A dynamic model for studying flow of water in single trees

Flow of water in a single tree was modeled in terms of the Darcy equation using a catena of four compartments: root, stem (further divided into discs), branches and leaves. Within each compartment or disc, water content was related to both water potential and conductivity of the xylem tissue using power or logarithmic functions, thus introducing both capacitance and variable resistance to flow in the model. Transpiration from the leaves to the atmosphere was used as the upper boundary to the model, and the soil-root interface as the lower boundary. Parameters for the water content, water potential and conductivity functions, together with physical dimensions were obtained by direct measurement or from the literature. A sensitivity analysis showed that the largest changes in simulated water potential and flow were associated with changes in the parameters directly controlling conductivity. Simulation of both smoothed diurnal changes and stepwise changes showed a phase lag down the tree, with flow tending to approach a steady state, but with changes in the gradients of water potential, water content and conductivity. A preliminary test of the model was made against field data using the Penman-Monteith equation to estimate the transpiration rate in a well-watered Pinus contorta Dougl. stand. Stem flow, water potential and water content were measured directly on a representative tree, which was subsequently harvested to provide dimensions and laboratory estimations of the parameters in the functions by direct measurement.