Integration of sapflow velocity in elliptical stems.

The estimation of water flux through the stem of a plant by point estimates based on the heat pulse technique requires integration of the velocity profile. The polynomial integration method and the weighted average technique both assume radial symmetry about the bole. A method is introduced that solves the equations for the ellipse in the weighted average technique, and includes an optimizing algorithm for the placement of sensors. The sensitivity of sapflow estimates through stems to increasing eccentricity is examined by means of analytical solutions and simulation. The error in sap flux measurement resulting from the radial approximation of the sapwood conducting area is expressed analytically and shown to be small over the range of eccentricities (e < 0.8) expected in nature. Simulations where radial symmetry is assumed for elliptical stems show substantial error in mean velocity (and thus flux) with modest eccentricities (e > 0.4).