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Summary Sapflow sensors were used to investigate vari-ation in sapflow velocity at different positions in the sapwood of three-year-old Eucalyptus globulus ssp. globulus Labill. trees. Sapflow velocity was measured at 5-mm intervals across the sapwood by moving two probe sets simultaneously on two opposite radii. Another probe set placed in a fixed position at right angles to the first two sets acted as a control. A sapflow velocity ratio was defined as the velocity given by each moving sensor divided by that given by the static sensor. Correlation between observations of sapflow velocity at different positions exceeded 95%, and the ratio of velocity between any pair of sensors was constant.

We observed radial variation in sapflow velocity across the sapwood with the lowest velocities at the center of the tree. Variation due to sensor position was high implying the need for large numbers of sensors for accurate estimates of sap flux. To overcome this need, we used a correction coefficient, namely a simple weighted average of the sapflow ratios with depth in the sapwood, for each fixed sensor. We recommend the use of three probe sets to estimate the correction coefficient. Sub-sequently, two probe sets can be placed at two fixed positions for routine measurements of sap flux.

Keywords: heat pulse velocity, sapflow sensor, sap flux, tran-spiration, xylem.

Introduction

Direct measurements of transpiration by heat pulse velocity have been considerably improved by the development of meth-ods for rapid and more accurate point estimates of sapflow velocity. However, because the nature of the sapwood varies widely with depth in a variety of tree species including Euca-lyptus (Dunn and Connor 1993), estimates of sap flux for a tree based on point samples may seriously depart from the true sap flux through the xylem. As a result, the greatest potential source of error in estimating stand transpiration with this

method is in the measurement of sap flux of individual trees (Hatton et al. 1995). The aim of this study was to develop a technique for measuring sap flux in E. globulus with a mini-mum number of sensors.

The use of a heat pulse as a tracer to measure transpiration in sapwood was proposed by Huber (Huber 1932, Huber and Schmidt 1937). The compensation method of Marshall (1958) was the first quantitative treatment to account for the physical presence of implanted sensors in the sapwood. When used in conjunction with numerical models that correct for the effects of wounding (Swanson and Whitfield 1981), the compensation technique can provide accurate point estimates of sapflow velocity. However, because sapflow velocity is known to vary throughout the sapwood, with peak velocity occurring 10--20 mm in from the cambium (Swanson 1967, 1974), esti-mates of sap flux based on point estiesti-mates of sapflow velocity need to account for this variation.

Sampling at several depths in the xylem with integration throughout the conducting area is one method for estimating sap flux. A least-squares polynomial can be fitted to point estimates of sapflow velocity and the function integrated across the sapwood conducting area and around the bole to obtain actual sap flux (Cohen et al. 1981, Green and Clothier 1988). An alternative method is based on a weighted average of sapflow velocity with depth (Hatton et al. 1990, 1992). For fast-growing Pinus patula Schlecht et Cham., particularly in the earlier stages of growth, sapflow velocity shows a cyclical pattern, with maxima and minima correlated with summer and winter wood, respectively (Dye et al. 1991). The use of several sensors to account for this variation during routine measure-ments is not practical.

We have investigated the variation in sapflow velocity across the radial profile of the sapwood of fast-growing E. globulus. The results were used to develop a correction coefficient for obtaining accurate estimates of sap flux from routine point measurements of sapflow velocity using two sets of sensors.

Variation of sapflow velocity in

Eucalyptus globulus

with position in

sapwood and use of a correction coefficient

DAOQUN ZANG,

1

C. L. BEADLE

2

and D. A. WHITE

2

1

Chinese Academy of Forestry, Beijing 100091, P.R. China

2

CSIRO Division of Forestry and Cooperative Research Centre for Temperate Hardwood Forestry, Locked Bag No. 2, Sandy Bay, Tasmania 7005, Australia

Received March 6, 1995

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Materials and methods

Sensor and theory

Measurements of heat pulse velocity were carried out with sapflow sensors (Model SF100 Greenspan Technology, Queensland, Australia). Three vertically aligned holes were drilled at each measurement position with a drilling jig to ensure that the holes were parallel. The probe sets, which included two stainless steel tubes located 10 mm above and 5 mm below a heater tube, were inserted into the holes. Each probe set included two thermistor pairs (Figure 1). One ther-mistor from each pair was housed in each stainless steel tube and the thermistors were spaced 5 mm apart within the tube. The thermistor pairs were connected in a Wheatstone bridge configuration and adjusted to zero output at intervals during the measurement period. The logger was programed to apply a heat pulse of 0.8 s duration.

