Does measuring azimuthal variations in sap flux lead to more reliable stand transpiration estimates?

Stand transpiration (E) estimated using the sap-flux method includes uncertainty induced by variations in sap flux (F) within a tree (i.e. radial and azimuthal variations) and those between trees. Unlike radial variations, azimuthal variations are not particularly systematic (i.e. higher/lower F is not always recorded for a specific direction). Here, we present a theoretical framework to address the question on how to allocate a limited number of sensors to minimize uncertainty in E estimates. Specifically, we compare uncertainty in E estimates for two cases: (1) measuring F for two or more directions to cover azimuthal variations in F and (2) measuring F for one direction to cover between-tree variations in F. The framework formulates the variation in the probability density function for E (σ_E) based on F recorded in m different azimuthal directions (e.g. north, east, south and west). This formula allows us to determine the m value that minimizes σ_E. This study applied the framework to F data recorded for a 55-year-old Cryptomeria japonica stand. σ_Efor m = 1 was found to be less than the values for m = 2, 3 and 4. Our results suggest that measuring F for one azimuthal direction provides more reliable E estimates than measuring F for two or more azimuthal directions for this stand, given a limited number of sensors. Application of this framework to other datasets helps us decide how to allocate sensors most effectively.