Parameterizing a model of Douglas fir water flow using a tracheid-level model

The theory of tree water flow proposed in Aumann & Ford (submitted) is assessed by numerically solving the model developed from this theory under a variety of functional parameterizations. The unknown functions in this nonlinear partial differential equation model are determined using a tracheid-level model of water flow in a block of Douglas fir tracheids. The processes of flow, cavitation, pit aspiration/deaspiration, flow through the cell wall and ray exudation in a block of approximately 79 000 tracheids are modeled. Output from the tracheid model facilitates determination of the hydraulic conductivities in the sapwood as a function of saturation and interfacial area between liquid and gaseous phases of water, the function governing the rate of change in saturation, and the function governing the rate of change in interfacial area. The models show complementary things. The tracheid model shows that capacitance, or the change in saturation per change in pressure, is not constant. When all refilling is stopped, it takes over 180 days for the hydraulic conductivity in the vertical direction to reach 1/4 of its maximal value, showing the robustness of the transpiration stream for conducting water. The shape of the functions determined with the tracheid model change with different tracheid-level assumptions. When these functions are used in the differential equation model, it is shown that cell-wall conductivity plays an important part in the lag in flow observed in many conifers. The flow velocities and rates of change in saturation predicted by the differential equation model agree with those measured in Douglas fir. Both models support the theory of tree water flow presented in Aumann & Ford (submitted) and undermine the theory that water flow in trees is analogous to the flow of current in electric circuits.