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Accurate measurements of sap flux density and stem water content are of major importance in understanding and quantifying plant–water relations, and hence in hydrological and climatological studies, ecosystem research, irrigation practices, colonization by fungi and insects, plant growth, fertilization, stress monitoring and forestry. At present, the sap flux density and stem water content can be measured simultaneously by magnetic resonance imaging (Van As et al., 2009), but this laboratory technique is expensive, necessitates specific tuning for different flow ranges and remains difficult to apply in the field despite recent progress (Jones et al., 2012). Although many methods have been developed to determine the sap flux density or stem water content separately, to our knowledge, no practically applicable method exists which combines both.
From thermodynamics, it is known that heat dispersion in sapwood is dependent on the specific heat capacity and thermal conductivity of the sapwood, which are both influenced by the stem water content and sap flux density. Therefore, since the first application of heat as a tracer in sapwood (Huber, 1932), many methods based on thermodynamic principles have been developed to determine the sap flux density (Marshall, 1958; Cohen et al., 1981; Swanson & Whitfield, 1981; Swanson, 1983; Granier, 1985; Nadezhdina et al., 1998; Burgess et al., 2001; Green et al., 2003; Clearwater et al., 2009; Testi & Villalobos, 2009). For these methods, a distinction can be made between those which continuously heat the sapwood and empirically link a measured temperature ratio to the sap flux density, and those which apply heat pulses to determine the heat velocity, based on the isotropic heat conduction–convection equation as mentioned in Marshall (1958), and necessitate a measurement of the water content to convert the heat velocity to the sap flux density.
Although each of these methods has its merits in sap flow research, they all have their specific limitations. For those applying heat continuously, the heat field deformation (HFD) method (Nadezhdina et al., 1998, 2012) and thermal dissipation probe (TDP) (Granier, 1985) are most often employed. Although the HFD method enables sap flux density measurements to be made at different depths in the sapwood and is capable of distinguishing high, low and reverse flows, it remains empirical and can lead to over- or underestimations depending on the sap flux density, water content and thermal characteristics of the wood (Vandegehuchte & Steppe, 2012b). The TDP method suffers from these same limitations and is known to largely underestimate the sap flux density (Steppe et al., 2010).
For the heat-pulse methods, the compensation heat-pulse method (CHPM) has the advantage that the thermal diffusivity does not need to be determined. However, it is incapable of determining low and reverse flows (Becker, 1998; Green et al., 2009; Steppe et al., 2010). This was partly resolved by Testi & Villalobos (2009), who used the average temperature gradient (calibrated average gradient method), extending measurement possibilities towards the lower sap flow range. This method, however, necessitates an empirical calibration which is dependent on the thermal characteristics of the sapwood. The heat ratio method (HRM) (Burgess et al., 2001) can measure both low and reverse flows, but performs poorly at high flow rates (Burgess & Dawson, 2008), and applies an inaccurate protocol to determine the thermal diffusivity, necessary as an input parameter for sap flux density calculations (Vandegehuchte & Steppe, 2012a). The Tmax method (Cohen et al., 1981) determines the thermal diffusivity correctly, but is based on a single point analysis and is hence susceptible to scatter. Moreover, like CHPM, it is unable to correctly estimate low and reverse flows (Green et al., 2009). For all these heat-pulse methods, the measurement and heater needles are inserted in the sapwood. This invasive character of the sensors creates a sapwood zone in which flow is interrupted, the so-called ‘wound effect’. This effect leads to an underestimation of the calculated heat velocity which can be corrected for by determining a wound correction equation based on thermodynamic modelling of the heat transport in the sapwood (Swanson & Whitfield, 1981).
As heat-pulse methods determine the heat velocity, a knowledge of the water content and dry wood density is necessary to obtain the sap flux density:
- (Eqn 1)
(qs, sap flux density (m3 m−2 s−1); Vh, heat velocity (m s−1); MC, sapwood water content (kg water (kg dry weight)–1); cdw, specific heat capacity of dry wood (1200 J kg−1 K−1; Edwards & Warwick, 1984); ρd, dry density of sapwood (kg m−3); ρs, density of the sap (assumed to be the density of water, 1000 kg m−3); cs, specific heat capacity of the sap (assumed to be that of water, 4186 J kg−1 K−1; Edwards & Warwick, 1984)). A full list of symbols used in the article can be found in Table 1. MC and ρd can be determined by taking a wood core. Although ρd will remain approximately equal for a specific tree, MC is known to vary both seasonally and daily, with annual changes of up to 70% and more depending on species and environment (Skaar, 1988; Wullschleger et al., 1996; Nadler et al., 2008). Hence, if MC is only determined once, this might induce large errors in the sap flux density obtained. Although relative changes in stem water content can be estimated by applications of methods, such as time domain reflectometry, resistivity tomography, γ-ray attenuation and electrical resistance, these methods require additional equipment, are difficult to interpret and struggle to take into account the spatial variability of the sapwood (Wullschleger et al., 1996; Nadler & Tyree, 2008; Bieker & Rust, 2012).
Table 1. List of symbols
| V h ||m s−1||Heat velocity|
| q s ||m3 m−2 s−1||Sap flux density|
| K ||W m−1 K−1||Thermal conductivity|
| c ||J kg K−1||Heat capacity|
| ρ ||kg m−3||Density|
| ρc ||J m−3 K−1||Volumetric heat capacity|
| D ax ||m2 s−1||Axial thermal diffusivity|
| D tg ||m2 s−1||Tangential thermal diffusivity|
| K ax ||W m−1 K−1||Axial thermal conductivity|
| K tg ||W m−1 K−1||Tangential thermal conductivity|
| q ||W m−1||Heat given off per unit length of the heat source|
| x ||m||Distance between the heater needle and the axial needle|
| y ||m||Distance between the heater needle and the tangential needle|
|ΔT||K||Temperature difference between the temperature during or after application of the heat pulse at a time t and the temperature before application of the heat pulse at a certain position (x,y) from the heater|
| T ||K||Temperature at a certain position (x,y) from the heater|
| w d ||kg||Oven dry weight|
| w f ||kg||Fresh weight|
| c w ||J kg−1 K−1||Specific heat capacity of water|
| c d ||J kg−1 K−1||Specific heat capacity of dry wood|
| K w ||W m−1 K−1||Thermal conductivity of water|
| K d ||W m−1 K−1||Thermal conductivity of dry wood|
|MC|| ||Water content (moisture to dry weight)|
| ρ w ||kg m−3||Density of water|
| ρ d ||kg m−3||Density of dry wood (sapwood after drying)|
| K d ||W m−1 K−1||Thermal conductivity of dry wood|
| F v || ||Void fraction of the wood|
| t m ||s||Time from the start of the heat pulse until the maximal temperature rise|
| t 0 ||s||Duration of the heat pulse|
Our study describes a new type of method and coupled sensor, referred to as Sapflow+, capable of the nondestructive measurement of high, low and reverse sap flows, thermal wood properties and water content of the sapwood based on thermodynamics. A theory is presented to determine these parameters based on the conduction and convection of a short-duration heat pulse away from an infinite line source in the sapwood. It is shown that, by using this theory, sap flow, thermal wood properties and water content can be determined by a four-needle probe. Results of both finite element modelling and laboratory experiments are presented which demonstrate the applicability of the theory for the measurement of the sap flux density and water content of fresh sapwood.