[Insert Fig. 4 here]
3.1.2 Performance of the heat-pulse based methods
Simulation results with synthetic data (See the generation procedure in SI on Simulations S1 & S2 ) are shown in Fig.5 . Among all four methods, the DRM calculation of V is consistently closest to the true value used to generate the synthetic data, deviating little from the true value for high (0.2% deviation at 80 cm h-1), low (0.5% at 20 cm h-1) and negative sap velocities (1.6% at -10 cm h-1). The coefficient of variation of estimates was also smallest for the DRM (e.g., 2% at 20 cm h-1 and 0.5% at 80 cm h-1). The HRM performs well at negative to low sap velocities (<40 cm h-1) but systematically underestimates true sap velocity when velocity is high. The CHPM only performs well at intermediate sap velocities (20-40 cm h-1), yielding a widely diverging range of estimates when true sap velocities are high, low or negative. The poor performance of the HRM and CHPM at high sap velocities is caused by very small temperature rises at the proximal temperature sensor (δ 1). Calculations that depend onδ 1 become unreliable under such conditions (Fig.S3a ). The CHPM also performs poorly when sap velocity is low because it relies on precise determination of the time whenδ 1=δ 3:δ 3 is small when sap velocity is low, leading to increased error (Fig. S3b ). The Tmax method is based on timing of peak temperature rise and is thus sensitive to noise at relatively low sap velocities (e.g., 35% coefficient of variation at 20 cm h-1).