carbon in the process of growth and reproduction, thus providing a link between carbon and water cycles. In this framework, the only parameter is the fractal dimensionality d of the root system. Values of d appear to relate to the relative roles of nutrient and water accessibility. Larger values of d lead to higher ET values. Known ranges of grassland root fractal dimensions predict reasonably the range of ET(P) in such ecosystems as a function of aridity index. Forests with shallower root systems, should be characterized by a smaller d and, therefore, ET that is a smaller fraction of P. The prediction of ET/P using the 3D percolation value of d matches rather closely results deemed typical for forests based on a phenomenology already in common use. We test predictions of Q with P against data and data summaries for sclerophyll forests in southeastern Australia and the southeastern USA. Applying PET data from a nearby site constrains the data from the USA to lie between our ET predictions for 2D and 3D root systems. For the Australian site, equating cited "losses" with PET underpredicts ET. This discrepancy is mostly removed by referring to mapped values of PET in that region. Missing in both cases is local PET variability, more important for reducing data scatter in southeastern Australia, due to the greater relief.