2.1 Study site

This study was conducted in a 30-year-old mixed tree plantation of E. citriodora and A. auriculiformis in South China Botanical Garden, Chinese Academy of Sciences, Guangzhou, China (23°10′48″ N, 113°21′04″ E). They were both introduced fast-growing tree species with D_s typically lesser than 20 mm. The stand has an average tree density of 1 tree per 10 m² and an open canopy of about 20 m in height. Leaf area index (LAI) varies from 0.8 to 1.1 throughout a year (LAI-2000, LI-COR Inc., Lincoln, NE, USA). Stem diameters at the breast height (DBH), that is, 1.3 m above ground, were 19.4 ± 9.3 and 19.1 ± 8.5 cm for E. citriodora and A. auriculiformis, respectively (Figure S1). The site has a typical subtropical oceanic monsoon climate, characterized by hot summers and warm winters with little frost and no snowfall. Annual average temperature, annual total solar radiation and annual total precipitation range from 21.4°C to 21.9°C, 4400 to 4500 MJ m⁻² and 1612 to 1909 mm, respectively. The soil is a gravely sandy loam with pH of 4.0–5.0, organic content of 2.3% and total nitrogen content of 0.07%.

2.2 Tree samples

Increment cores were taken from 22 A. auriculiformis and 26 E. citriodora. DBH was measured in two perpendicular directions with a digital calliper (Mitutoyo Corporation, Japan), averaged for each tree, respectively. Tree height and crown depth were measured with a hypsometer TruPulse 200 Rangefinder (Laser Technology, USA). Tree canopy spans at two perpendicular directions were measured with a tape metre, denoted as a and b, and the crown area was calculated as πab. Boundaries between the sapwood and heartwood were identified visually by the colour change: from pale white sapwood to yellow brown or even reddish heartwood in both species. Sapwood area (A_s) for each tree was calculated as the area of the stem ring of estimated D_s, assumed constant in all directions. The allometric relationships between A_s and DBH were fitted with power functions (y = a*x^b) for each species, respectively.

Another 6 trees; 3 A. auriculiformis with DBH of 15.3, 22.4 and 26.7 cm; and 3 E. citriodora with DBH of 16.8, 19.5 and 22.0 cm were selected for J_s measurements. DBH of these 6 sample trees fell within the 0.25–0.75 quantiles of species-specific DBH distributions (Figure S1) and corresponded to a D_s range of 13–19 mm (65–95% of the original Granier probe length). Tree bark thickness was measured with a digital veiner calliper (Stanley Electric, London, OH, USA) for each tree in the middle of a 1.5 × 1.5 cm trunk bark, which was cut when the HD probe was installed. It was used to backwardly derive D_s from the allometric relationships. The accurate D_s for these 6 trees were also determined by colour change of the increment cores taken at the end of the experiment. Comparisons between the measured D_s (or the A_s calculated from D_s measurements) and the allometrically derived D_s (or the A_s allometrically simulated by DBH) were made to evaluate the allometric equations.

2.3 Measurements

J_s were measured continuously using the 20 mm long home-made HD probes according to Granier (1987). The electric resistance of the probe was about 10 Ω and the heating power maintained at 0.2 W. All sensors were installed on the northern sides of tree trunks at the breast height; 2 mm diameter aluminium sleeves coated with conductive paste were pre-installed before the instalment of probe sensors to facilitate HD and minimize temperature gradients along the probe length. All gauges were wrapped in aluminium foil to prevent solar heating. The sensor output voltages were collected every 30 s, averaged over 10 min and recorded with a DL2e data logger (Delta-T Devices Ltd, Cambridge, UK). Zero flow conditions were identified when the sensor output voltage reached the maximum and maintain stable over a 2 h period with atmospheric vapour pressure deficit (VPD) < 0.05 k Pa at night-time (Oishi et al., 2008). As evident from Equation 1, it is not necessary to convert the output voltages to ΔT because the conversion factor (43 μV/°C) would be cancelled when J_s were calculated (Morris & Langari, 2020).

