Improved theory for calculating sap flow with the heat pulse method

Sap flow rate in the xylem of plant stems can be estimated by measuring the velocity of a pulse of heat introduced into the stem. In the method suggested by Cohen et al. [Plant Cell Environ. 4 (1981) 391], the heat pulse is introduced with a line heat source, inserted radially into the stem or trunk. A temperature probe, positioned downstream from the line heat source, is used to measure the travel time of the heat pulse at various depths within the xylem. The sap flow sensor commercially available from Thermal Logic (Pullman, WA) can be used to implement this method, but it uses a heating duration about 10 times longer than that employed by Cohen et al. [Plant Cell Environ. 4 (1981) 391]. The longer heater duration violates the instantaneous heat input assumption of the model used by Cohen et al. [Plant Cell Environ. 4 (1981) 391] to estimate travel time of the heat pulse. In this paper, we present theory for estimating sap flow rate that explicitly accounts for the finite time duration of the heat input. The pulsed heating theory is used to quantify the error in sap flow rate that results from applying the instantaneous heating model to experimental results obtained with non-instantaneous heat inputs. For the relatively small heating duration (0.25–1.5 s) and relatively large probe spacing (0.015 m) used by Cohen et al. [Plant Cell Environ. 4 (1981) 391], the error in estimates of sap flow rate will rarely exceed 1%. For the relatively large heating duration (8 s) and relatively small probe spacing (0.006 m) of the Thermal Logic sensor, error in estimates of sap flow rate may exceed 20%.