Heat Field Deformation (HFD) vs Linear Heat Balance (LHB):  A critical comparison of two sap flow methods based on the same instrumentation

<p>As a way to estimate evapotranspiration (ET), Heat Field Deformation (HFD) is a widely used method to measure sap flow of trees based on empirical relationships between heat transfer within tree stems and the sap flow rates. As an alternative, the Linear Heat Balance (LHB) method implements the same instrumental configuration as HFD but calculates the sap flow rates using analytical equations that are derived from fundamental conduction-convection heat transfer equations. In this study, we systematically compared the sap flow calculated using the two methods from four Norway spruce trees. We aimed to evaluate the discrepancies between the sap flow estimates from the two methods and determine the underlying causes. Diurnal and day-to-day patterns were consistent between the sap flow estimates from the two methods. However, the magnitudes of the estimated sap flow were different, where LHB resulted in much lower estimates in three trees and slightly higher estimates in one tree compared to HFD. We also observed larger discrepancies in negative (downward) than in positive (upward) sap flow, where the LHB resulted in lower reversed flow than HFD. Consequently, the seasonal budget estimated by LHB can be as low as ~20% of that estimated by HFD. The discrepancies can be mainly attributed to the low wood thermal conductivities for the studied trees that lead to substantial underestimations using the LHB method. In addition, the sap flow estimates were very sensitive to the value changes of the empirical parameters in the calculations and, thus, using a proper case-specific value is recommended, especially for the LHB method. Overall, we suggest that, despite the strong theoretical support, the correctness of LHB outputs depends largely on the tree individuals and should be carefully evaluated.&#160;</p>