where n t is the number of time steps in the averaging window and σ DRM is the lesser ofσ 12 and σ 23 at each point in time. An efficient algorithm to minimize SEDRM is to locate the moment of minimum σ DRM, compute the SEDRM for time windows of varying width around the moment and choose the width that gives the smallest SEDRM. We tested a variety of values forn t.
Note that all equations were derived from Marshall’s (1958) model (Eqn.1 ) under the assumption of an instantaneous heat pulse, whereas in reality the heat pulse occurs has a finite pulse length oft 0. We corrected for this by shifting each temperature timecourse by -t 0/2 before applying Eqn. 1 . The effect of this treatment is shown in Supporting Information (SI) Notes S1 and Fig. S1 .
2.2 Theoretical test of the DRM, HRM, CHPM and Tmax methods
2.2.1 Comparison of heat-pulse based methods
To assess the theoretical viability of the DRM in comparison to other heat pulse methods, and to help optimize operational considerations such as the size and timing of averaging window(s), we used Eqn. 1to simulate timecourses of temperature following a heat pulse. We compared the predicted values of V DRM (Eqn.7 ) with V HRM (Eqn. 4 ), and also with two other estimates of V , based, respectively, on the CHPM (SR Green & Clothier, 1988) and the Tmax method (Cohen et al., 1981) as modified by Kluitenberg and Ham (2004). In the CHPM, sap velocity is calculated at the time point (t C(1,3)) when the temperature rises for Probe #1 and #3 are equal, so that the ratio of temperature rises is unity and the logarithmic term in Eqn. 4disappears, giving sap velocity as