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

Abstract

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. Stand transpiration (E) estimated using sap flux methods includes uncertainty induced by azimuthal variations and between-tree variations in sap flux density (F). 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. 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. 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. 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.