Heat pulse velocity (u) was measured by the compensation technique (Swanson and Whitfield 1981). Sapflow velocity (V) was calculated after Swanson and Whitfield (1981), Mar-shall (1958) and Dunlap (1912) as described by Olbrich (1991).

Experimental Procedure

The measurements were made between February and May 1993 at an experimental plantation near Lewisham in southern Tasmania, Australia (Honeysett et al. 1996). The trees were from selected families of the King Island provenance of Euca-lyptus globulus ssp. globulus Labill. and located in a plot that was irrigated to maintain soil water deficits at approximately 30 mm below field capacity. At this soil water deficit, growth was not limited by the availability of water. Five trees were

selected for this study, Trees 1, 2, and 3 for Experiment 1, and Trees 4 and 5 for Experiment 2. Diameters at 1.3 m (breast height) varied between 9.6 and 13.8 cm and bark thickness varied between 2 and 4 mm.

Experiment 1 Heat pulse velocity was measured with two probe sets in fixed positions. They were placed such that the inner sensor of each set was 15 mm and 25 mm inside the cambium on the east and west sides, respectively, and at 0.1 m and 0.2 m above ground. The heat pulse interval was 30 min. Data were collected over a 5--7 day periodthough only daytime observations were used for analysis. The four observations made at each interval were treated as one record. Data were excluded if the time required to reach thermal balance between the upper and lower thermistors of each probe exceeded 150 s. Two cores were taken to the center of the stem of each tree for determination of sapwood density and water content after data collection was completed. The data were converted to sapflow velocity as described. Regression and principal components analyses were used to evaluate the relationship between sap-flow velocities estimated by the four pairs of sensors in each probe set.

Experiment 2 Branches below 1 m were excised. Four probe sets were placed in holes drilled in the four cardinal radii at approximately 0.1 m intervals and between 0.5 and 1.0 m above ground. Two probe sets were located on the northern and southern radii, one initially at the periphery of the sapwood and the second toward the center (Figure 1). For Trees 4 and 5, these positions were, respectively, 5 and 60 mm, and 5 and 50 mm inside the cambial ring. The profile of heat pulse velocity was measured at 5-mm intervals across the sapwood by moving the two probe sets simultaneously every 30 min (sometimes 15 or 45 min) for Tree 4 and every 10 min for Tree 5, 2 min before

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the heat pulse. The heat pulse interval was 15 and 10 min for Trees 4 and 5, respectively. The moving sensors were then transferred to the eastern and western radii and the experiment repeated. The second pair of probe sets was placed at right angles to the moving pair in fixed positions 15 and 10 mm inside the cambium. These were recorded at the same intervals as for the moving sensors and were used to calculate the sapflow velocity ratio (R, see below). For the north--south and east--west profiles, the fixed sensor on the western and northern radii, respectively, was used to calculate R. Cores were taken to the centers of the trees at the end of the experiment and sap flux calculated as for Experiment 1.

Sapflow velocity ratio and correction coefficient

Sapflow ratio (R) was calculated as the sapflow velocity meas-ured by the moving sensors (Vm) divided by the sapflow

veloc-ity measured by the appropriate fixed sensor (Vs). For i = that position. The average ratio at the ith position (Ri) is given

by:

A correction coefficient (C) to estimate the true sapflow velocity at each fixed sensor was calculated from the weighted average of the sapflow velocity ratios on the profile. The ratios were weighted by the areas (Ai) represented at each position.

