Introduction

The thermal dissipation probe (TDP) method invented by Granier (1985, 1987a) is widely used to estimate individual tree and forest stand transpiration (Granier 1987b; Andrade et al. 1998; Oliveras and Llorens 2001; Fiora and Cescatti 2006; Lüttschwager and Remus 2007; Chu et al. 2009), owing to its simplicity, sensitivity and low cost. This technique is based on the temperature difference (ΔT) between a heated probe (settled downstream) and a reference probe (settled upstream) (Fig. S1). The sap flow carries heat away from the heated probe and, thus, ΔT becomes smaller with an increase in flux. When there is no sap flow, the temperature difference reaches the maximum difference (ΔTm). Granier (1985, 1987a) developed an empirical formula to calculate the sap flow based on a relationship between sap flow and a dimensionless coefficient k:

$$ F = a\, \times \,k^{b} ;\quad k = \frac{{\Delta T_{\text{m}} - \Delta T}}{\Delta T}, $$

where F is the sap flux density (kg m−2 s−1) and it can be calculated through the weight variation on a balance (kg) per unit of sap wood area (m−2) and per unit of time (s−1) directly; a = 0.119 and b = 1.231; k is a dimensionless coefficient related to the temperature difference between the heated and a reference probe.

The TDP technique was originally validated with three tree species (Pseudotsuga menziesii (Mirb.) France; Pinus nigra J. F. Arnold; Quercus robur L.) and was claimed to be independent of tree species or wood anatomy (Granier 1985; Granier et al. 1990). This claim has been supported by results that the heat dissipation estimates of water use compare well with estimates from different sap flow techniques and other methods (Diawara et al. 1991; Köstner et al. 1998; Mcculloh et al. 2007). However, some uncertainties and limitations have also been found to cause errors and influence the measurement accuracy. Two main error sources are radial nonuniformity in the conduit diameter and density distribution and temperature gradients in the stem (Köstner et al. 1998; Clearwater et al. 1999; Lu et al. 2004). Sap flux densities would be underestimated by TDP when radial sap velocity gradients along the probe are present (Clearwater et al. 1999; James et al. 2002; Steppe et al. 2010). Recently, Bush et al. (2010) found that TDP with Granier’s original calibration considerably underestimated the sap flux density in four ring-porous species. These errors were mainly attributed to the shallow sap wood depth and the seating of the probe in non-conducting wood. Sun et al. (2012) reported, however, that ring-porous species are less underestimated with Granier’s original calibration formula than diffuse species and conifers. Xylem conduit diameter and density determine the hydraulic conductance (Tyree and Zimmermann 2002). Information on the conduit diameter and density distribution would be crucial for understanding these discrepancies (Swanson 1983; Green and Clothier 1988), but as yet there have been no studies on the association between the TDP measurement accuracy and the anatomical characteristics of different wood types.

The TDP method is based on the thermal conduction and convection between sap flow, a heated probe and the surrounding wood matrix (Granier 1985). Therefore, a natural temperature gradient in the xylem could influence the ΔT that is measured by the probes (Köstner et al. 1998; Do and Rocheteau 2002). The ΔTm measurement could be one of the main sources of error in the TDP estimation of sap flow and could be significantly influenced by temperature differences between the probe and the surrounding wood matrix (Köstner et al. 1998; Do and Rocheteau 2002; Regalado and Ritter 2007). The ΔTm measurement is usually conducted before dawn, when the sap flow is believed to have stopped. The environmental temperature at night, however, is naturally lower than during the day. The thermal conductivity of water and the water-saturated xylem matrix varies with temperature (Pitts and Sissom 1998). Although much attention has been paid to whether the sap flow at predawn has completely stopped or not (Regalado and Ritter 2007), it is not yet clear whether the temperature fluctuations between night and day influence the ΔTm measurement.

