[Insert Fig. 5 here]
The applicable range of the HRM depends on the magnitude of error in measured temperature rise (See Fig. S4 ), which in turn depends on the precision of the temperature sensor (σ T) and the amount of heat generated during the heat pulse. The useful range of the HRM could be extended by increasing heat pulse duration.
3.1.3 Sensitivity to the k
Among the four heat pulse methods, the HRM was the most sensitive to uncertainty in k . Calculations of V are directly proportional to k using the HRM. Estimates of V from the DRM are also sensitive to k at low sap velocities (< 20 cm h-1) because V DRM is dominated by V 12 (V HRM, Eqn. 4 ) under such conditions (Fig. 6 ). However, when sap velocity is high, V DRM equalsV 23, which is much less sensitive to k ; this is because V 23 is the sum of two terms, of which only one depends directly on k (Eqn. 6 ). The CHPM is completely insensitive to uncertainty in k , while the Tmax method is strongly influenced by noise at high sap velocities. Usingk as estimated using either Eqn. 13 or Eqn. 14considerably improves the accuracy of the DRM (and HRM) at low sap velocities.