Water and solute flows in the coupled system of xylem and phloem were modeled together with predictions for xylem and whole stem diameter changes. With the model we could produce water circulation between xylem and phloem as presented by the Münch hypothesis. Viscosity was modeled as an explicit function of solute concentration and this was found to vary the resistance of the phloem sap flow by many orders of magnitude in the possible physiological range of sap concentrations. Also, the sensitivity of the predicted phloem translocation to changes in the boundary conditions and parameters such as sugar loading, transpiration, and hydraulic conductivity were studied. The system was found to be quite sensitive to the sugar-loading rate, as too high sugar concentration, (approximately 7 MPa) would cause phloem translocation to be irreversibly hindered and soon totally blocked due to accumulation of sugar at the top of the phloem and the consequent rise in the viscosity of the phloem sap. Too low sugar loading rate, on the other hand, would not induce a sufficient axial water pressure gradient. The model also revealed the existence of Münch "counter flow", i.e., xylem water flow in the absence of transpiration resulting from water circulation between the xylem and phloem. Modeled diameter changes of the stem were found to be compatible with actual stem diameter measurements from earlier studies. The diurnal diameter variation of the whole stem was approximately 0.1 mm of which the xylem constituted approximately one-third.T. Hölttä ( ) · T. Vesala · S. Sevanto

ABSTRACT

A dynamic model for simulating water flow in a Scots pine (Pinus sylvestris L.) tree was developed. The model is based on the cohesion theory and the assumption that fluctuating water tension driven by transpiration, together with the elasticity of wood tissue, causes variations in the diameter of a tree stem and branches. The change in xylem diameter can be linked to water tension in accordance with Hookeâ s law. The model was tested against field measurements of the diurnal xylem diameter change at different heights in a 37-year-old Scots pine at Hyytiälä, southern Finland (61 degrees 51' N, 24 degrees 17' E, 181 m a.s.l.). Shoot transpiration and soil water potential were input data for the model. The biomechanical and hydraulic properties of wood and fine root hydraulic conductance were estimated from simulated and measured stem diameter changes during the course of 1 day. The estimated parameters attained values similar to literature values. The ratios of estimated parameters to literature values ranged from 0.5 to 0.9. The model predictions (stem diameters at several heights) were in close agreement with the measurements for a period of 6 days. The time lag between changes in transpiration rate and in sap flow rate at the base of the tree was about half an hour. The analysis showed that 40% of the resistance between the soil and the top of the tree was located in the rhizosphere. Modeling the water tension gradient and consequent woody diameter changes offer a convenient means of studying the link between wood hydraulic conductivity and control of transpiration.

The effect of drought on forest water use is often estimated with models, but comprehensive models require many parameters, and simple models may not be sufficiently flexible. Many tree species, Pinus species in particular, have been shown to maintain a constant minimum leaf water potential above the critical threshold for xylem embolism during drought. In such cases, prediction of the relative decline in daily maximum transpiration rate with decreasing soil water content is relatively straightforward. We constructed a soil-plant water flow model assuming constant plant conductance and daily minimum leaf water potential, but variable conductance from soil to root. We tested this model against independent data from two sites: automatic shoot chamber data and sap flow measurements from a boreal Scots pine (Pinus sylvestris L.) stand; and sap flow measurements from a maritime pine (Pinus pinaster Ait.) stand. To focus on soil limitations to water uptake, we expressed daily maximum transpiration rate relative to the rate that would be obtained in wet soil with similar environmental variables. The comparison was successful, although the maritime pine stand showed carry-over effects of the drought that we could not explain. For the boreal Scots pine stand, daily maximum transpiration was best predicted by water content of soil deeper than 5 cm. A sensitivity analysis revealed that model predictions were relatively insensitive to the minimum leaf water potential, which can be accounted for by the importance of soil resistance of drying soil. We conclude that a model with constant plant conductance and minimum leaf water potential can accurately predict the decline in daily maximum transpiration rate during drought for these two pine stands, and that including further detail about plant compartments would add little predictive power, except in predicting recovery from severe drought.

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