The concentration of ions such as potassium in the perfusing deionized water is well known to influence xylem hydraulic conductance (van Ieperen et al. 2000, Zwieniecki et al. 2001). In a preliminary experiment, we found that the xylem hydraulic conductance would be reduced when perfusing ethanol solution. The thermal conductivity of water can be reduced by adding salt and ethanol (Abu-Hamdeh and Reeder 2000). The TDP method is based on thermal conduction and convection between flowing sap, trunks and probes (Granier 1985). The composition of the sap could thus influence its thermal conduction and convection, but this variable has not yet been tested.

In this study, a calibration experiment on two ring-porous species, two diffuse-porous species and two conifers was conducted. The objectives were: (1) to compare the measurement accuracy of the TDP technique in species with different wood types and to investigate the relationship among accuracy, conduit diameter and density distribution; (2) to test the effects of different environmental temperatures on the measurement accuracy and ΔTm; (3) to investigate whether perfusing fluid composition influences TDP-based sap flow measurement accuracy.

Materials and methods

Plant collection site

Six tree species were selected, including two ring-porous species (Quercus variabilis Blume and Robinia pseudoacacia L.), two diffuse-porous species (Platanus orientalis L. and Populus tomentosa Carr.) and two conifers (Platycladus orientalis (L.) Franco and Pinus bungeana Zucc.). All plant materials except for P. bungeana were collected from the Xiaolangdi forest ecosystem observation station in Jiyuan of the Henan province (35°01′N, 112°28′E), China. The average annual temperature and precipitation values are 12.4–14.3 °C and 641.7 mm, respectively. The main vegetation types are broadleaf trees, conifers, shrubs and brush. P. bungeana was collected in the courtyard of the Chinese Academy of Forestry, Beijing, China.

Sap flow rate measurements

Stem segments (over 40 cm in length and 30–35 mm in diameter) lacking apparent scars were cut with a handsaw in the morning, immediately immersed in deionized water and brought back to the laboratory within half an hour. The segments were then cut to 20 cm in length, and both ends were shaved with a sharp carpenter plane. The bark of the upstream end of the segment (natural morphological lower end) was peeled away with a knife to prevent any water movement through the bark. All of the above operations were conducted under water and as quickly as possible. Each segment was connected to a low-pressure flow meter (LPFM) (Sperry et al. 1988) with the rubber compression seal of a HPFM (high-pressure flow meter, Dynamax HT, USA). Then, a rectangle of bark was removed, and two Granier style probes (10 mm in length, with the same distance between heater and reference needle, same dimension) were inserted into the stems opposite each other with the aid of an electric portable drill. A lanoline paste prevented the sap from leaking. The probes were connected to a data logger (RR1008, Yugen, Beijing, China). Temperature differences between the heated probe and the reference probe were monitored, and the mean values were recorded every 1 min. Information on the selected stems is presented in Table 1.

Table 1 Wood type, stem diameter (mean ± SD) and number of plants of the six species used
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An LPFM measurement of water flow was undertaken under gravity-induced pressure gradients (Sun et al. 2011). The surface level of a solution was set to a height that would provide the necessary hydrostatic pressure to drive a filtered (0.4 μm) 25 mmol l−1 KCl solution through the stem segment. The efflux was continuously collected through a piece of plastic tubing into a vial placed on a 0.0001 g balance (AR2140, Ohaus, Parsippany, NJ, USA) connected to a computer running the LPFM software.

Experimental design

Different sap flux density

A hydrostatic pressure gradient from 1 to 6 kPa was applied stepwise by changing the water source height to obtain a range of sap flux density values for each stem segment. The flow rate was measured at room temperature. Each measurement lasted for at least 15 min after the TDP-measured ΔT reached a steady state. For P. bungeana, negative pressure was applied with a vacuum pump to obtain a greater pressure difference and faster sap flux.

Temperature of the environment

The stem segment was packaged tightly with a plastic bag, submersed in a water bath, and surrounded by a copper coil connected to a circulating cooling system to maintain the desired temperature (± 0.1 °C). About two extra meters of input tubing were coiled and submersed in the water bath to equilibrate the input solution at the same temperature as that of the water bath before flowing into the segment. The environmental temperature was changed in steps from 25 to 20 °C, 10, and 0 °C. A hydrostatic pressure of 4 kPa was applied and maintained during the measurements. Sap flow density and flow rate were monitored for at least 15 min after the TDP-measured ΔT reached steady state. The ΔTm under different temperatures was recorded for 60 min at zero sap flux.

