An empirical study of the wound effect on sap flux density measured with thermal dissipation probes

Abstract

The insertion of thermal dissipation (TD) sensors on tree stems for sap flux density (SFD) measurements can lead to SFD underestimations due to a wound formation close to the drill hole. However, the wound effect has not been assessed experimentally for this method yet. Here, we propose an empirical approach to investigate the effect of the wound healing on measured sap flux with TD probes. The approach was performed for both, diffuse-porous (Fagus sylvatica (Linnaeus)) and ring-porous (Quercus petraea (Lieblein)) species. Thermal dissipation probes were installed on different dates along the growing season to document the effects of the dynamic wound formation. The trees were cut in autumn and additional sensors were installed in the cut stems, therefore, without potential effects of wound development. A range of water pressures was applied to the stem segments and SFDs were simultaneously measured by TD sensors as well as gravimetrically in the laboratory. The formation of wounds around sensors installed in living tree stems led to underestimation of SFD by 21.4 ± 3 and 47.5 ± 3.8% in beech and oak, respectively. The differences between SFD underestimations of diffuse-porous beech and ring-porous oak were, however, not statistically significant. Sensors with 5-, 11- and 22-week-old wounds also showed no significant differences, which implies that the influence of wound formation on SFD estimates was completed within the first few weeks after perforation. These results were confirmed by time courses of SFD measurements in the field. Field SFD values decreased immediately after sensor installation and reached stable values after ~2 weeks with similar underestimations to the ones observed in the laboratory. We therefore propose a feasible approach to correct directly field observations of SFD for potential underestimations due to the wound effect.

Introduction

The thermal dissipation (TD) method developed by Granier (1985, 1987) has become one of the most widespread methods for determination of tree transpiration, due to low costs and the easily comprehensible sensor construction (Davis et al. 2012). This is especially advantageous for studies focused on the estimation of water balances (Schäfer et al. 2002, Holst et al. 2010) or partitioning of evapotranspiration at the stand level (Herbst et al. 2007, 2008, Oishi et al. 2010, Clausnitzer et al. 2011, Gebauer et al. 2012, Ringgaard et al. 2012), where a large number of sensors are needed. However, numerous studies report considerable errors using the TD method (Bush et al. 2010, Hultine et al. 2010, Sun et al. 2011, Reyes-Acosta et al. 2012, Paudel et al. 2013), which gave the largest underestimations in comparison to other methods (Steppe et al. 2010). Some sources of uncertainty have been frequently described, such as the great spatial variability of sap flux density (SFD) within species (i.e., circumferential variability, Saveyn et al. 2008; and radial variability, Ford et al. 2004, Gebauer et al. 2008) and between species (e.g., Sun et al. 2011), bad positioning of the sensor probes (Clearwater et al. 1999, Shin'ichi and Tadashi 2010), inadequate determination of the ΔT₀ (see below) parameter (Wullschleger et al. 2011, Vergeynst et al. 2014) and systematic errors due to the lack of species-specific calibrations (Lu et al. 2004, Bush et al. 2010). Substantial effort has been made to improve the accuracy of the TD method but a large fraction of the SFD remains still underestimated by this method (Steppe et al. 2010) and the specific causes remain unclear.

The wound formation in response to sensor insertion into the xylem has been suggested as one of the largest sources of error in SFD estimation with TD sensors (Steppe et al. 2010, Wullschleger et al. 2011), although no experimental study has tested this hypothesis yet. The TD sensors consist of two probes of stainless steel equiped with thermocouple junctions that are inserted within the tree stem, usually within previously inserted aluminum tubes of 20 mm length and 2 mm diameter. The upper probe is constantly heated, whereas the lower sensor acts as a reference, and the temperature difference between the two probes (ΔT) is used to calculate SFD with an empirical function (Granier 1985). The insertion of TD probes within the sapwood represents, therefore, an unavoidable disturbance of the conductive tissue surrounding the measurement point. The first direct and immediate vessel disruption, consequent air embolism and the interruption of water flux around the drilled holes (Dujesiefken et al. 1999) may cause an inherent measurement error with all invasive methods. This error is, nonetheless, accounted for as long as the method is calibrated under similar conditions. More problematic is the indirect and later effect associated with the wounding reaction of the wood tissue close to the damaged area. This reaction was already described by the CODIT principle (Compartmentalization Of Damage In Trees, Shigo 1984, Liese and Dujesiefken 1996, Dujesiefken et al. 2005). According to that principle, the damaged sap wood tissue is actively isolated from the healthy one by sealing the water conduction elements and structural components in order to encapsulate spreading fungi and prevent the cavitation in the affected vessels. Hence, a tissue die back of parenchyma cells occurs after air embolism, followed by the formation of a reaction zone surrounding the wound, the so-called compartmentalization. This reaction zone, detectable as a discoloration of sapwood, is characterized by the closure of vessels, phenols accumulation and changes in wood properties, with the consequent reduction in its conductive capacity and the alteration of the heat transport. Since the TD method is based on the heat conductivity of the wood, the alteration of this property associated with the wounding reaction can bias SFD estimations systematically.

Potential alterations in wood thermal and physical properties stemming from an active wounding reaction are not included in the standard TD calibration equation. Granier’s (1985, 1987) empirical equation was developed using TD sensors that were installed after cutting the stem segments and, therefore, an active compartmentalization and wound formation did not occur. Empirical validations on wound-affected sensors are then imperative to accurately describe the effects of wood physical and anatomical alterations on the measured SFD. The effect of the wound effect on SFD estimates was, however, never studied up to now despite the wide recognition of this effect, for example, for the heat pulse method (Cohen et al. 1981, Swanson and Whitfield 1981). The magnitude of errors, its dynamics and time frame, as well as potential effects of different species, phenology or environmental factors are also completely unknown. The main objectives of this study were firstly to determine experimentally the magnitude of SFD underestimation associated with wound formation, and secondly, to develop an approach to account for the wound effect on TD measurements in the field. Therefore, sets of TD probes were installed at different dates along the growing season in diffuse- and ring-porous trees (Fagus sylvatica and Quercus petraea). At the end of the growing season, the trees were cut and additional sets of sensors were installed in each stem segment after logging (‘After Cut’, AC). We compared SFD measured by sensors installed in living trees with AC sensors and the gravimetric reference observations in the laboratory. We expected a better performance of AC sensors, while higher underestimations on probes installed in living trees. We also hypothesized larger underestimations in earlier installed probes and in ring-porous species.

