Sapflow+: a four-needle heat-pulse sap flow sensor enabling nonempirical sap flux density and water content measurements.

• To our knowledge, to date, no nonempirical method exists to measure reverse, low or high sap flux density. Moreover, existing sap flow methods require destructive wood core measurements to determine sapwood water content, necessary to convert heat velocity to sap flux density, not only damaging the tree, but also neglecting seasonal variability in sapwood water content. • Here, we present a nonempirical heat-pulse-based method and coupled sensor which measure temperature changes around a linear heater in both axial and tangential directions after application of a heat pulse. By fitting the correct heat conduction-convection equation to the measured temperature profiles, the heat velocity and water content of the sapwood can be determined. • An identifiability analysis and validation tests on artificial and real stem segments of European beech (Fagus sylvatica L.) confirm the applicability of the method, leading to accurate determinations of heat velocity, water content and hence sap flux density. • The proposed method enables sap flux density measurements to be made across the entire natural occurring sap flux density range of woody plants. Moreover, the water content during low flows can be determined accurately, enabling a correct conversion from heat velocity to sap flux density without destructive core measurements.