Perfusing fluid composition

Three different solutions (25 mmol l−1 KCl, deionized water and 30% ethanol) were selected to test whether the perfusing medium has any effect on the TDP measurement. The three solutions were applied to each stem segment with a constant pressure gradient. The sap flow rate for each solution was monitored for at least 15 min after the TDP-measured ΔT reached steady state.

Determination of sap wood area, conduit diameter and density

After obtaining all the measurements, we used a silicone rubber injecting method described by Sperry et al. (2005) to determine the sapwood area, xylem conduit density and diameter for the six tree species. Briefly, silicone rubber was freshly made by mixing liquid silicone and hardener at a ratio of 10:1 (10 g RTV141 Part A plus 1 g RTV141 Part B) (Rhodorsil RTV 141, Cranbury, NJ, imported by Walco Materials, Escondido, CA). Uvitex, a fluorescent whitening agent (Ciba Uvitex OB, Ciba specialty Chemicals, Tarrytown, NY), was dissolved in chloroform (1% w/v) and then added to the silicone to make it visible under UV light. The stems were injected with silicone at 0.05 MPa for 24 h. Then, the silicone was allowed to cure (harden) for 3 more days at room temperature (20 °C) prior to sectioning. The cured stems were cross-sectioned at a distance of 2.0 mm from the injection surface. The density and diameter of the conduits were measured under a fluorescent microscope. The stems of the young trees did not form real heartwood, except for R. pseudoacacia, which had an apparent heartwood part (pith area) that was impermeable for water (Table 3). The stem cross area was used for the other five species to calculate sap flux density, whereas the sapwood area of R. pseudoacacia was used for this calculation.

Statistical analysis

The sap flux density measured by the TDP (FTDP) was calculated with the original empirical formula established by Granier (1985). The sap flux density measured by the LPFM (FLPFM) was calculated using the LPFM software. Underestimation (%) = [(FLPFM − FTDP)/FLPFM] × 100%.

The results were analyzed using an ANOVA with Duncan’s multiple comparisons and the mixed procedure of the SAS version 8.0 software package (SAS Institute Inc., Cary, NC, USA). All statistically significant differences were tested at the p = 0.05 level.

Results

Calibration of thermal dissipation probes

Plotting the sap flux densities determined by LPFM against k yielded a calibration formula with a least-squares power equation for the six species (Fig. 1). The values of the two parameters (a and b) obtained from this experiment deviated to different degrees from that of the original formula (a = 0.119, b = 1.231) established by Granier (1985). The discrepancy was most pronounced in the two ring-porous species (Q. variabilis and R. pseudoacacia), followed by the two diffuse-porous species (P. tomentosa and Platanus orientalis). The two conifers had parameter values that were relatively similar to those determined with Granier’s. The new formulae for the six species were able to well describe the relationship (R2 = 0.77 – 0.98) between k and the sap flux density in a certain range (> 0.01 kg m−2 s−1).

Fig. 1
figure 1

Relationship between k and the real sap flux density (kg m−2 s−1) measured by LPFM (solid curves). The solid curves were fit with a least-squares power function. The dashed curves represented the original Granier’s formula

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For all species, the Granier equation underestimated the sap flux density measured by the LPFM method to various degrees. The extent of underestimation varied according to species and sap flow (Fig. 2). The two ring-porous species were most underestimated, followed by the two diffuse-porous species, and then the two conifers. The underestimation values in the two ring-porous species were relatively stable and high, whereas in the other four species, they were high only in the low sap flux range and relatively low at high flux. The extent of underestimation reached as high as 70–95% in the ring-porous species or in the other species at very low sap flux density. As the sap flux density increased, the extent of underestimation decreased and was very low for a period of time in the diffuse-porous species and the conifers. The ring-porous species also adapted the new formulae not well (R2 = 0.77, 0.86) compared to other two wood types. We also observed a fairly high degree of variation between stems obtained from different trees of the same species. Although there was a similar pattern of variation across all six species, the absolute values for the underestimation were different for the three sets of samples (varying pressure, temperature and media) of the same species (Figs. 2, 3, 4).

