Analytical approach extending the Granier method to radial sap flow patterns

The Granier thermal dissipation (TD) method is probably the most applied method to compute the transpiration flux of trees, due to its simplicity and effective compromise between theory and data availability. Starting from the heat transfer equations at the basis of Granier’s method, the objective of this paper is to derive an analytical solution for the transpiration flux to extend the sap flow equations to the radial domain. We adopted a flexible approach to cope with the differences in radial sapflow density (SFD) profile shapes that are known to occur in relation to wood anatomy (diffuse porous vs. ring- or non-porous xylem). With this purpose, we investigated the robustness of the equations developed on some experimental and reliable radial SFD measurements available in literature to test the influence of considering or not considering the active zone close to the cambium, where most of the species-specific differences are likely to be observed. Moreover, the parameters derived by the extended formulation, are interpreted as descriptive of species-specific radial sap flow patterns. The reliability of the suggested procedure was checked against several experimental SFD profiles from literature: i) monotonically increasing SFD from the centre of the stem towards the cambium, ii) increasing SFD from the centre of the stem and then constant SFD towards the cambium, and iii) increasing SFD from the centre of the stem to a maximum SFD and then decreasing towards the cambium. Results show that according to the suggested procedure, an increasing number of parameters depending on the SFD profile complexity are required to synthetically describe the transpiration flux of different tree species. For the simplest case of monotonically increasing SFD, which could be assumed as standard under conditions of a diffuse porous tree structure, only two parameters with a clear physical meaning are required