Materials and methods

Plant material and study site

The trees included in this study are located in a mixed deciduous forest (Leinefelde, Thüringen, Germany, 51°20′13″N, 10°22′07″E and 450 m above sea level). Climate in the study area is subatlantic-submontane with an annual mean temperature of 8.2 °C and an annual mean precipitation of 577 mm (2003–2014, O. Kolle, Max Planck Institute for Biogeochemistry, Jena, personal communication). The forest is relatively homogenous and composed of even-aged stands where European beech (F. sylvatica) is the dominant species (97% of relative abundance) with accompanying sessile oak (Q. petraea, 3%). Tree height and diameter at breast height were 33 m (SD: 7.2 m) and 44 cm (SD: 12.4 cm), respectively (2012, M. Mund, Max Planck Institute for Biogeochemistry, Jena, personal communication).

Two beech trees (diffuse-porous) and two oak trees (ring-porous) were selected for this experiment, so that the effect of wound formation could be investigated on species with different xylem anatomies (Table 1). Trees with regular concentric growth, and no evidence of knots, scars, diseases or irregularities in the stem surface were chosen.

Table 1.

Characteristics and dimensions of trees used in the study.

Tree stem	Oak 1		Oak 2		Beech 1		Beech 2
Stem segment	Segment 1	Segment 2	Segment 1	Segment 2	Segment 1	Segment 2	Segment 1	Segment 2
Diameter (cm)	35.65	35.33	38.04	35.49	31.51	31.04	31.02	30.88
Sapwood depth (cm)	1.54 ± 0.13		0.54 ± 0.07		10.61 ± 2.4		13.41 ± 1.97
Sapwood area (cm2)	149.41		55.25		663.46		895.17

Thermal dissipation method

The TD sensors used in this study were constructed manually according to Davis et al. (2012) and the specifications of the original design of Granier (1985). Each sensor consisted of two probes of 20-mm length and 1.1-mm diameter stainless steel needles and a T-type thermocouple (copper–constantan). Thermocouples were made by using copper wire of 0.10-mm diameter (Reichelt Elektronik, Germany) and fine-gauge constantan wire insulated with Teflon with a diameter of 0.13 mm (OMEGA Newport Electronics GmbH, Germany). Both wires were connected using a commercial tin solder. The upper probe of each sensor was continuously heated at constant power (0.2 W), whereas the lower probe was not heated and measured the ambient temperature of the wood tissue. The constantan ends of the two thermocouples were connected to measure the temperature difference (ΔT) between the probes. The temperature difference was measured every 60 s, and the average of 10 min was recorded on a data logger (CR1000, Campbell Scientific, Logan, UT, USA) and two multiplexers (AM16/32, Campbell Scientific).

ΔT is then related to the SFD (cm³ cm⁻² h⁻¹) using the empirical equation developed by Granier (1985),

$$\mathrm{SFD}=0.0119{\times K}^{1.231}$$

(1)

where 0.0119 and 1.231 are empirically determined coefficients and K is a dimensionless value defined as

$$K=\frac{∆T_0-∆T}{∆T}$$

(2)

ΔT₀ is the value of ΔT obtained under zero flow conditions or the maximum temperature difference between the two needles and ΔT is the measured temperature difference at a given SFD. This empirical formula was developed by Granier (1985, 1987) for measuring SFD in trees with a stem diameter >40 mm. It was initially established experimentally from measurements on two conifers [Pseudotsuga menziesii (Mirb.) Franco and Pinus nigra (Arnold)] and one ring-porous hardwood species (Quercus pedunculata Ehrh.), providing an independent relationship between K and SFD on the three species studied. The equation depends on the heat field created by the heated probe and, therefore, on the particular physical properties of wood and probes and on the quantity of heat applied. Since the empirical calibration has little physical basis (Smith and Allen 1996, Clearwater et al. 1999), a recalibration is needed in those cases in which any of the factors is modified. The hand-made sensors used in this study were previously tested against commercially available sensors (Type SF, Ecomatik, Dachau/Munich, Germany) in order to prove their accuracy and reliability (results not shown).

Field experimental setup

Six sets of TD sensors were installed at different dates in the growing season (Day of year (DOY) 134, 208 and 253; spring, summer and fall sensors, respectively) in each of the selected trees in the field. Sensors were equally distributed in two 80-cm stem segments located at two heights (0.9–1.7 and 2.2–3 m from the base). Hence, each stem height contained three sensors per sampling date located at predefined positions around the stems, so that each state of wound development would be present along the circumference. A minimum horizontal distance of 20 cm and vertical distance of 40 cm were maintained between consecutive sensors, and vertical alignment was avoided to prevent thermal interferences. Stem diameters at the point of sensors insertion ranged from 31.4 to 34.1 cm for beech and from 35.3 to 39.2 cm for oak (Table 1).

For sensor insertion, the bark was carefully removed at the point and two holes of 2 mm diameter, 2 cm depths and 10 cm apart were drilled radially into the sapwood. A template was used in order to minimize displacement errors during installation. Once the holes were drilled, an aluminum tube of 2 mm diameter and 0.2 mm thick wall was inserted into each hole, so that it was tightly fitted and completely immersed into the wood (see Table 1 for details on sapwood depth of each stem segment). Sensor probes were then inserted into each correspondent aluminum tube, which was previously filled with silicon grease to increase thermal conductivity. Silicon grease was replaced periodically in order to prevent errors associated with silicon aging. Finally, sensors were protected from damages and meteorological conditions and trees were wrapped with aluminum foil to minimize possible interferences with natural temperature gradients (Do and Rocheteau 2002a, Lubczynski et al. 2012). Nonetheless, a pilot study showed that the natural temperature gradient rarely exceeded 0.2 °C on the study site, so this effect can be considered negligible (Do and Rocheteau 2002a).