Photosynthetically active radiation (PAR) (μmol m⁻² s⁻¹) was quantified with an LI-190SA quantum sensor (LI-COR, Inc., Lincoln, NE, USA). Temperature (T) (°C) and relative air humidity (RH) (%) were measured by a thermo-hygrometer (HygroClip 2, Rotronic AG, Switzerland). VPD (k Pa) was calculated from T and RH according to Campbell and Norman (1998). Soil water content (SWC) (%) at 30 cm depth was measured at three different locations with SM150 soil moisture sensors (Delta-T Devices Ltd., Cambridge, UK). Soil pH was measured with a FieldScout SoilStik pH Meter (PH400, Spectrum Technologies Inc., Fort Worth, TX, USA). Soil organic matter (SOM) content was determined by dichromate oxidation with external heat and titration with ferrous ammonium sulphate by using the method of Mebius (1960). Total soil nitrogen (N) was measured by a standard Elemental Analyzer (Vario EL, Germany). Precipitation (mm) was recorded in a nearby meteorological station. All sensors except the SM150 were deployed at the canopy, mounted on a 16.5 m steel tower. Meteorological measurements were synchronized with J_s measurements.

2.4 Data analyses

J_s from 7:00 to 18:00, 15–25 November 2013, were used for analyses. Data were analysed with SAS (Version 9.1.3, SAS Institute, NC, USA) and SigmaPlot (Version 12.1, Systat Software Inc., CA, USA). Clearwater corrections were carried out according to Equation 2 for each tree, respectively. J_s underestimation was evaluated through comparisons between the corrected and monitored J_s. D_s inaccuracies were assumed to be bidirectional—D_s could be either overestimated or underestimated. Clearwater corrections were reapplied at a step of 0.1 mm within an assumed D_s error range of 2 mm. The adjusted J_s were then compared with the corrected J_s, and the difference between them was defined as the absolute error. The relative error was calculated by dividing the absolute error with the corrected J_s. The relationship between the relative error in J_s and J_s was fitted by polynomial models omitting non-significant high order terms at each level of the D_s error and extrapolated to a range that corresponded to a corrected J_s of ≤90 g m⁻² s⁻¹ for comparison convenience among trees and between species. The responses of the relative error in J_s to D_s uncertainties and D_s were analysed by fixing J_s to constant levels. All results were considered statistically significant if p < 0.05.

3.1 Micrometeorology

The average of daily mean (07:00–18:00) PAR was 268.37 ± 58.90 μmol m⁻² s⁻¹ from 15 to 25 November 2013, with the maximum and minimum daily mean radiation of 354.54 (on 16 November) and 165.03 μmol m⁻² s⁻¹ (on 19 November), respectively. Daily mean temperature reached the maximum of 25.17°C on 23 November, and the highest daily mean RH of 83.20% occurred on 24 November following a 9.3 mm precipitation event. Daily mean VPD increased from 0.77 kPa on 15th to 1.72 kPa on 18th and then fluctuated downward to the minimum of 0.53 kPa on 24 November. Daily mean SWC decreased continuously from 29.70% on 15 to 25.67% on 23 November, indicating the soil drying process along with the progression of dry seasons (generally from late October to early April of the next year) in south subtropical China (Niu et al., 2016). The slight rebounding of SWC on 24 and 25 November was driven by the aforementioned precipitation event (Figure S2).

3.2 The A_s–DBH allometry

Figure 1 showed the allometric relationships between A_s and DBH for A. auriculiformis and E. citriodora, respectively. It also displayed (by filled stars) the A_s calculated independently from D_s measurements. We derived the D_s backwardly from the allometrically simulated A_s for the 6 sample trees (Table 1). Results showed that the allometric equations overestimated D_s in our present study. The error was 1.6, 1.5 and 1.1 mm for A. auriculiformis with DBH of 15.3, 22.4 and 26.7 cm, and 1.3, 1.5 and 1.3 mm for E. citriodora with DBH of 16.8, 19.5 and 22.0 cm, respectively. The corresponding relative error (absolute error/D_s) was 10.7%, 8.8%, 6.1%, 10.3%, 10.5% and 8.2%, respectively. In terms of tree species, the relative error was 8.6% ± 2.3% and 9.7% ± 1.3% for A. auriculiformis and E. citriodora, respectively.