Because the distance (d) between positions on the profile was constant, Ai is half the area of a ring of radius rp,i measured to

the center of the stem. Thus:

Ai= 0.5π((rp,i+0.5d)2−(rp,i− 0.5d)

2)

rp,id

and the total conducting area A is:

A=

Ai

The weighting factor (wi) for each position on the profile was

calculated as:

Equations 2 and 4 are combined and the correction coefficient (C) of the static sensor expressed as:

C=

(Riwi) i= 1

m

. (5)

If Vk is the sapflow velocity observed at a static sensor k and

n is the number of static sensors, during routine measurements, the average sap flux in the sapwood is:

V

The total sap flux is:

Sapflux=AV __

. (7)

Sources of variation

The data for Trees 1, 2, and 3 in Experiment 1 were examined by analysis of variance using the model:

yi,j= µ+ Vt,i + Vs,j+ ei,j , (8)

where yi,j is the ith record of sapflow velocity at position j, µ is

the grand mean across all measurement times and sensors, and Vt,iand Vs,j are fixed effects due to sampling time and sensor

pair, respectively, and ei,j is the error. Variation in sapwood

water content and density are not included in this model because a single value was used to calculate all sapflow veloci-ties. The fixed effect Vs,j is inclusive of the variation caused by

sensor position, errors in wound size measurement and vari-ation in probe separvari-ation. All sources of random varivari-ation are included in the error term. For each tree the total sums of squares (s2) is given by:

s2=st2+ss2+se2, (9)

where st2, ss2 and se2 are the sums of squares for sampling time,

sensor pair and error, respectively.

The data for Trees 4 and 5 in Experiment 2 were examined using the model:

yj= µ + Vs,j+ ej , (10)

where yj is the average ratio (R) at position j, µ is the grand

mean, and Vs,j is the variation of average ratio (R) due to

position and ej is the error. For each tree the total sums of

squares (s2) is given by:

s2=ss

2+

(4)

The number of sensors (r; i.e., the number of measurement positions on the profile) required to attain a given accuracy for the sapflow measurement was determined by:

r=tα2ss2/δ2, (12)

where tαis the value of the t-statistic at significance level α,ss

is the estimated standard error of either Vs (Experiment 1) or R

(Experiment 2) and δ is the desired accuracy. The value of r was estimated for all the trees used in the experiments.

Results and discussion Experiment 1

The first principal component accounted for 98.0--98.5% of the variance sums of squares (Table 1). The total of the three other components was less than 2% and can be ignored. Thus, the measurement of sapflow velocity by one sensor pair is expressed in the same terms as a linear combination of all four sensor pairs. The correlation coefficients for all combinations of the four sensor pairs on the two probe sets varied between 0.944 and 0.983 (Table 2), demonstrating that measurements by any one sensor pair can be used to estimate measurements made by another sensor pair.

Regression analyses showed that the relationship between sapflow velocity (V) measured by a single sensor and sapflow velocity estimated from the average of the three other sensors was always linear (r2 = 0.92--0.97, Figure 2, Table 3). Al-though the mean sapflow velocity estimated by each sensor varied by a factor of > 2 in some instances, the intercepts did not differ significantly from zero.

Thus, one point measurement is potentially a good predictor of V at another point in the system or the mean of several measurements. In a similar study with Pinus radiata D. Don, Hatton and Vertessy (1989) found a high correlation between sapflow velocities at any two depths within an individual tree. Our results also confirm that the flow of water through stems is well defined and that regularities in the distribution of V should be amenable to a relatively simple analysis to determine total sap flux.

Experiment 2

The sapflow ratios (Ri) were always lower in the middle of the

stem and higher near the periphery (Figure 3). For Tree 4, variation in Ri in the northern, southern and western radii

showed a cyclic pattern with two pronounced peaks on either side of the stem center. This pattern was not observed on the eastern radius. In Tree 5, there was little evidence of a cyclic pattern except on the eastern radius and maximum Ri was

observed 10--15 mm inside the cambium on all radii. Previous studies have shown that variation in sapflow velocity across the sapwood is a function of species, individuals within a species and radii within the same stem (Swanson 1967, 1974, Hatton and Vertessy 1989). Dye et al. (1991) concluded that the cyclic patterns of V on a given radius were associated with the production of summer and winter wood in Pinus patula. The peaks observed in Tree 4 corresponded to the production of summer wood in the second and third years of growth; how-ever, the outer peaks also corresponded to the peak positions of V that Swanson (1967, 1974) observed 10--20 mm inside the cambium of the outer summer wood ring of a range of species.