Trees were logged just before the end of the growing season (DOY 287), i.e., 22, 11 and 5 weeks after the installations of spring, summer and fall sensors, respectively. The TD sensors were previously removed to avoid damage during the logging operation, while the aluminum tubes remained within the stems, encapsulated by the wounded areas. Two 80-cm long sections of each stem, including the preinstalled aluminum tubes at all installation dates, were cut and wrapped in plastic foil to prevent desiccation and carefully transported to the laboratory.

Laboratory SFD measurements with gravimetric reference

Once in the laboratory, the upper and the lower cut surfaces of the stem segments were previously recut with a fine-tooth saw and visible blocked vessels were reopened with a razor blade. Additional sensors were installed (‘AC’) following the procedure described above. These measuring points are considered as reference sensor measurements since the wound reaction is an active mechanism of defense that involves hormone production and biochemical reactions (Shigo 1984). It is hence not expected to occur in cut stems. The existing holes were also equipped again with randomly chosen TD sensors. Therefore, each segment contained a total of 12 sensors (3 sensors × (3 sampling dates + 1 AC)).

The whole segments were then erected in the natural growth direction with their lower extremes immersed in water (Figure 1). A 2-cm strip of the bark was removed at the top of the stems to facilitate the installation of an acrylic plate. The airtight connection between plate and tree segment surface was achieved with a rubber band and sealant. The valve in the middle of the plate was connected to a vacuum pump, which enabled the application of different pressures (Figure 1). The water passing through the cut stem segments was weighed every 2 min using an electronic balance (model Europe 4000 AR, Gibertini, Novate Milanese, Germany, accuracy of 0.01 g, for lower flux rates and model QS64B, Sartorius AG, Goettingen, Germany, accuracy of 5 g, for higher flux rates). This setup was previously tested to check the absence of thermal interferences between consecutive sensors by activating the heating alternatively on half of the sensors and checking the temperature changes on the other half of non-heated sensors (Do and Rocheteau 2002b, Lubczynski et al. 2012).

Figure 1.

Schematic diagram of the sap flux calibration system used in the laboratory for testing the accuracy of wound-affected and wound-free TD sensors. Water is sucked through the stem segment into the Erlenmeyer flask by the pump.

The described experimental setup enabled the comparison of SFD measured by sensors installed in living trees (i.e., with wound healing reaction: spring, summer, fall sensors) to the freshly installed sensors (i.e., without healing reaction: AC sensors) under the same flux density conditions. For that, constant pressures were applied through the segments, resulting in an SFD of 0–25 cm³ cm⁻² h⁻¹ (gravimetrical reference). This range is within the magnitude reported in the literature (Granier 1985) and previously observed in the field by sensor measurements. Sensors were shifted randomly to different measuring points in the stem between each validation test to ensure that differences were not associated with possible sensor bias. The value of ΔT₀ in Eq. 2 was determined as the maximum ΔT values that were recorded within a 24-h period at zero flow conditions. For this, stem segments were left partially immersed in water to ensure that the wood tissue is rehydrated by capillary rise and to obtain a stable record of ΔT₀ (Figure 1). Sensor SFD was calculated according to Eqs (1) and (2). The gravimetric SFD, considered as the reference flux hereafter, was calculated from the rate of change in the mass of water collected and normalized for the conducting sapwood area.

The sapwood area of oak was determined visually at the end of the experiment by the change of color between sapwood and heartwood. For beech, a 0.1% solution of methylene blue was dissolved in water and sucked through the stem segments. Transversal slices were excised, photographed and the colored area was quantified with the image-processing software ImageJ (Schindelin et al. 2012).

Linear regressions were fitted to the gravimetric SFD values and the corresponding sensor records, both for each date of installation and per tree species. Errors of the linear regression parameters were calculated by bootstrapping the observations 1000 times. The same approach was followed when comparing the pooled wound-affected measurements with AC results. The effect of the date of sensor installation and the tree species on the relationship between TD sensor SFD estimates and gravimetrical values were tested using analyses of covariance (ANCOVA) with ‘species’ or ‘date of installation’ as fixed factors and the gravimetrical sap flux as the covariate. Data were root-transformed to improve normality and homoscedasticity. The same approach was used to explore the relationship between wound-affected sensors and AC sensors.

Since linear regressions were not forced to have zero intercept, relative SFD underestimations and errors vary depending on the sap flux range. For this reason, the differences between gravimetric flow and estimates by TD sensors are expressed as the mean percentage of the gravimetric flux that is underestimated by the TD sensors. For each mean measured value of gravimetric and sensor flux (see data points in Figures 3 and 4), the percentage of gravimetric SFD underestimated by TD sensors is calculated using the following expression:

$$\%\mathrm{SFD}\mathrm{underestimated}\mathrm{by}\mathrm{TD}=\frac{{\mathrm{SFD}}_{\mathrm{grav}}-{\mathrm{SFD}}_{\mathrm{sensor}}}{{\mathrm{SFD}}_{\mathrm{grav}}}\times 100$$

where ${\mathrm{SFD}}_{\mathrm{grav}}$ is the mean measured value of reference gravimetric flux and ${\mathrm{SFD}}_{\mathrm{sensor}}$ is the mean measured value by TD sensors. A similar expression was used to calculate the percentage of SFD underestimated by TD sensors due to the wound effect only (see Figure 5):

$$\begin{array}{c}\%\mathrm{Wound}\mathrm{effect}\mathrm{SFD}\mathrm{underestimation}\hfill \\ =\frac{{\mathrm{SFD}}_{\mathrm{sensor}\mathrm{AC}}-{\mathrm{SFD}}_{\mathrm{sensor}\mathrm{wounded}}}{{\mathrm{SFD}}_{\mathrm{sensor}\mathrm{AC}}}\times 100\hfill \end{array}$$

where ${\mathrm{SFD}}_{\mathrm{sensor\; AC}}$ is the mean value of SFD measured by AC sensors and ${\mathrm{SFD}}_{\mathrm{sensor\; wounded}}$ is the mean value of SFD measured by wound-affected sensors (i.e., spring, summer and autumn sensors).

