Incorporation of transfer resistance between tracheary elements into hydraulic resistance models for tapered conduits

The model of West, Brown and Enquist (1999) shows that hydraulic resistance in trees can be independent of path length, provided that vascular conduits widen sufficiently from tree top to base. We demonstrate that this result does not depend theoretically on branching architecture or cross-sectional conductive area of the stem. Previous studies have shown that pit membrane resistance, encountered when water moves between either tracheids or vessels, accounts for up to 60% of the total resistance in stem segments. When pit membrane resistance, which is neglected by most whole-tree hydraulic models, was incorporated in hydraulic models in three different ways, the near invariance of hydraulic resistance was preserved. If relative pit resistance was independent of tracheid size or if tracheid dimensions were scaled to minimize wood resistivity, the minimum conduit taper required for path length independence equaled that in the original model of West et al. (1999). Under the most realistic model, in which relative pit resistance increased with tracheid radius, this value was doubled. Such taper is not possible within the typical size range of tracheids over the entire length of moderately tall trees, but it might be possible for vessel-bearing trees. Preliminary results indicated that although tracheid radius in the outer growth ring initially increased basipetally from the top of an 18-m tall Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco), it stabilized at mid-trunk. Also, conduit taper was not constant in this species, violating a key assumption of the model of West et al. (1999), on which the invariance of hydraulic resistance depends.