Interpreting the Heat Field Deformation method: Erroneous use of thermal diffusivity and improved correlation between temperature ratio and sap flux density

Abstract

The Heat Field Deformation (HFD) method is a modern technique to assess sap flux density in trees by applying an equation which relates an empirical temperature ratio to the thermal diffusivity of the sapwood. However, this relation is based on a misinterpretation of thermal diffusivity, leading to physically incorrect units of sap flux density. Moreover, the HFD method has recently been shown to occasionally underestimate actual sap flux densities, raising the question whether species specific calibration is necessary. This paper calls attention to a correct interpretation of thermal diffusivity and investigates the correlation between sap flux density and the HFD temperature ratio based on a 3D Finite Element Model. It is shown that the original terms linking the HFD temperature ratio to sap flux density do not follow fundamental thermodynamics and, therefore, the HFD method should be considered merely empirical. Besides, the method is not only dependent on sapwood characteristics but also on sap flux density itself, necessitating a specific calibration equation.