Field data analysis

Field data were evaluated to detect the progressive underestimations of SFD due to the wound development in living trees. Data from sensors with 10-week-old wounds (spring sensors) were compared with data from sensors installed on the DOY 208 (summer sensors). Autumn sensors were not used for this comparison to avoid obscuring the results with leaf senescence at the end of the growing period. To reduce confounding effects of changing meteorological conditions, we selected periods of potentially similar transpiration. Vapor pressure deficit (VPD) and global radiation were used to model non-water limited transpiration (potential transpiration, PT) by combining a hyperbolic response curve of photosynthesis with the Ball–Berry–Leuning model of stomatal conductance, neglecting cuticular conductance (Leuning 1995, Berry and Roderick 2005)

$$\mathrm{PT}=\frac{a}{C_{\mathrm{a}}}\frac{\alpha F_{\mathrm{GPP},\mathrm{sat}}{Q}_{\mathrm{PPFD}}}{F_{\mathrm{GPP},\mathrm{sat}}+\alpha Q_{\mathrm{PPFD}}}\frac{1}{\frac{1}{\mathrm{VPD}}+\frac{1}{D_0}}$$

(3)

where a = 9 Pa(air)⁻¹ and D₀ = 1 kPa(H₂O) are empirical coefficients, C_a is the atmospheric CO₂ concentration as an approximation of the concentration at the leaf surface (400 µmol(CO₂) mol(air)⁻¹), F_GPP,sat is the gross primary productivity at saturated light intensity (35.3 μmol(CO₂) m⁻² s⁻¹), Q_PPFD is the measured photosynthetic photon flux density (mol(photons) m⁻² s⁻¹), α is the apparent quantum yield (0.099 µmol(CO₂) mol(photons)⁻¹) and VPD is the (water vapour deficit) (kPa(H₂O)). Specific values of the above constants are not relevant because PT is evaluated only relative to PT of DOY 209. Delayed responses of SFD to environmental drivers associated with tree water storage (Köstner et al. 1998, Burgess and Dawson 2008) were avoided by selecting values measured from 10:00 to 16:00 h when the highest daily flow rates usually occur. The average PT between 10:00 and 16:00 h of DOY 209 plus a range of 0.09 mmol(H₂O) m⁻² s⁻¹ was used as a threshold to select days with comparable sap flow conditions. We report in the following mean values with standard errors.

Results

Response of SFD to stepwise changes in flow rate

Figure 2 represents an example of the typical sensor responses in beech to stepwise changes in flux rates in response to different pumping pressures. Sap flux density values from AC sensors were closer to the gravimetric reference, which indicate good performance of the self-made TD sensors using Granier's original calibration (Granier 1985). In contrast, all wound-affected sensors underestimated SFD compared with the gravimetric reference. In this particular case, the 5-week-old fall sensors showed the smallest underestimations of all wound-affected sensors, which would be expected in case of a continuous degeneration of accuracy with time since installation. However, underestimations were not always larger in older wounds (cf. Figure 3). Additionally, underestimation of SFD was also larger in absolute values at higher flow rates than at low flow rates.

Figure 2.

Thermal dissipation sensor response to stepwise changes in pumping pressure and hence flow rate through a cut stem segment in European beech. The gray area highlights the various pressure-exposed conditions, while the white bands in-between are experimental interruptions due to emptying of the Erlenmeyer flask and pump adjustments. Sap flux density measured gravimetrically every 2 min (blue dots) is compared with TD sensors (colored lines), installed at different dates on living tree stems. Lines represent arithmetic means of three sensors and shaded areas represent the corresponding standard errors.

Figure 3.

Comparison of SFD determined gravimetrically with TD sensors for the calibration tests performed on beech segments. (a) Sensors installed 22 weeks before tree cutting (spring). (b) Sensors installed 11 weeks before cutting (summer). (c) TD Sensors installed 5 weeks earlier (fall). (d) Sensors installed after tree cutting (AC). Black circles are average values for one calibration step (34–108 sensor readings averaged per data point), including standard errors of the TD sensors and the gravimetric measurements. Black solid lines are linear fits, while dashed lines are the 1:1 lines. Gray areas represent the errors of the linear fits.

Note that the suction-based verification system had to be interrupted periodically in order to empty the Erlenmeyer flask, which is reflected as a drop in the SFD values between each pressure rate as well as in the middle of the largest flow rate (700 mbar). Nonetheless, to ensure that the interruptions did not influence the results, these values were not included in further analyses.

Validation of SFDs in cut stem segments

For each installation date, SFD measurements from sensors installed in each beech segment were averaged for each pressure step (34–108 sensor readings averaged per data point, depending on the duration of each calibration step) and compared with the corresponding gravimetric reference (Figure 3). Note that linear regressions were not forced to have zero intercept, which implies that the SFD underestimations will vary depending on the sap flux range. Freshly installed AC sensors were able to detect the highest proportion of the gravimetric flux (mean of 86.1 ± 5.7%), whereas spring (72.0 ± 4.7%), summer (61.8 ± 3.9%) and fall sensors (58.0 ± 5.0%) underestimated the reference SFD values by similar magnitudes. The differences between AC sensors and the rest of the installation dates were significant (P = 0.0002), using an ANCOVA with date of sensor installation as fixed factor and gravimetrical sap flux as the covariate. Note that the mean values are not simply the slopes in Figure 3 because they include the offsets.

