The analysis of physical background of tree sap flow measurement based on thermal methods

The underlying physics of three specific thermal methods to measure tree sap flow was investigated. All these methods utilize local heating and measure heat dissipation caused by moving water. The application of heating was specific for each of the methods tested, herewith distinguishing the following alternatives: (1) thin needle perpendicular to stem surface, (2) rectangular plate directed vertically towards stem axis and (3) constrained volume. For all alternatives, sap flow volume can basically be estimated from the observed temperature change and applied energy. The original equations applicable for some of these methods were derived either empirically (Granier 1985 Ann. For. Sci. 42 193-200) or from simplified heat balance equations (Cermak et al 1973 Biol. Plant. 15 171-8). The aim of this study was to rigorously verify these particular methods by a detailed physical analysis, using a numerical solution of the heat conductivity equation in a three-dimensional coordinate system. The analysis showed that the dependence of sap flow on wood temperature in a certain point inside the heated domain could be satisfactorily approximated (r(2) >= 0.99) by specific curves of hyperbolic type for all three considered configurations of heating. However, the sensitivity of this dependence to uncertainty factors (wood heat conductivity, non-homogeneity of sap flow radial profile and external temperature gradients) was strongly affected by the size of the heated domain. In general, the sensitivity of the temperature field in wood to all uncertainty factors decreased with increasing volume of the heated domain. Thus, the sap flow sensor based on needle heating was most sensitive to uncertainty factors, whereas the volume heating showed a relatively stable temperature field. The simple heat balance model applied for the restricted volume approach (Kucera et al 1977 Biol. Plant. (Praha) 19 413-20) proved to be a satisfactory approximation for the volume heating method.