Correction coefficient

The variation in sapflow velocity with position in the sapwood limits both the accuracy with which V can be estimated and the potential for using a single model to describe its radial vari-ation. Dye et al. (1991) suggested random placement of sen-sors as an effective approach to estimate V when confronted

Table 1. Principal component analysis for sapflow velocity measurements of four sensor pairs used in Trees 1, 2, and 3 in Experiment 1. The four components are denoted as C1, C2, C3 and C4.

Latent roots Variation (%)

Component Tree 1 Tree 2 Tree 3 Tree 1 Tree 2 Tree 3

C1 23401 39556 39368 97.97 98.45 98.16

C2 269 386 475 1.13 0.96 1.19

C3 165 172 198 0.69 0.43 0.49

C4 50 64 64 0.21 0.16 0.16

Table 2. Correlation matrix of sapflow velocity for Trees 1, 2, and 3 in Experiment 1. The four sensor pairs used in each tree are denoted as S1, S2, S3 and S4.

S4 0.971 0.967 0.970 1

Tree 2

S1 1

S2 0.967 1

S3 0.956 0.974 1

S4 0.944 0.961 0.980 1

Tree 3

S1 1

S2 0.979 1

S3 0.970 0.968 1

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with such variation. Hatton et al (1995) found that stratified sampling with depth and quadrant significantly reduced sam-pling variance compared to random samsam-pling in Eucalyptus populnea F. Muell when four sensors were used. Alternatively,

many sensors can be used. Swanson (1983) used 16 probes but this is an expensive solution and may seriously interrupt flow through the sapwood. Our finding that the ratio of sapflow velocity between any two points in a profile remains constant in E. globulus allowed the development of a system of meas-urement based on only two probe sets positioned at right angles to each other in the stem. Thus, accurate estimates of V are based on the calculation of a correction coefficient (C) obtained from measurements with three probe sets before routine measurements commence. The average values of R across the profiles and of C were higher for Tree 4 than for Tree 5. There were also small differences in both variables depending on which fixed sensor was used to estimate R (Table 4). Large tree to tree variation highlights the need for a simple approach for accurately estimating sap flux in one tree if heat pulse velocity is used to estimate canopy transpiration.

The method adopted here was similar to that of Hatton et al. (1990), where information from each sensor was weighted by the proportion of conducting area that each sensor represents. Ideally, each sensor has equal areal weighting. The assumption was made that measurements on a single radius were repre-sentative of the annuli to which each sensor pertained. The advantages of this approach are that relative values of V can be investigated at frequent intervals (every 5 mm in this investi-gation to give > 40 points on the profile of Trees 4 and 5), heterogeneity of V with radial position is accounted for and, by expressing V in terms of R, this variation can be incorporated into a single factor C for use in routine measurements with only two probe sets. For Trees 4 and 5, the weighted average sapflow ratio expressed as C was always greater than the average ratio expressed as R because sapflow was, on average, lower in the inner part of the ring than in the outer part of the ring (Figure 3).

Sources of variance

The ratios of ss2/se2 were 2.09, 2.86 and 2.91 for Trees 1, 2 and

3, respectively (Table 5). Thus, variation due to sensor pair, which includes sensor position, wound size measurement and variation in probe separation, was more important in determin-ing sapflow velocity than all other random errors considered together, suggesting that increased sensor numbers would im-prove the accuracy of sap flux estimated for each tree. Figure 2. Average sapflow velocity of three sensor pairs in

Experi-ment 1 as a function of that measured by a single sensor pair. Symbols S1, S2, S3 and S4 refer to the sensor pairs that were located 10, 15, 20 and 25 mm inside the cambium, respectively, on the two probe sets and the respective fitted least-squares regressions for each.

Table 3. Regression analysis of sapflow velocity for each sensor pair with average sapflow velocity for the other three sensor pairs as used in Experiment 1 and Figure 2. The four sensor pairs used in each tree are denoted as S1, S2, S3 and S4.

