How many sap flow sensors and wood cores are required to accurately measure the sap flux of one tree?

Transpiration flux estimations for individual trees usually rely on point-information obtained from a limited number of sap flow sensors and wood core samples. The underlying assumption is that sap flux densities and wood properties are sufficiently homogeneous within one tree and well represented by a few sensor measurements and wood samples. If this assumption is justified or not, however, has rarely been experimentally tested and quantitatively evaluated. Our objective was to quantify the variability of individual sap flux measurements within one tree and to answer the question how the observed uncertainty could most effectively be reduced.

We installed 23 sap flow sensors into, and took 30 wood core samples from one specimen of Pinus sylvestris. Eventually, we obtained six stem cross sections from the same tree. This extensive sampling allowed us to asses the within-tree variability of sap flow velocities, wood densities and sapwood depths. Based on our various measurements, we applied a boot-strapping scheme to quantify the uncertainty of tree level transpiration flux estimates that would result from different numbers of installed sap flow sensors and extracted wood cores.

Our results indicate that the temporal courses of sap flux densities within our studied tree were highly correlated to each other (R² >= 0.98), but their absolute values varied considerably (coefficient of variation (CV) of 11.3% and 26.6% for outer and inner measurement depths, respectively) without showing a remarkable spatial pattern. Wood densities were the least variable parameter (CV of 2.5%), while the uncertainty of the conducting sapwood area varied across six stem cross sections (CVs between 8% and 14%).

We conclude, that the within-tree variability of sap flux densities and sapwood areas – even for a tree stem without any remarkable anomalies – can quickly lead to considerable errors of sap flux estimates. In our case, the heterogeneity of sap flux densities (especially within the inner sapwood) was so high, that it dominated the overall uncertainty. Consequently, the most effective way to reduce the uncertainty of our sap flux estimates was to increase the number of installed sap flow sensors, while additional wood core information only started to pay off in conjunction with higher numbers (≥4) of installed sap flow sensors. A reduction of the overall sap flux uncertainty (CV of 16 % for one sap flow sensor and one wood core) to a CV around 5% would have required at least seven sap flow sensors combined with information of eight wood cores, but could as well have been achieved with ten sap flow sensors combined with the information of two wood cores.