3.3 Sap flux density (J_s)

The output voltages of the probe sensors in our present study were between 0.2 and 0.7 mV, varying among trees and between species. For the 3 trees of A. auriculiformis corresponding to DBH of 15.3, 22.4 and 26.7 cm, the ΔV_max was 0.458 ± 0.008, 0.540 ± 0.026 and 0.436 ± 0.002 mV, respectively. For the 3 trees of E. citriodora corresponding to DBH of 16.8, 19.5 and 22.0 cm, the ΔV_max was 0.348 ± 0.004, 0.594 ± 0.004 and 0.440 ± 0.008 mV, respectively.

In the present study, E. citriodora tended to have larger J_s than A. auriculiformis. Great variability of J_s existed among individual trees within each species. The averages of daily mean J_s from 07:00 to 18:00 during the 11 days of the experiment were 13.27 ± 2.59, 22.67 ± 3.65 and 7.83 ± 1.21 g m⁻² s⁻¹ for the 3 trees of A. auriculiformis with DBH of 15.3, 22.4 and 26.7 cm, respectively. For the 3 trees of E. citriodora, corresponding to DBH of 19.5, 22.0 and 16.8 cm, the averages of daily mean J_s were 11.71 ± 2.12, 29.92 ± 4.30 and 33.97 ± 5.57 g m⁻² s⁻¹, respectively. Typical diurnal patterns of J_s were unimodal, peaking at 11:30–14:00 for both species (Figure S3). The maximum J_s were 47.81 and 70.18 g m⁻² s⁻¹ (Table 1 and Figure S3), occurring on the same day (15 November), for A. auriculiformis and E. citriodora, respectively.

3.4 Underestimation of J_s

The 20 mm long HD probes remarkably underestimated J_s, and the underestimation magnitude tended to be larger at higher J_s and in trees with shallower sapwood (Figure 2). For A. auriculiformis with D_s of 17.0 mm, J_s were underestimated by 4.2 and 11.6 g m⁻² s⁻¹ at the rates of 20 and 40 g m⁻² s⁻¹, respectively, while at the rate of 45 g m⁻² s⁻¹, J_s were underestimated by 12.5 and 21.2 g m⁻² s⁻¹ in E. citriodora with D_s of 15.9 and 12.6 mm, respectively. Taking considerations together, we found that the magnitude of J_s underestimation increased monotonically with the decrease of D_s even across different tree species. The relationships between the measured and corrected J_s could be fitted significantly by quadratic equations (R² > 0.99, p < 0.01). At the rate of 40 g m⁻² s⁻¹, the 20 mm long HD probes underestimated J_s by 19.0, 22.0, 24.7, 27.6, 30.3 and 33.3 g m⁻² s⁻¹, corresponding to 50.0%, 55.0%, 61.8%, 69.0%, 75.9% and 83.1%, for trees with D_s of 17.9, 17.0, 15.9, 14.9, 14.3 and 12.6 mm, respectively (Figure 2).

3.5 Responses of the relative error in J_s to D_s uncertainties

Figure 3 demonstrated how the Clearwater corrections were affected by the D_s error of up to a 2.0 mm range. Positive error in D_s meant that D_s were overestimated, resulting in underestimation of J_s; negative error in D_s signified underestimation of D_s, leading to overestimated J_s. The relative error in J_s increased with D_s error and was also J_s dependent (Figures 3 and 4). The underestimation of D_s generally had larger effect on J_s corrections than the overestimation of D_s of the equal magnitude. As in the relationships between the measured and corrected J_s in Figure 2, the responses of the relative error in J_s to D_s error could also be fitted significantly by quadratic equations (R² > 0.99, p < 0.01).

3.6 Responses of the relative error in J_s to J_s

The relative error in J_s was positively correlated with J_s. The relationships between them could be fitted by linear regression models. Figure 4 showed the regressions of the relative error in J_s to J_s at the D_s error of ±0.5, ±1.0, ±1.5 and ±2.0 mm. All the regressions were statistically significant with R² > 0.99 and p < 0.01. As the error in D_s changed from −2.0 to 2.0 mm (except for the non-error or 0 mm error condition), the slopes and intercepts of the regression equations decreased monotonically and quadratically (R² > 0.99, p < 0.01) from positive to negative. Logically, if the step of the D_s error change was small enough, series of linear regressions for the relative error in J_s to J_s would be generated, and their slopes and intercepts would form quadratic parabolas spanning across the second and fourth quadrants in rectangular coordinate systems with the slopes (or intercepts) and D_s error as the longitudinal and horizontal ordinates, respectively (Figure 6a).