Fig. 2
figure 2

The underestimation of sap flux density by TDP with Granier’s equation compared to the LPFM method. The sap flux density in the x axis was measured with LPFM

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Fig. 3
figure 3

The curves exhibit changes in the sap flux density, measured by TDP and LPFM, according to the environmental temperature decreasing from 25 to 0 °C. The vertical bars show changes in the underestimation of Granier’s equation of the TDP method. Means and SE (standard error of the mean) are shown for n = 4–6. UE refers to the underestimation

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Fig. 4
figure 4

The underestimation values of the TDP method with Granier’s equation (a) and sap flux density (b) in the three perfusing media (25 mmol l−1 KCl, deionized water and 30% ethanol). The sap flux density of each stem with 25 mmol l−1 KCl were normalized to 100%, and the sap flux density of the other two solutions was normalized accordingly. Mean ± SE (standard error of the mean, n = 4–6) values are shown

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Environmental temperature effect

In all six species, when the environmental temperature was lowered stepwise from 25 to 20 °C and 10 °C, both FLPFM and FTDP declined while the TDP underestimation remained unchanged (Fig. 3). When the temperature was further reduced to 0 °C, however, the underestimation was significantly (p < 0.05) reduced and almost disappeared for all species except R. pseudoacacia. The FTDP for P. bungeana and P. tomentosa was even slightly higher than the real sap flux density measured by LPFM. FLPFM and FTDP declined with decreasing temperature in a more or less parallel manner from 25 to 10 °C, although the reduction of FTDP was less, especially for the two ring-porous species.

There were no significant differences in the ΔTm detected by TDP at the different environmental temperatures from 25 to 0 °C for all three measured species (Table 2). The ΔTm of Q. variabilis was significantly smaller than in the other two species (R. pseudoacacia, and Platycladus orientalis). As environmental temperature was decreasing, however, there was a clear increase in ΔTm observed in this experiment; the more rapidly the temperature changed, the greater ΔTm became.

Table 2 The ΔTm (°C) measured by TDP at different environmental temperatures for three species
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Perfusing fluid composition effect

The extent of underestimation in 30% ethanol was slightly greater than that in 25 mmol l−1 KCl and deionized water in all six species except for R. pseudoacacia, in which the extent of underestimation was the same for all three media. These differences were not statistically significant, however, except for P. tomentosa, for which there was a significant difference observed in the underestimation in the three different solutions (p < 0.05, Fig. 4a). The sap flux density varied in the three different media, with the 25 mmol l−1 KCl solution having the greatest density, followed by deionized water and then 30% ethanol (Fig. 4b).

Characteristics of the conduit density and diameter distributions

The densities and diameters of conduits declined from the outermost layers to the innermost layers in all six species (Table 3). In the outermost 5 mm, the diameter of the conduits was the largest and the density was the lowest. The ring-porous species had the largest vessel diameters and the lowest densities, whereas the conifers had the smallest diameters and highest densities of tracheids, with the vessels of the diffuse-porous species in the middle. R. pseudoacacia had an apparent heartwood part (pith area) without any vessels.

Table 3 The conduit density and diameter distributions from the outermost layer to the pith in six species
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Discussion

