Zijuan Deng1*
Heather Vice3
Matthew E Gilbert3
Mark A Adams2
Thomas N Buckley3*
1Centre for Carbon, Water and Food, the University of Sydney; Current: College of Science and Engineering, Flinders University, Australia
2School of Science, Faculty of Science, Engineering & Technology, Swinburne University of Technology, Australia
3Department of Plant Sciences, University of California, Davis, CA, United States
*Corresponding authors:
Zijuan Deng
zijuan.deng@flinders.edu.au/rosedeng0810@gmail.com
*These authors contributed equally to this work.
Abstract
Sap velocity measurements are useful in fields ranging from plant water relations to hydrology at a range of scales. Heat-pulse based techniques are among the most common methods to measure sap velocity, but most lack the ability to measure velocities across a wide range, including very high, very low and negative velocities (reverse flow). We propose a new method, the double-ratio method (DRM), which is robust across an unprecedented range of sap velocities and can provide real-time estimates of the thermal diffusivity of wood. The DRM employs one temperature sensor proximal and two distal to the heat pulse probe and facilitates several theoretical, heat-based approaches to quantifying sap velocity. We tested the DRM using whole-tree lysimetry inEucalyptus cypellocarpa and found strong agreement across a wide range of velocities.
Keywords:
Sap flow, sap flux, sap velocity, heat-pulse based technique,Eucalyptus cypellocarpa , thermal diffusivity, double-ratio method
1 Introduction
Sap velocity measurements using heat-tracing techniques have been important means for studying plant water relations from whole-plant to catchment scale in the tree physiology, forestry and hydrology communities (Thomas N. Buckley, Turnbull, Pfautsch, & Adams, 2011; Thomas N Buckley, Turnbull, Pfautsch, Gharun, & Adams, 2012; Cermak, Kucera, Bauerle, Phillips, & Hinckley, 2007; Steppe, Vandegehuchte, Tognetti, & Mencuccini, 2015; Wilson, Hanson, Mulholland, Baldocchi, & Wullschleger, 2001). There are many heat-dissipation-based methods, but all have one or more weaknesses. Constant-power or Granier style probes (Granier, 1985) are inexpensive and robust but require empirical calibration (Clearwater, Meinzer, Andrade, Goldstein, & Holbrook, 1999), consume large amounts of electrical power and cannot accurately measure small or negative sap velocities. Heat-pulse based methods such as the Tmax method (Cohen, Fuchs, & Green, 1981), compensation heat pulse method (CHPM) (SR Green & Clothier, 1988), heat field deformation method (HFD) (Nadezhdina, Cermak, & Nadezhdin, 1998), heat ratio method (HRM) (Burgess et al., 2001), and Sapflow+ method (Vandegehuchte & Steppe, 2012c) use little power and are traceable to first principles, but also have critical limitations. Tmax, CHPM and HFD cannot measure low or negative velocities (Steve Green, Clothier, & Jardine, 2003; Vandegehuchte & Steppe, 2012c); Sapflow+ suffers from difficulty in model identification; and the HRM fails at high sap velocities (Bleby, McElrone, & Burgess, 2008; Flo, Martinez-Vilalta, Steppe, Schuldt, & Poyatos, 2019; Pearsall, Williams, Castorani, Bleby, & McElrone, 2014).
In most heat pulse-based methods, sapwood thermal diffusivity, k , is a crucial parameter in calculation of the sap velocity (López-Bernal, Alcántara, & Villalobos, 2014; Vandegehuchte & Steppe, 2012a). An arbitrary value of k is usually set or obtained from empirical function related to sapwood moisture content (mc ) (Burgess et al., 2001; Marshall, 1958; Vandegehuchte & Steppe, 2012a). Howeverk is seemingly not constant, and can change over seasons (Burgess et al., 2001; Chen, Miller, Rubin, & Baldocchi, 2012) or even diurnally (López-Bernal et al., 2014), with uncertain consequences for the accuracy of calculated sap velocity. Velocity estimates from the Tmax method depend only on k and known parameters. Therefore if sap velocity is known to be zero, such as at night time after prolonged wet conditions, k can be directly inferred and then treated as a constant until such a time that it can be re-measured (Burgess et al., 2001). Inverse modelling has also been used to calibrate k (Chen et al., 2012; Vandegehuchte & Steppe, 2012a), notwithstanding measurement uncertainties and issues with probe alignment. For example, empirical functions to infer k from sapwood properties andmc could be validated at low sap velocities under 20 cm h-1 (Vandegehuchte & Steppe, 2012b), however, such procedures require knowledge of mc , which may vary diurnally (López-Bernal et al., 2014). k has never been estimated in vivo , in real time, at higher sap velocities.
Pearsall et al. (2014) proposed a method for extending the range of sap velocities that can be reliably measured using heat pulse approaches. They combined the HRM and CHPM, using the HRM to detect small and negative sap velocities and the CHPM to detect high sap velocities. One limitation of that approach is the lack of a non-arbitrary method to selecting whether to use the HRM- or CHPM-derived estimate of sap velocity at any given time. Another concern is that this approach alternates between two very different measurement approaches: an average over time of sap velocity estimated from the ratio of temperature rises in two sensors (HRM), or an inference based on estimation of the single instant at which two temperature rises are equal (CHPM). Thus, research communities that rely on sap velocity measurements lack a single method that is at once energy-efficient, objective, robust and capable of measuring negative, low and high sap velocities with a single measurement principle.
We developed a new and efficient algorithm, the double-ratio method (DRM), that combines many of the strengths of existing methods and is robust across an unprecedented range of sap velocities, from moderate negative velocities to very large positive velocities. The DRM is an extension of the HRM in which an additional temperature sensor (Probe #3) is installed distal to both temperature sensors used in the HRM. The DRM estimates sap velocity based on the same principles as the HRM – namely, by calculating the ratios of heat pulse-induced temperature rises measured in different probes. Two different velocity estimates are produced – one based on Probe #2 and #1 and another based on Probe #3 and #2 – and the value with the lesser intrinsic uncertainty (which is calculated based on temperature rises and probe positions) is retained. Furthermore, the presence of a third sensor also enables CHPM estimates of flow, which can be combined with DRM-based estimates to allow real time estimation of k under high-velocity conditions. We tested the DRM experimentally using weighing lysimeters and examined its capability by numerical modelling. We discuss the strengths and weaknesses of the DRM in relation to other commonly used heat-pulse based techniques.
2 Materials and Methods
2.1 Theory
2.1.1 Background: heat pulse theory and the HRM
Marshall (1958) showed that an instantaneous heat pulse at time t= 0 causes an increase in temperature (δ i) at both axial (x i) and azimuthal (y i) positions relative to the heater at timet (s), with negative and positive x ivalues indicating positions proximal and distal to the heater, respectively: