Noise-induced errors in heat pulse-based sap flow measurement methods

Abstract

Heat-pulse (HP) methods based on Marshall’s theory have been widely used in sapflow meters to measure plant water uptake since the 1950s. Some of the popular HP methods include (i) the compensation heat pulse (CHP) method, (ii) the T-max method, and (iii) the heat ratio (HR) method. Most other sap flow methods use some variations of these basic methods. Although all these methods are based on the same theory, in practice, their accuracy varies depending on the estimated HP velocity. Some of the often cited reasons for the differences in the performance of these methods are (i) wound effect, (ii) asymmetrical spacing of temperature probes, (iii) low logging frequency, (iv) sensor resolution, (v) electronic noise, (vi) drift in temperature measurements, etc. However, it is unclear why these error artifacts affect the performance of different methods at different HP velocity ranges. Here, we use mathematical model simulations to show that the presence of noise in temperature measurements constrains the measurable range of HP velocities of these different methods depending on the noise intensity. Using Monte Carlo simulations we quantitatively assess the accuracy of these methods. While typical HP measurements log temperature data every second for about 3 min, most HP methods only use a few data points. We show that when the signal-to-noise ratio (SNR) of these chosen data points is small, the accuracy suffers. By employing a sum of squares error minimization (SSEM) approach that minimizes the errors between observed and model-predicted temperatures using all the observed data points, we show that noise induced errors in sap flow measurement can be virtually eliminated over a range of conditions. Our findings provide a mechanistic understanding of the origins and impacts of the noise-induced errors in sap flow measurements and the mathematical framework to overcome the same.