3.7 Responses of the relative error in J_s to D_s

Figure 5 showed the responses of the relative error in J_s to D_s at J_s rates of 10, 50 and 90 g m⁻² s⁻¹. Linear regression models were fitted under conditions with ±0.5, ±1.0, ±1.5 and ±2.0 mm error in D_s. As those observed in responses of the relative error in J_s to J_s (Figure 4), the intercepts of the regression equations also decreased monotonically from positive to negative (R² > 0.99, p < 0.01) as the error in D_s changed from −2.0 to 2.0 mm (except for the non-error or 0 mm error condition), during which, however, the regression slopes increased monotonically from negative to positive. Both the responses of the slopes and intercepts to the D_s error could be fitted quadratically. Similarly, if the step of the D_s error change was small enough, series of linear regressions for the relative error in J_s to D_s would be generated, and their slopes (or intercepts) would form quadratic parabolas, which spanned across the first and third (or the second and fourth) quadrants in rectangular coordinates with the slopes (or intercepts) and D_s error as the longitudinal and horizontal ordinates, respectively (Figure 6b).

4.1 D_s derivation from the A_s–DBH allometric relationships

The allometric relationships tended to overestimate A_s and thus D_s (Figure 1 and Table 1). Because bark thickness was necessary for the D_s derivation from allometric relationships between A_s and DBH, its variability (such as azimuthal variation) and measurement inaccuracies may potentially influence the estimated D_s. Although previous studies have suggested that bark thickness was related to DBH (Williams et al., 2007; Zeibig-Kichas et al., 2016), we found no significant correlation (p > 0.1) and thus could not eliminate the potential impact of bark thickness on the A_s–DBH relationships by simply setting it as a covariate. An alternative way would be to set up relationships between A_s (or D_s) and the inside bark DBH (Lassen & Okkonen, 1969). However, this approach should still accommodate the azimuthal variation of bark thickness (Stangle & Dormann, 2018).

4.2 Clearwater corrections and J_s variability

It is implied in the original design that the HD (or Granier) sensors (20 mm long) could only be reasonably used when they were in complete contact with the hydraulically active portion of stem-sapwood (Lu et al., 2004). Clearwater corrections were put forward to deal with the situation that part of the HD sensors was inserted into the heartwood (Clearwater et al., 1999). Previous studies have observed that the 20 mm long HD sensors tended to underestimate J_s in trees with drastic changes over the radial profiles of J_s (Bush et al., 2010; Pataki et al., 2011). For ring-porous species, water was mainly transported by the large vessels in the outermost part of sapwood, and J_s decreased rapidly even within the 20 mm length of probe sensors (Gebauer et al., 2008). In diffuse-porous and coniferous species, J_s changed along the sapwood far thicker than 20 mm (Wullschleger & King, 2000). Although both A. auriculiformis and E. citriodora were diffuse-porous hardwoods, their D_s were less than 20 mm, and part of the probes was in contact with non-conducting heartwood, leading to the underestimation of J_s. The application of Clearwater corrections therefore might have improved the J_s estimation in the present study (Figures 2 and S3), as has also been reported in Quercus prinus and Quercus velutina (Renninger & Schaefer, 2012).

Tree-to-tree variability in J_s is widely regarded as the main source of uncertainties in estimating forest transpiration (Kumagai et al., 2008). Great variability in J_s (Clearwater corrected) was also detected among individual trees in the present study. These observations agreed with the findings in Cryptomeria japonica, Robinia pseudoacacia and Quercus liaotungensis (Kume et al., 2012; Shinohara et al., 2013). Tree size, canopy structure and spatial heterogeneity of SWC are all possible factors that may affect the water use at individual tree scale (Dalsgaard et al., 2011; Meinzer et al., 2001). On the other hand, J_s were comparatively larger in E. citriodora (25.20 ± 11.86 g m⁻² s⁻¹) than in A. auriculiformis (14.59 ± 11.86 g m⁻² s⁻¹). This reflected the intrinsic discrepancy of xylem hydraulic structure and water conservation mechanisms between different tree species even in response to similar soil water status.

