Development and verification of a water and sugar transport model using measured stem diameter variations

In trees, water and sugars are transported by xylem and phloem conduits which are hydraulically linked. A simultaneous study of both flows is interesting, since they concurrently influence important processes such as stomatal regulation and growth. A few mathematical models have already been developed to investigate the influence of both hydraulically coupled flows. However, none of these models has so far been tested using real measured field data. In the present study, a comprehensive whole-tree model is developed that enables simulation of the stem diameter variations driven by both the water and sugar transport. Stem diameter variations are calculated as volume changes of both the xylem and the phloem tissue. These volume changes are dependent on: (i) water transport according to the cohesion-tension theory; (ii) sugar transport according to the Munch hypothesis; (iii) loading and unloading of sugars; and (iv) irreversible turgor-driven growth. The model considers three main compartments (crown, stem, and roots) and is verified by comparison with actual measured stem diameter variations and xylem sap flow rates. These measurements were performed on a young oak (Quercus robur L.) tree in controlled conditions and on an adult beech (Fagus sylvatica L.) tree in a natural forest. A good agreement was found between simulated and measured data. Hence, the model seemed to be a realistic representation of the processes observed in reality. Furthermore, the model is able to simulate several physiological variables which are relatively difficult to measure: phloem turgor, phloem osmotic pressure, and Munch's counterflow. Simulation of these variables revealed daily dynamics in their behaviour which were mainly induced by transpiration. Some of these dynamics are experimentally confirmed in the literature, while others are not.