Similar patterns were obtained in the case of oak (Figure 4), where AC sensors were able to detect a higher (ANCOVA, P = 0.0015) proportion of the flux (72.0 ± 7.8%), compared with spring (40.0 ± 5.1%), summer (52.6 ± 10.5%) and fall sensors (30.8 ± 6.1%). Nonetheless, due to the very thin sapwood area of one tree (0.54 cm), only two segments could be tested, which explains the larger uncertainty of the results. This limitation was also reflected in larger intercepts and errors of the linear regressions.

Figure 4.

Comparison of SFD determined gravimetrically with TD sensors for the calibration tests performed on oak segments. (a) TD Sensors installed 22 weeks before tree cutting (spring). (b) Sensors installed 11 weeks before cutting (summer). (c) TD Sensors installed 5 weeks earlier (fall). (d) Sensors installed after tree cutting (AC). Black circles are average values for one calibration step (34–108 sensor readings averaged per data point), including standard errors of the TD sensors and the gravimetric measurements. Black solid lines are linear fits, while dashed lines are the 1:1 lines. Gray areas represent the errors of the linear fits.

Wound-affected sensors performed better in beech compared with oak, although differences were statistically marginal and with a significant interaction of species with the gravimetrical flux (P = 0.046, ANCOVA with species as fixed factor and gravimetrical sap flux as covariate). However, wound-free sensors have a similar performance in both, beech and oak (ANCOVA, P = 0.55) with no significant interactions.

Since the date of installation did not exert a significant effect on the proportion of the SFD detected by wound-affected sensors, the underestimations associated with wound formation were determined by comparing all spring, summer and fall sensors simultaneously with sensors not affected by wounds (AC) (Figure 5). In beech, wound-affected sensors detected a mean of 78.6 ± 3.0% of the flux density measured by AC sensors. Therefore, the wound effect was responsible for ~21.4 ± 3.0% of the total underestimations from wounded sensors, with increasing values at higher SFDs (Figure 5a). In the case of oak, only 52.5 ± 3.8% of the wound-free SFD values were detected by wound-affected sensors. Consequently, ∼47.5 ± 3.8% of the SFD was underestimated due to the wounding effect. An ANCOVA with species as independent factor and sap flux from AC sensors as covariate showed, however, that the seemingly large differences between beech and oak were not significant (P = 0.13), although the interactions were significant.

Figure 5.

Comparison of SFD determined gravimetrically against all TD sensors installed 5, 11 and 22 weeks before tree cutting: (a) European beech and (b) sessile oak. Symbols are average values for one calibration step, including standard errors of the TD sensors and the gravimetric measurements. Black solid lines are linear fits, while dashed lines are the 1:1 lines. Gray areas represent the errors of the linear fits.

Circumferential variability of SFDs in stems

An assessment of the circumferential variability of the SFD was performed to check for the randomized location of sensors around the tree stem. Under the maximum gravimetric flow (beech: 23.3 cm³ cm⁻² h⁻¹; oak: 14.1 cm³ cm⁻² h⁻¹), sensor SFD ranged from 6 to 26.6 cm³ cm⁻² h⁻¹ for beech and 0.7 to 14.7 cm³ cm⁻² h⁻¹ for oak. Figure 6 shows that AC sensors were located in areas of both high as well as low hydraulic conductivity. Moreover, AC sensors always detected higher SFD than wound-affected sensors in both low conductive areas (e.g., beech 315°) and high conductive areas (e.g., beech 45°).

Figure 6.

Circumferential variability of SFD in cut stem segments of beech (left) and oak (right) under maximal flow rates. The colored lines represent the locations of sensors of different wound ages around the stems. The different intensities of blue along the rings represent the measured SFD by TD sensors at maximum gravimetric flow. Thermal dissipation sensor measurements were linearly interpolated in this figure. The sensors were installed in two rows and with at least 40-cm vertical distance between sensors. Overlapping in the figure is the result of the projection on a single plane.

Evaluation of the development of the wound effect in field data

In order to evaluate the progressive development of the wound effect in living trees, we compared the SFD from freshly installed sensors in beech trees (summer sensors installed on DOY 208) with the SFD from wound-affected sensors that were installed 10 weeks earlier (spring sensors installed on DOY 134). Only data from days with comparable PT rates were used to minimize confounding meteorological effects on the detection of a potential drifting trend on recently installed sensors. A total of 24 middays fulfilled the criterion PT = 0.6 ± 0.099 mmol m⁻² s⁻¹. Field SFD values from sensors with 10-week-old wounds (spring sensors) were 22–47% lower than the ones from freshly installed sensors (summer sensors) a few days after their installation (Figure 7). These values coincide with the underestimation obtained from the laboratory experiment at similar SFD ranges (Figure 5). As wounds develop on the recently installed sensors, differences between summer and spring sensors decreased progressively until they almost converged after 13 days. The differences between both sets of sensors became stable 2 weeks after summer installation with ~7.5 ± 15.1% lower flux densities on spring sensors, which may be indicative of the advanced state of wound development on the most recently installed sensors.

Figure 7.

(a) Time series of SFD measurements of beech in the field showing the progressive development of the wound effect on freshly installed summer sensors. (b) Percentage of the sap flux measured by freshly installed summer sensors that is underestimated by old spring sensors. The dashed line shows the mean underestimation by wound-affected sensors obtained in the laboratory calibration experiment.

Figure 8.

Idealized diagram of the proposed approach to correct field SFD measurements for the wound effect. Different line styles represent SFD values from different sets of sensors installed consecutively in living trees. The diagram does not intend to represent real sap flux magnitudes or time spans for wound effect development.