4.3 Responses of Clearwater corrections to D_s error

Based on the assumption that a trunk's cross-section is generally composed of a light, high-water-content zone at the outermost part and a darker, phenolic-and-resin-rich area at the centre (Bamber, 1976; Hillis, 1968), sapwood is frequently differentiated from heartwood by wood translucence and colour changes. However, these methods may introduce great uncertainty into the estimation of D_s because the underlying anatomical assumptions do not strictly apply to every species (Pfautsch et al., 2012; Jeremic et al., 2004). D_s varied remarkably with species, tree ages, environmental conditions and even azimuthal directions (Gebauer et al., 2008; Taylor et al., 2002; Ward et al., 2013). For some species, the water content in the transitional zone and heartwood is similar to that of the sapwood. Pathogenic invasion and tree injury can also alter anatomical characteristics, creating false sapwood–heartwood boundaries (Pallardy, 2008; Ward & Pong, 1980). Quiñonez-Piñón and Valeo (2018) compared the colour change method with microscopic anatomy analyses in Trembling Aspen (Populus tremuloides Michx.) and found that the former approach biassed the D_s estimation by as much as 1.8 cm. We speculated that the assumed D_s error of less than 2 mm were of low to moderate levels. However, remarkable error (≤50%) was still brought about into the Clearwater corrections. They increased nonlinearly with the D_s error and were asymmetric with respect to the reference zero line (Figure 3). The nonlinearity is intrinsic to Equation 2, and the asymmetry otherwise implies that the conservative strategy should not be a sensible policy in D_s estimation.

4.4 Responses of Clearwater corrections to D_s and J_s

Although the absolute and relative error in Clearwater corrections responded nonlinearly to D_s uncertainties, its responses to J_s and D_s at specific D_s error could be fitted significantly by linear regressions. Decreasing D_s as well as increasing J_s jointly increased the relative error in J_s up to 50%. Bush et al. (2010) suggested that Clearwater corrections should only be used when D_s exceeded 50% of the sensor length. A_s has been shown in the present study, even within this range, considerable error in J_s was introduced by D_s inaccuracies.

The relative error in J_s tended to be larger in E. citriodora than in A. auriculiformis at specific D_s error. Two reasons may account for this discrepancy. On the one hand, D_s of the sample trees were different between species. The average D_s were 16.6 ± 1.5 and 14.3 ± 1.7 mm for A. auriculiformis and E. citriodora, respectively. The relative error in J_s was negatively related to D_s (Figure 5). Therefore, if other conditions were the same, D_s error of equal magnitude would certainly produce larger relative error in J_s in E. citriodora due to its smaller D_s. On the other hand, in sap flow measurements with the HD sensors, the maximum temperature difference under zero flow conditions (ΔT_max) is often probe-specific and may be related to wood property and microclimate conditions (Lu et al., 2004). In the present study, the output voltages of the HD sensors under zero flow conditions (ΔV_max) were separately determined for each tree every 2–3 days. Difference in ΔV_max would result in different voltage output (ΔV) under specific sap velocity, leading to different sensitivity of J_s to D_s error, even when (ΔV_max − ΔV)/ΔV kept constant. Therefore, the discrepancy of ΔV_max and thus ΔV at specific J_s may also contribute to the difference of the relative error in J_s between tree species.

4.5 Limitations and cautions

This study was based on the assumption that the original Granier calibration of the HD sensors was independent of woody material, which had been validated in a number of diffuse-porous species (Bush et al., 2010; Catovsky et al., 2002; McCulloh et al., 2007). This kind of universality, however, has been challenged by the findings of significant underestimation of J_s in Fagus grandifolia and Tamarix spp. (Hultine et al., 2010; Steppe et al., 2010). General models based on heat transfer principles and wood properties such as wood density and water content are urgently needed for reconciliating these controversial results. On the other hand, inserting the probes tangentially into the sapwood provides an alternative way to avoid being in contact with the non-conducting heartwood (Lu et al., 2004). However, error can still occur when J_s varied radically within the <20 mm sapwood. In such conditions, shorter sensors (e.g., 1 cm long effective measuring elements) (James et al., 2002) should be employed to minimize the error associated with J_s changes between adjacent sapwood layers.