Scaling theory to extrapolate individual tree water use to stand water use

Extrapolation of measurements of water use by individual trees to that for a stand of trees is a critical step in linking plant physiology and hydrology. Limitations in sampling resources and variation in tree sizes within a stand necessitate the use of some scaling relationship. Further, to scale tree water use in space as well as time, the relationship must reflect the changing availabilities of energy and water supply. It is argued here that tree leaf area is the most appropriate covariate of water use to achieve this aim. However, empirical results show that the relationship is not always linear. A theory is developed, based on the concepts of hydrological equilibrium (sensu Nemani and Running, 1989) and ecological field theory (Walker et al., 1989) which accounts for (occasional) non-linear behaviour of the flux/ leaf area relationship in evergreen trees. A key feature of this theory is the notion of a non-linear, quasi-equilibrium reflecting plant water stress. An equation is derived from these concepts and a standard, explicit treatment of tree water use (Landsberg and McMurtrie, 1984), which is used to characterise this relationship. This equation has the form Q = aIA + bΨsAf. The theory is tested against field data and published reports on Eucalyptus tree water use.