Discussion

Despite the widespread use of the TD method to study the ecophysiological responses of tree transpiration, considerable measurement errors have been reported for this technique (Moore et al. 2010). Indeed, TD has been identified between several thermal methods as the one with the largest uncertainty, both by empirical comparisons and by modeling studies (Tatarinov et al. 2005, Steppe et al. 2010). Several potential reasons have been suggested, but the real causes for the uncertainty remain unclear. Recent model simulations identified the wound formation in response to the sensor insertion as one of the most important sources of errors for the TD technique (Wullschleger et al. 2011). No experimental results were, however, available up to now to corroborate the contribution of the wound effect to TD uncertainties and to provide insights into the mechanisms involved. This study provides, for the first time, empirical information on the influence of the wounding process on the accuracy of the TD method. Results presented here point to the wound healing reaction as one of the most important sources of error, which is supported by consistent results from both field data and laboratory validation experiments. Concerns arise immediately about the reliability of tree transpiration estimates based on TD measurements. The information given in this article allows us to design a strategy to correct field TD measurements and get an insight on the magnitude of the potential underestimations associated with the wound reaction.

Magnitude and characteristics of the wound effect on the TD method

The wound effect, which happened on sensors installed on living tree stems, was responsible for around 21.4 and 47.5% SFD underestimation in beech and oak trees, respectively (Figure 5), according to the laboratory validation test. The same range of SFD underestimation (22–47%) was also visible in the field during the first 10 days on wound-affected sensors (Figure 7). This source of error could explain, at least in part, the progressive loss of accuracy frequently observed on long-term field measurements (Köstner et al. 1998, Moore et al. 2010). The wound effect was indeed responsible for about two-thirds of the total SFD underestimations of wound-affected TD sensors when they were compared with the gravimetrical reference (Figures 3 and 4). These findings raise serious doubts not only about the estimations of the ecosystem water balance based on upscaled TD data, but also when determining the sensitivity of SFD to environmental variables at the medium and long terms.

The underestimations obtained here are well within published ranges from model simulations (Wullschleger et al. 2011). However, model results led to over- and underestimations, whereas the empirical results of this study always showed SFD underestimations. A possible reason could be associated with the extension of the wounded area beyond the perforation holes. The axial extensions of the wounds observed here were 292 ± 33 and 777 ± 63 mm² for TD sensors inserted in oak and beech, respectively (Marañón-Jiménez et al. 2014), which are much larger than the values reported for the heat pulse velocity method (3.14–15.20 mm²) and used in the model simulations of Wullschleger et al. (2011). In this wounded area around the point of probes insertion, the accumulation of gels, formation of tyloses and thickening of cell walls may obstruct the conductive vessels (Zimmermann 1979, Rioux et al. 1998) thus reducing hydraulic conductivity and heat transfer (Dimond 1955, Sun et al. 2008, Collins et al. 2009, McElrone et al. 2010). Actually, TD sensors also registered an increasing trend in night-time ΔT₀ values in the field (data not shown), likely as a result of the progressive wound healing isolation of TD sensors after their insertion. The extent of the physical and anatomical transformations is indeed directly linked to a reduction of sensor performance (Barrett et al. 1995, Wullschleger et al. 2011). The application of a constant heat source by the heated probes and the larger size of sensors in the TD method may lead to a more extensive wood physical transformation compared with other heat transfer-based techniques and hence intensify the effects of the wound reaction on SFD estimates.

In our experiment, AC sensors installed in cut stem segments, i.e., without wound reaction, measured ~14–28% lower flux densities than the gravimetric reference. This deviation falls within the range of underestimations reported in other studies, such as 3–27% (Reyes-Acosta et al. 2012), 14.3% (Häberle et al. 2013), up to 50% (Hultine et al. 2010) and even 60% (Steppe et al. 2010). Possible reasons have been attributed to species-specific differences of the empirical relation between sensor signal and SFD (Bush et al. 2010, Sun et al. 2011), to the radial and circumferential variability of sap flux within the tree (Gebauer et al. 2008) and to errors of the sensor location (Clearwater et al. 1999, Lu et al. 2004, Shin'ichi and Tadashi 2010). In any case, AC sensors in this study always detected a greater proportion of the real SFD than wound-affected sensors, which allowed us to discern the wound effect as an intrinsic reason for the underestimations of the TD method.

Time frame for wound effect development

The progressive wound development was reflected in the field data when wound-affected sensors installed previously were compared with freshly installed sensors (Figure 7). Differences between both sets of sensors were largest within the first days, presumably due to the still absent wound formation effects on the most recently installed sensors. The magnitude of the differences falls, in fact, within the range of the underestimations obtained in the laboratory experiment (Figure 5). As the wounding reaction also takes place in sensors installed more recently, SFD values get progressively closer until they (almost) converge. This may mark the point when wounds have reached an asymptotic extension, so we can set the time frame for the development of the wound bias to within the first 2 weeks after sensor installation. This period is consistent with the time span reported in other studies for wound development, e.g., 14–21 days in Smith and Allen (1996), 10–20 days in Swanson and Whitfield (1981) and 7 days after pruning in Sun et al. (2006). Considering this time frame, wounds would have already reached maturity in living tree stems around all sets of sensors at the moment of tree cutting, which explains why no differences were found between the sensors installed at different dates (spring, summer and fall sensors) in the laboratory validation experiment (Figures 3 and 4).