Effects of conduit characteristics and flow rates

In this experiment, the sap flux was underestimated by the TDP method using the original Granier’s formula to various degrees compared with the LPFM method in the six tree species. Our results are consistent with previous reports (Clearwater et al. 1999; Bush et al. 2010; Steppe et al. 2010; Wullschleger et al. 2011). The degree of underestimation varied mainly according to wood type, with conifers < diffuse-porous < ring-porous (Fig. 2). Using the new calibration formulae, the results become much better. The new formula worked the best for the conifers, followed by the diffuse-porous species, and then the ring-porous species. Depending on this to obtain more accurate sap flux as possible as we can in practice, some tips need to be paid more attention. The heat removal from the heated probe by sap flow depends on how close the probe is seated to the conduits (Swanson 1983; Smith and Allen 1996; Steppe et al. 2010) and how large the conduits that the probe allocates are. In a work on kiwifruit vines, Green and Clothier (1988) found that the heat pulse method substantially underestimates the flux; this discrepancy was attributed to the anatomical structure of the kiwifruit, which has large xylem vessel diameters (0.1–0.5 mm) and interstitial distances (0.1–0.8 mm). A longer time for thermal equilibration between the sap and woody matrix is needed with larger distances between the probe and the xylem conduits. According to the Hagen–Poiseuille law, the hydraulic conductivity of the conduits is proportional to the fourth power of the conduit radius (Tyree and Zimmermann 2002). To a large degree, the bigger conduits determine or contribute more to the sap flux density (Dichio et al. 2013). Considerable variations were observed in conduit diameter and density between the six species and a radial variation in the conduit lumen area and distribution (Table 3). Because the gradient of diameters from the outer to inner xylem is universal, and the larger conduits determine the hydraulic conductivity and sap flow density, the shorter probes may be safe and better for measuring sap flow density regardless of wood styles from theoretical viewpoint. The ring-porous species have the lowest density of vessel pores and the largest pore diameter (Table 3). The probe has a greater chance of seating in a location that is relatively far from the large vessels; therefore, there is a higher chance for the TDP to underestimate sap flow for ring-porous species even after new calibration. So, more than one probe needed to measure the sap flux for a stem in field and the fastest flux may be chosen instead. For R. pseudoacacia, a ring-porous species, only the 1- or 2-year xylem was active, and the conducting zone was very narrow, as reported by Bush et al. (2010). The mean active sapwood width was 2.27 ± 0.28 mm, and beyond this range, there were no vessels. Therefore, most of the 10 mm probe was seated in the no sap flow zone, and the ΔT in this zone was close to the ΔTm defined by Granier (1985). As a result, the underestimation in R. pseudoacacia was the greatest, and the error might override any influences from other sources of error, such as sap flux density, environmental temperature and perfusing fluid composition. So, it is necessary to determine the sapwood of the stems to choose the proper probe length (Fig. S1). Additionally, as Bush et al. (2010) reported, it was impossible to correct the calculation of the sap flux density with the method described by Clearwater et al. (1999), because the active sapwood was too narrow. There were also big vessels and low vessel density in Q. variabilis, another ring-porous species; the diameter varied significantly in the radial direction, which could contribute to the radial variation in sap flux density and thereby result in substantial errors in sap flow measurements with the TDP method (Clearwater et al. 1999; James et al. 2002). As expected, the two diffuse-porous species had larger diameters and smaller densities of xylem conduits than the conifers (Table 3). A higher density of conduits could produce a more uniform laminar flow over a given cross area, which could explain the smallest underestimation in the conifers.

The measurement accuracy was also influenced by the sap flux density. The underestimation of the actual sap flux density by the TDP method (even using the new calibration formulae) was more pronounced in the low sap flux density regime of the diffuse-porous species and conifers (Fig. 2). When sap flow is small (about < 0.01 kg m−2 s−1, may be different depending on wood types), the transverse heat exchange between the probe and the surrounding woody matrix could be fairly significant and interfere with the longitudinal thermal convection caused by the sap flow. When the sap flux density is large enough (about > 0.01 kg m−2 s−1), the longitudinal thermal conduction and convection, which is what the TDP method is based on, are dominant, and the error caused by transverse thermal exchange is eliminated. Therefore, the TDP method may be only applied in a certain sap flux range and for different species this range may differ. The interference from the transverse thermal exchange would be associated with the variation in wood properties. The two conifers had the most significant differences in the underestimation at low sap flow, followed by the two diffuse-porous species. The underestimation of the two ring-porous species, especially R. pseudoacacia, was not significantly reduced at higher sap flux density. Thus, wood with a low density and large diameter of vessels in the ring-porous species could dominate the measurement underestimation by TDP.

