The Hydraulic System of Trees: Theoretical Framework and Numerical Simulation

Empirical studies pose the problem of the physiological integration of the tree organism, which is also important on the scale of ecosystems. Recently, spatially distributed models emerged, which approach this problem by reflecting the close linkage between physiological processes and the structures of trees and tree stands. In the case of water flow, the tree organism can be regarded as hydraulic system and the branched tree architecture as hydraulic network. Previous models of the hydraulic system either did not take into account the network structure, or they had shortcomings regarding the translation of the underlying physiological assumptions by the discrete computation method. We have developed a theoretical framework which takes the form of a numerical simulation model of tree water flow. A discrete initial boundary value problem (IBVP) combines the phenomena of Darcy flow, water storage and conductivity losses in the hydraulic network. The software HYDRA computes the solution of the IBVP. The theoretical derivation and model tests corroborate the consistent translation of the physiological assumptions by the computational method. Simulation studies enabled us to formulate hypotheses on the following points: (1) differences in the hydraulic segmentation between Picea abies and Thuja occidentalis, (2) responses of the hydraulic system to rapid transpiration changes and to a scenario of drought stress, and (3) how these responses depend on architectural quantities of the trees. The simulation studies demonstrated our possibilities of deriving theoretically well-founded hypotheses about the functioning of the hydraulic system and its relation to system structure. The numerical simulation model is designed as a tool for structure–function studies, which is able to treat tree architecture as independent variable. The model supports the integration of data on tree level, and it can be used for computer experiments which quantify the dynamics of the hydraulic system according to the concepts of system theory.