This time frame should be, nonetheless, considered as a first orientation to demarcate potentially wound-affected measurements. The rate of wound healing reaction might be influenced by several factors such as tree phenological status, climatic conditions, age, growth rate and sensor location (Liese and Dujesiefken 1996, Shortle et al. 1996, Dujesiefken et al. 1999, 2005, Sun et al. 2006, Moore et al. 2010). For example, injuries compartmentalize faster in spring when the physiological mechanisms involved in the defense and prevention of pathogens infections are fully active (Dujesiefken et al. 1999, 2005). The increased activity of parenchyma in the early growing season may promote an improved wound reaction due to a better formation of accessory substances (Dujesiefken et al. 2005). Higher temperatures may also facilitate a faster wound reaction, increasing the efficiency of tissue compartmentalization (Moore et al. 2010). As a mechanism involved in the wound healing reaction, tyloses formation occurred 30–45 days after injury in winter but already within the first 3 days during the growing season (Shibata et al. 1981). According to these factors, we would expect a less efficient and more extended wound reaction on injuries performed in fall. In addition, young trees (Shortle et al. 1996) and, in general, fast growth rates (Dujesiefken et al. 2005) are related to a faster injury repair. Tyloses development is also much slower in latewood and in the base than in the apical trunk (Sun et al. 2006). In summary, wound development and hence the consequent measurement errors may occur progressively along a variable time frame, which makes it difficult to predict the magnitude of inaccuracies at a particular time. This highlights the necessity for a feasible procedure to determine the time frame of wound development and the corrections needed to account for this relevant source of error.

Species-specific factors

A greater impact of the wound effect on ring-porous species has been associated with their wider vessels, which makes them more vulnerable to cavitation and microorganism invasion, and less efficient in embolism repair compared with diffuse-porous species (Liese and Dujesiefken 1996, Dujesiefken et al. 2005, Moore et al. 2010). When the sapwood is perforated for sensor installation, air comes into the damaged vessels through the drilled hole due to the under-pressure existing inside the vessels. The bigger vessels of ring-porous species are then more vulnerable to embolism and less capable of repairing from cavitation (Sperry and Sullivan 1992, Cochard and Tyree 1990). Air bubbles inside caveated vessels reduce the heat transfer between water in the xylem stream and the thermocouples of the sensor, leading to an apparent decline in the measured flux (Moore et al. 2010). Moreover, vessels affected by irreversible cavitation suffer a series of anatomical transformations that isolate the injured area, preventing pathogens colonization and further embolism (Zimmermann 1979, Cochard and Tyree 1990, Dujesiefken et al. 1999). The accumulation of phenols and pectic substances (gels), tyloses formation and thickening of cell walls can occlude partially or totally the vessels, leading to an irreversible reduction in the hydraulic conductivity of the affected tissue (Zimmermann 1979, Rioux et al. 1998, McElrone et al. 2010). Accordingly, SFD measured by sensors surrounded by a wounded tissue is expected to be directly related to the extension of the caveated vessels and to the anatomical processes involved in the wound healing reaction. Several experiments using either staining or microscopy have detected the wound formation beyond the point of the insertion probes of heat pulse sensors and have found a direct relation between the extent of the physical and anatomical transformations and sensor accuracy (Barrett et al. 1995). Vulnerability to irreversible cavitation and the subsequent anatomical changes are also genetically determined (Biggs 1987, Saitoh et al. 1993). Impacts on the accuracy of invasive sap-flow sensors due to the physical disruption encountered when drilling holes and the subsequent wound anatomical transformation may then be strongly species dependent.

We could not find, however, consistent differences on the sap flux underestimations between oak (ring-porous) and beech (diffuse-porous), but we cannot reject the hypothesis of species-specific differences on the wound formation and subsequent measurement errors, since the experimental calibration of TD sensors in oak has large uncertainties. The thin sapwood of one of the oak trees tested (0.54 cm depth) did not allow a good comparison with gravimetrical measurements despite the implementation of the Clearwater correction (Clearwater et al. 1999), which has probably limited applicability if only one-third of the sensor length is in contact with conducting tissue. This shortcoming is reflected in the data by lower accuracy also shown by AC sensors, low correlation coefficients with the reference gravimetrical flux, larger intercepts and higher estimation errors of the linear regressions parameters, similar to what Bush et al. (2010) observed for several ring-porous species. Further investigations are still needed in order to determine the vulnerability to wound-related uncertainties of different species on the SFD measured with invasive sensors.

Recommendations to improve the accuracy of the TD method in the field

The timing and magnitude of the wound reaction after sensor installation may be influenced by many factors such as species, tree phenology, tree age, growth rate, climatic conditions, sensor size and location, and sap flux rates (Shortle et al. 1996, Dujesiefken et al. 1999, 2005, Moore et al. 2010). It is therefore questionable to apply a general empirical correction, which was derived in the laboratory such as presented here, to data in the field. A laboratory calibration for each particular case is, on the other hand, very laborious and in most cases not feasible due to logistic reasons or lack of infrastructure. We therefore present here an alternative and feasible approach to establish the wound correction needed for a given species in any particular forest stand.

The assumption underlying this approach and confirmed by data presented here is that TD probes estimate the correct SFD in the first few days after sensor installation and SFD estimates gradually decrease to biased, lower values within a few weeks as wounds develop around inserted sensors. The effects of wound formation on SFD estimates seem to change mainly in the first 2–4 weeks after installation (this study, Swanson and Whitfield 1981, Smith and Allen 1996), a period after which a further wound extension, if any, does not add further bias on sensor measurements. In order to estimate the bias resulting from wounding, we therefore recommend installing several sets of sensors sequentially in time instead of installing all sensors at once. The detailed approach presented here counts on several steps:

• A first set of sensors is installed in living trees early in the growing season at time t₁, SFD₁(t₁), where the subscript 1 indicates the first set of sensors (Figure 8). These sensors will exhibit a wound effect and hence give biased, low estimates of SFD after several weeks dt₁: SFD₁(t₁ + dt₁). The number of replicate sensors to install per sampling date depends on the variability of SFD within and between trees, which varies according to the characteristics of the study site, sapwood depth and tree species (Oren et al. 1998, James et al. 2002, Kumagai et al. 2005, Saveyn et al. 2008, Tsuruta et al. 2010, Kume et al. 2012). Ring-porous species with narrow sapwood may need particularly larger numbers of replicate sensors, since errors associated with sensor location may result in higher spatial variability (Oren et al. 1998, Clearwater et al. 1999). We recommend performing a pilot study ahead to obtain an estimation of the SFD variability within and between trees and estimate from this the required numbers of sensors (Quinn and Keough 2009).

