Abstract 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.

中文翻译：

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将 Granier 方法扩展到径向树液流模式的分析方法

摘要 Granier 热耗散 (TD) 方法可能是计算树木蒸腾通量的最常用方法，因为它简单且有效地兼顾了理论和数据可用性。从基于 Granier 方法的传热方程开始，本文的目的是推导出蒸腾通量的解析解，以将树液流方程扩展到径向域。我们采用了一种灵活的方法来处理已知与木材解剖结构（扩散多孔与环状或无孔木质部）相关的径向 sapflow 密度 (SFD) 剖面形状的差异。带着这个目的，我们研究了在文献中可用的一些实验性和可靠的径向 SFD 测量值上开发的方程的稳健性，以测试考虑或不考虑靠近形成层的活动区的影响，其中可能观察到大多数物种特异性差异。此外，由扩展公式得出的参数被解释为描述特定物种的径向树液流动模式。建议程序的可靠性根据文献中的几个实验 SFD 曲线进行了检查：i) 从茎的中心向形成层单调增加 SFD，ii) 从茎的中心增加 SFD，然后向形成层增加 SFD，以及iii) 从茎的中心增加 SFD 到最大 SFD，然后向形成层减少。结果表明，根据建议的程序，需要根据 SFD 剖面复杂性越来越多的参数来综合描述不同树种的蒸腾通量。对于单调递增 SFD 的最简单情况（在扩散多孔树结构条件下可以假设为标准），只需要两个具有明确物理意义的参数。