Effects of environmental temperature and perfusing fluid composition

Heat storage in the stem and differences in heat conductance between day and night could falsify the zero-flux determination and ΔTm measurement (Köstner et al. 1998). ΔTm is recognized as one of main sources of error in the TDP estimation of sap flow (Köstner et al. 1998; Lu et al. 2004; Regalado and Ritter 2007). In field measurements of sap flow with TDP, ΔTm is usually measured at predawn once the sap flow is believed to have stopped. However, the thermal conductivity of water and the water-saturated xylem matrix could be reduced with decreasing temperature (Pitts and Sissom 1998). Therefore, ΔTm values could vary according to environmental temperature. The environmental temperature at night is usually far lower than during the daytime. If the ΔTm significantly varies with environmental temperature, the ΔTm measured at night would not be suitable for measuring the temperature difference between the heated probe and the reference probe in the daytime.

Between 0 and 25 °C, ΔTm was not found to be significantly different in three studied species (Table 2). This result indicates that the measurement of ΔTm at nighttime is valid, but a significant increase in ΔTm was found when the environmental temperature was changing from high to low in the experiment, indicating that the metal probe exhibited a greater thermal conductivity and more rapid change in temperature than the xylem wood matrix. The heated probe lost less heat to the surrounding wood matrix when it was warmer than the probe before heating. This observation suggests that the prompt changes in environmental temperature, which causes temperature gradients between the heated/unheated probe and the wood matrix, significantly influence the ΔTm and ΔT measurements. This result agrees with the report of Do and Rocheteau (2002).

As expected, the sap flux density declined with decreasing temperature likely due to changes in water viscosity (Wan et al. 2001). The temperature change from 25 to 10 °C did not alter the underestimation of the sap flow by TDP (Fig. 3). To our surprise, at 0 °C, the difference in the sap flow measured with TDP and LPFM disappeared in all of the studied species except R. pseudoacacia. The mechanism underlying this result is unclear.

The thermal conductivity of water can be reduced by adding KCl and ethanol (Abu-Hamdeh and Reeder 2000). However, this change in thermal conductivity did not significantly alter the underestimation of the sap flux density by TDP in any of the species. It appears that the changes in the thermal conductance and convection were not large enough to alter the temperature determination by TDP. In contrast, the additions of KCl and ethanol into perfusing deionized water were found to differentially change sap flow, with KCl increasing the flow and ethanol decreasing the flow. The changes in sap flow rate played a role in the underestimation of TDP: a negative relationship observed between the sap flow and the underestimation in most species, particularly in P. tomentosa.

Conclusion

This study demonstrates that the original TDP calibration equation provided by Granier (1985) is not universally applicable to all woody species. We found that anatomical features of the xylem, including sap wood depth, radial diameter, and the density distribution of conduits, influence the original calibration. Results show that the TDP technique with Granier’s original equation underestimated the sap flux density to various degrees in six species of three wood anatomical types. R. pseudoacacia, a ring-porous species, possessed a shallow sap wood depth that was less than the probe length, and its calibration deviated by at least 60% from the original calibration. Our calibration results for two conifers, with small diameters and high densities of tracheids, were consistent with Granier’s calibration within 30%. Because of the larger diameters and lower vessel densities in the two diffuse-porous species, however, the original calibration significantly underestimated sap flow. As expected, the two ring-porous species had the largest diameters and lowest densities of vessels; accordingly, the estimates obtained with the original equation deviated substantially from the actual sap flux density. Therefore, when using the TDP method, a new calibration is highly recommended for each species together with the sapwood depth determination and more probes may be applied for one stem in the field to obtain the more exact sap flux.

Environmental temperature drop from 25 to 0 °C did not result in different ΔTm values, verifying that a ΔTm measured at night is a valid reference for ΔT in daytime. The composition of potassium and ethanol in the perfusing deionized water did not alter the measurement accuracy with TDP, suggesting that the technique is independent of fluid ionic or organic strength at least in the present experimental conditions.