Modeling the partitioning of evapotranspiration using invasion percolation theory

The partitioning between soil evaporation and transpiration from plants is an important process of water and carbon cycles and surface energy balance. Its quantification is prone to errors because of the complexity of flow geometry, which is affected by the variation of root length density over depth and time and the dynamics of soil hydraulic properties in the rhizosphere. Root water uptake and concurrent evaporation depend on the forces (capillarity, gravity, and viscous losses) controlling water flow and propagation of the drying front. We simulate the water flow from the soil to the atmosphere using invasion percolation models, draining elements as a function of the retaining forces depending on the lengths of the potential flow paths. The partitioning between evaporation and transpiration is simulated for different pore size distributions, root length densities, and vegetation covers controlling the transpiring area. Starting with a three dimensional percolation model (to reproduce the connectivity of the liquid phase) at the column scale consisting of elements in the submillimeter range, we deduce one-dimensional partitioning rules for wet and dry soils. As an outlook, we discuss how these rules can be (i) implemented in large scale models and (ii) tested by measuring vapor fluxes above and below canopy.