A statistical method for estimating wood thermal diffusivity and probe geometry using in situ heat response curves from sap flow measurements

The heat pulse method is widely used to measure water flux through plants; it works by using the speed at which a heat pulse is propagated through the system to infer the velocity of water through a porous medium. No systematic, non-destructive calibration procedure exists to determine the site-specific parameters necessary for calculating sap velocity, e.g., wood thermal diffusivity and probe spacing. Such parameter calibration is crucial to obtain the correct transpiration flux density from the sap flow measurements at the plant scale and subsequently to upscale tree-level water fluxes to canopy and landscape scales. The purpose of this study is to present a statistical framework for sampling and simultaneously estimating the tree's thermal diffusivity and probe spacing from in situ heat response curves collected by the implanted probes of a heat ratio measurement device. Conditioned on the time traces of wood temperature following a heat pulse, the parameters are inferred using a Bayesian inversion technique, based on the Markov chain Monte Carlo sampling method. The primary advantage of the proposed methodology is that it does not require knowledge of probe spacing or any further intrusive sampling of sapwood. The Bayesian framework also enables direct quantification of uncertainty in estimated sap flow velocity. Experiments using synthetic data show that repeated tests using the same apparatus are essential for obtaining reliable and accurate solutions. When applied to field conditions, these tests can be obtained in different seasons and can be automated using the existing data logging system. Empirical factors are introduced to account for the influence of non-ideal probe geometry on the estimation of heat pulse velocity, and are estimated in this study as well. The proposed methodology may be tested for its applicability to realistic field conditions, with an ultimate goal of calibrating heat ratio sap flow systems in practical applications.