Variable Tree 1 Tree 2 Tree 3

S1 S2 S3 S4 S1 S2 S3 S4 S1 S2 S3 S4

X coefficient 1.51 1.37 0.71 0.69 2.08 2.07 0.78 0.41 1.73 1.86 0.84 0.45

SE of coefficient 0.02 0.02 0.01 0.01 0.05 0.04 0.01 0.01 0.02 0.03 0.01 0.01

Constant 0.44 0.06 0.06 0.37 0.29 0.65 0.07 0.57 0.54 0.71 0.15 0.19

SE of Y estimate 0.97 0.98 0.89 0.92 2.37 1.80 1.11 1.13 1.36 1.40 1.16 0.99

r 2 0.97 0.96 0.96 0.96 0.92 0.95 0.97 0.96 0.96 0.96 0.96 0.95

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In Experiment 2, only one source of variation in sapflow velocity, sensor position, was considered in detail. A decision as to whether spatial variation warrants explicit consideration in integrating sapflow velocity should be based on an analysis of its contribution to total variation in sapflow velocity. Sources of variation in sapflow velocity include temporal as well as spatial variation (Dye et al. 1991), errors in estimation of wound width (Olbrich 1991), variation in the water content and density of the sapwood and systematic errors resulting from the application of equations to calculate µ and V.

The number of sensors (r) required to estimate sapflow velocity to a desired accuracy of 10% was as high as 72 for Tree 2 in Experiment 1 at the 95% confidence interval: even for a desired accuracy of 25%, up to 13 sensors were required

at the 90% confidence interval (Table 6). For the same range of accuracies and confidence intervals, between four and 65 sensors would be required for Trees 4 and 5 (Table 7). Thus acceptable accuracy demands measurement of sapflow at a large number of points in E. globulus to allow for its large variation with position in the sapwood. The use of a method incorporating a correction coefficient as described is a simple means of resolving this problem.

Conclusions

We observed cyclic variations in sapflow velocity (V) with position in the sapwood of Eucalyptus globulus. The high correlation between V at different points in the system enabled

Figure 3. Sapflow velocity ratio (R) ex-pressed as sapflow velocity of the moving sensor (Vm) divided by that of the static

sensor (Vs) as a function of position in

sap-wood for Trees 4 and 5 in Experiment 2. The symbols refer to the ratio calculated from each of the sensor pairs on the static sensor. The dotted line marks the center of the tree.

Table 4. Mean and standard error of sapflow velocity ratios (R) and correction coefficients (C) for the static sensors. The two sensor pairs on the static sensors are denoted S1 and S2.

Variable Tree 4 Tree 5

E--W profile N--S profile E--W profile N--S profile

S1 S2 S1 S2 S1 S2 S1 S2

Mean R 0.853 0.787 0.992 0.870 0.555 0.576 0.504 0.502

Standard error 0.302 0.282 0.191 0.164 0.211 0.220 0.196 0.197

C 0.962 0.881 1.027 0.904 0.647 0.672 0.567 0.563

Table 5. Total sum of squares (s2) and sums of squares for sampling time (st2), sensor pair (ss2) and error (se2) for Trees 1, 2 and 3 in Experiment 1.

The means and standard errors (ss_) are those for sensors S1 to S4 in Table 3; se is the standard error per observation.

s2 st2 ss2 s2e ss2/se2 Mean ss

_

se

_

Tree 1 28154 21843 4270 2041 2.09 12.92 2.44 1.69

Tree 2 65910 31188 25731 8990 2.86 18.05 7.51 4.46

(7)

the development of a correction coefficient based on a deter-mination of the ratio of sapflow velocity at different points on a radial axis through the stem to that at a fixed position. Differences in this ratio and the correction coefficient were observed among trees. The correction coefficient applied to data collected from two fixed positions provided a solution for determining V of single trees to an acceptable level of accuracy that would otherwise be possible only through the use of a large number of sensors.

