Tranzflo NZ Ltd 
Specialists in Sap Flow Sensors 
Calibration of heatpulse methods 
Tranzflo NZ Ltd, 15 Parata St, Palmerston North 4410, NEW ZEALAND Tel: +6463574600 Fax: +6463574601 Email: stevegreen@inspire.co.nz 
Calculations of V_{Z} and V_{M} assume that the heater and temperature probes have no effect on the measured heat flow. In reality, convection of the heatpulse is disturbed by the presence of the heater and temperature probes, and by the disruption of xylem tissue associated with their placement. These perturbations produce a systematic underestimation in the measured heatpulse velocity (Cohen et al., 1981; Green and Clothier, 1988). Consequently, the heatpulse velocity must be corrected for any probeinduced effects of wounding. This correction can either be done empirically (e.g. Cohen et al., 1981), or it can be based on physical principals, using an equation of the form: , Eq. [7] where V [m s^{1}] is the corrected heatpulse velocity and V_{H} is the raw heatpulse velocity that has been calculated using either Eq. [4] or Eq. [5].
Green et al (2003) presented a set of correction factors to account for the combined influence of sensor thermal properties and the subsequent blockage of sap streams. Our correction factors were computed using a numerical solution to Eq. [2]. The scientific paper can be downloaded by clicking here
The calibration model uses a finite difference form of Eq. 2 that is solved using an alternatingdirectionimplicit scheme in two dimensions (von Rosenberg, 1969). The numerical grid is set at 80.0 by 40.0 mm, with a spatial resolution of 0.1 mm, and the time step is set at 0.1 s. Thermal properties of the sapwood are taken from the data of Siau (1971) and Dunlap (1912), and thermal properties of the sensors are derived from data in Carslaw and Jaeger (1959). A ‘zero flow’ condition is assumed to occur within the wound width that exists in line with the sensors and parallel to the flow direction. The combined effect of stem moisture content, probe placement, and the woundwidth are simulated over a range of sap flows. A set of correction coefficients (ai’s) is then determined from the ratio of the measured heatpulse velocity to that ‘imposed’ across the model flow domain.

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