• A second set of sensors is then installed around 4 weeks later (at time t₂) in the same trees (Figure 8). These sensors should record the correct SFD during the first few days, SFD₂(t₂), and then exhibit slowly decreasing SFD due to the wound effect, similar to the first sensor set.

• The decreasing trend in SFD associated with the wound formation might well be overshadowed by increasing or decreasing SFD due to changing environmental conditions. We therefore propose to use PT (Eq. 3) to select times with very similar meteorological conditions and hence similar transpiration rates. Here we used a definition of potential, non-water limited transpiration for selection because actual transpiration rates are not known, or rather the target is variable. This also takes into account the correlation between the meteorological variables. Filtered SFD data should clearly reveal the progressive drift on the second set of sensors, i.e., SFD₂, when they are compared with the first sensors with already fully developed wounds, i.e., SFD₁.

• Once wounds have also developed (at time t₂ + dt₂) on the sensors installed more recently, a similar wound effect will bias all SFD estimates, so that sap flux values from both sets of sensors will converge, i.e., SFD₁(t₂ + dt₂) ~ SFD₂(t₂ + dt₂) (Figure 8). Nonetheless, final SFD estimates from different installations might still differ due to the intrinsic spatial variability of sap flux. This may be especially true for narrow xylem trees, due to slight variations in the length of the sensor inserted within the sapwood (Oren et al. 1998, Clearwater et al. 1999). In our case, there was a 7% offset in sap flux rates between spring (SFD₁(t₂ + dt₂)) and summer (SFD₂(t₂ + dt₂)) installations (Figure 7), which is well within observed sap flux variations between trees (Köstner et al. 1998) or at different points in one tree (Saveyn et al. 2008). Calculating a correction factor using the differences between both sensor sets could, therefore, introduce some systematic bias. We therefore recommend using the first sensors only as a reference, wound-affected estimate to determine the time frame (dt₂) of the wound reaction in the second set of sensors, i.e., when the asymptotic values from both sensor sets ‘almost’ converge or SFD₂(t₂ + dt₂)/SFD₁(t₂ + dt₂) = constant (Figure 8). The correction for the second sensors should then be calculated using the ratios of the values at the beginning of installation (leaving out probably the first day for signal stabilization) to the asymptotic values after a few weeks, corrected for any trend still present after filtering for potential transpiration. Therefore, the wound correction for the second set of sensors is

  $$c_2=\frac{{\mathrm{SFD}}_2\left(t_2\right)}{{\mathrm{SFD}}_2\left(t_2+{\mathrm{d}t}_2\right)}$$

  and, in order to correct sap flux estimates, SFD₂ will be multiplied by c₂ after the time point t₂ + dt₂.

• The magnitude of wound bias and the time frame for wound development might be influenced by tree phenology. We therefore recommend installing another, third set of sensors 4 weeks later (SFD₃). The procedure of data selection and filtering is the same as for the second set of sensors (Point (iv)) as well as the calculation of the wound effect correction c₃. Both, the first and second set of sensors can be used at this point as wound-corrected estimates of SFD.

• Finally, the mean $\bar{c}$ of all correction factors from the second and third set of sensors will be used to correct the SFD estimates from the set of sensors installed first (Point (i)), i.e., SFDc₁ = $\bar{c}\times$SFD₁ after the time point t₁ + dt₁, where $\bar{c}$ is the average of all correction factors for each individual sensor of the second and third installations.

Summary and conclusions

Invasive SFD measurements can exhibit considerable underestimation of actual SFDs. The causes of this measurement bias have not been identified for the TD method despite its widespread use. The study presented here identified wound healing in response to sensor insertion within living tree stems as one of the most important sources of errors associated with the TD method. Laboratory as well as field observations showed that the wound reaction led to a 21–47% underestimation of SFD. This bias appeared progressively after sensor installation and reached its maximum after about 2 weeks. The wound effect is likely influenced by climatic conditions, phenology and tree species, among others, so that a general implementation of the observed correction factor is probably not advisable. We propose instead an easy and practical approach to detect and account for the wound effect in field observations: an initial installation of sap-flow sensors serves as reference to determine the time frame of wound development. The influence of the wound reaction on SFD can then be observed by selecting times with potentially similar sap flux ranges and comparing with the newly installed sensors. Sap flux values can then be corrected by using the initial and the final converged values of each sensor. This avoids biasing toward the specific sample of the reference installation.

This study represents a crucial step forward toward more accurate sap flux measurements with the TD method. The approach should, however, be independent of the observational method and be applicable to other invasive sap-flow techniques as well. Further investigations might be warranted to better understand the influence of the wound reaction on SFD measurements, including species-specific wood anatomical transformations, their spatial extent and functional significance in relation to the accuracy of TD sensors.

Acknowledgments

We thank the members of the field-research groups of the Max Planck Institute for Biogeochemistry, Jena and the Chair of Bioclimatology of the University of Göttingen, the forestry office of Leinefelde for their support with cutting the trees and Dr Martina Mund for providing inventory data of the field site. Special thanks go to all members of the field-research group of the UFZ Department Computational Hydrosystems for their support during field and laboratory experiments, in particular to Arndt Piayda, Martin Schrön, Hendrik Zöphel and Sebastian Gimper.

Conflict of interest

None declared.

Funding

German Federal Ministry of Education and Research—INFLUINS—(03 IS 2001A); Andalucía Talent Hub Program to S.M.J., launched by the Andalusian Knowledge Agency, co-funded by the European Union's Seventh Framework Program, Marie Skłodowska-Curie actions (COFUND - Grant Agreement 291780) and the Ministry of Economy, Innovation, Science and Employment of the Junta de Andalucía.

Author notes

These authors contributed equally to this work.