Simulation of water flow in the branched tree architecture.

Abstract

The model HYDRA, which simulates water flow in the branched tree architecture, is characterized. Empirical studies of the last decades give strong evidence for a close structure-function linkage in the case of tree water flow. Like stomatal regulation, spatial patterns of leaf specific conductivity can be regarded as a strategy counteracting conductivity losses which may arise under drought. Branching-oriented water flow simulation may help to understand how damaging and compensating mechanisms interact within the hydraulic network of trees. Furthermore, a coupling of hydraulic to morphological modelling is a prerequisite if water flow shall be linked to other processes. Basic assumptions of the tree water flow model HYDRA are mass conservation, Darcy’s law and the spatial homogeneity of capacitance and axial conductivity. Soil water potential is given as a one-sided border condition. Water flow is driven by transpiration. For unbranched regions these principles are condensed to a nonlinear diffusion equation, which serves as a continuous reference for the discrete method tailored to the specific features of the hydraulic network. The mathematical derivation and model tests indicate that the realization of the basic assumptions is reproducible and sufficiently exact. Moreover, structure and function are coupled in a flexible and computationally efficient manner. Thus, HYDRA may serve as a tool for the comparative study of different tree architectures in terms of hydraulic function.