A dynamic model for water flow in a single tree: evidence that models must account for hydraulic architecture

A model is presented for the dynamics of water flow in a single eastern white cedar tree (Thuja occidentalis L.). The model takes into account the spatial and temporal dependence of the evaporative flux from leaves in the crown. It also accounts for the quantitative hydraulic architecture of the tree, i.e., the model characterizes the tree as a branched catena of > 4000 stem segments in which account is taken of the segment length, diameter, hydraulic resistance, and the total area of leaves attached to the segment. Input values needed to run the model are measurements of evaporative flux, hydraulic conductance of stems versus stem diameter, and leaf and stem water storage capacitances. Output parameters are the spatial and temporal characterization of stem and leaf water potentials, stem and leaf water deficits, sap flow rate, and relative sap velocity. The input and output values of the branched catena model are compared and contrasted to that of an unbranched catena model. It is shown that the branched catena model fits independently measured field parameters better than an unbranched catena model. Close correspondence is found between model predictions and field measurements of shoot water potential, pressure gradients in stems, hysteresis in sap velocity between the lower and upper parts of the tree, and diurnal changes in stem and leaf water deficits. This model is discussed in terms of both the hydraulic architecture of trees and the potential application of the model to questions of tree morphology, ecology, physiology and evolution.