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

Allen G Hunt; Muhammad Sahimi; Boris A Faybishenko; Markus Egli; Behzad Ghanbarian; Fang Yu

doi:10.1016/j.scitotenv.2023.162905

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

Sci Total Environ. 2023 Jun 15:877:162905. doi: 10.1016/j.scitotenv.2023.162905. Epub 2023 Mar 16.

Authors

Allen G Hunt¹, Muhammad Sahimi², Boris A Faybishenko³, Markus Egli⁴, Behzad Ghanbarian⁵, Fang Yu⁶

Affiliations

¹ Department of Physics, Wright State University, 3640 Colonel Glenn Highway, Dayton, OH 45435, USA.
² Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, CA 90089, USA.
³ Energy Geosciences Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA.
⁴ Department of Geography, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland.
⁵ Porous Media Research Lab, Department of Geology, Kansas State University, Manhattan, KS 66506, USA. Electronic address: ghanbarian@ksu.edu.
⁶ Department of Forestry, Beihua University, 3999 Binjiangdong Road, Jilin 132013, China.

PMID: 36933712
DOI: 10.1016/j.scitotenv.2023.162905

Abstract

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_f of the root system. Values of d_f appear to relate to the relative roles of nutrient and water accessibility. Larger values of d_f 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_f and, therefore, ET that is a smaller fraction of P. The prediction of ET/P using the 3D percolation value of d_f 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.

Keywords: Forests; Grasslands; Percolation theory; Roots; Water balance.