Optimal sap flux sensor allocation for stand transpiration estimates: a non-dimensional analysis

Key message: Measuring between-tree variations in sap flux density rather than azimuthal variations should be prioritized for reliable stand transpiration estimates based on sap flux methods. Context: Stand transpiration (E) estimated using sap flux methods includes uncertainty induced by azimuthal variations and between-tree variations in sap flux density (F). Aims: This study examines whether or not measuring F for two or more azimuthal directions to cover azimuthal variations in F leads to more reliable E estimates. This examination was done under the assumption that azimuthal and between-tree variations in F are not systematic and when a limited number of sensors are available. Methods: We first non-dimensionalized the theoretical framework established by a previous study and developed a general hypothesis. We then validated the hypothesis quantitatively by numerical experiments. Results: The non-dimensionalized theory allowed us to hypothesize that measuring F for one azimuthal direction would reduce uncertainty in E estimates more effectively than measuring F for two or more azimuthal directions. Results of the numerical experiments were found to support this hypothesis. Conclusion: When the aforementioned assumptions are satisfied, allocating sensors to measure F for one azimuthal direction to cover between-tree variations in F always leads to more reliable E estimates.