Acknowledgments

We thank the Australian Centre for International Agricultural Re-search for supporting this study and the senior author as visiting scientist, Mr. Dale Worledge for technical assistance, Messrs D. and P. Tinning for the plantation site and water supply for irrigation and Dr. P.J. Dye for sharing his ideas and enthusiasm for the work. Dr. P.J. Sands provided valuable comments on the manuscript.

References

Cohen, Y., M. Fuchs and G.C. Green. 1981. Improvement of the heat pulse method for determining sap flow in trees. Plant Cell Environ. 4:391--397.

Dunlap, F. 1912. The specific heat of wood. USDA For. Serv. Bull. No. 110.

Dunn, G.M. and D.J. Connor. 1993. An analysis of sap flow in mountain ash (Eucalyptus regnans) forests of different age. Tree Physiol. 13:321--336.

Dye, P.J., B.W. Olbrich and A.G.Poulter. 1991. The effect of growth rings in Pinus patula on heat pulse velocities and sap flow measure-ment. J. Exp. Bot. 42:867--870.

Green, S.R. and B.E. Clothier. 1988. Water use on kiwi fruit vines and apple trees by the heat pulse technique. J. Exp. Bot. 39:115--123. Hatton, T.J., E.A. Catchpole and R.A. Vertessy. 1990. Integration of

sapflow velocity to estimate plant water use. Tree Physiol. 6:201--209.

Hatton, T.J., D. Greenslade and W.R. Dawes. 1992. Integration of sapflow velocity in elliptical stems. Tree Physiol. 11:185--196. Hatton, T.J., S.J. Moore and P.H. Reece. 1995. Estimating stand

transpiration in a Eucalyptus populnea woodland with the heat pulse method: measurement errors and sampling strategies. Tree Physiol. 15:219--227.

Hatton, T.J. and R.A. Vertessy. 1989. Variability of sapflow in a Pinus radiata plantation and the robust estimation of transpiration. In Hydrology and Water Resources Symposium. Australian Institute of Engineers, Christchurch, New Zealand, pp 6--10.

Honeysett, J.L., D.A. White, D. Worledge and C.L. Beadle. 1996. Growth and water use of Eucalyptus globulus ssp. globulus and E. nitens in irrigated and rainfed plantations. Aust. For. In press. Huber, B. 1932. Beobachtung und messung pflanzliche saftströme.

Berl. Deutsche Bot. Ges. 50:89--109.

Huber, B. and E. Schmidt. 1937. Eine kompensationsmethode zu thermoelektrischen messung langsamer saftströme. Berl. Deutsche Bot. Ges. 55:514--529.

Marshall, D.C. 1958. Measurement of sap flow in conifers by heat transport. Plant Physiol. 33:385--396.

Olbrich, B.W. 1991. The verification of the heat pulse velocity tech-nique for estimating sap flow in Eucalyptus grandis. Can. J. For. Res. 21:836--841.

Swanson, R.H. 1967. Seasonal course of transpiration of Lodgeple pine and Engelmann spruce. In Proc. Int. Symp. For. Hydrology. Eds. W. E. Sopper and H. W. Lull. Pergamon Press, Oxford, pp 417--432.

Swanson, R.H. 1974. Velocity distribution patterns in ascending xy-lem sap during transpiration. In Flow----Its measurement and con-trol in science and industry. Ed. R. B. Dowdell. Instrument Society of America, Pittsburgh, pp 1425--1430.

Swanson, R.H. 1983. Numerical and experimental analysis of heat pulse velocity theory. Ph.D. Diss., Univ. Alberta, Edmonton, Can-ada, 298 p.

Swanson, R.H. and D.W.A. Whitfield. 1981. A numerical analysis of heat pulse velocity theory and practice. J. Exp. Bot. 32:221--239. Table 6. The number of sensors (r) required to determine sap flux to accuracies (S) of 10 or 25% at confidence intervals (P) of 90 or 95% for Trees 1, 2 and 3 in Experiment 1. The means and standard errors (ss_) are those for sensors S1 to S4 in Table 5. The degrees of freedom = 30.

Mean s_s P = 95% P = 95% P = 90% P = 90%

S = 10% S = 25% S = 10% S = 25%

Tree 1 12.92 2.44 15 4 10 3

Tree 2 18.05 7.51 72 18 50 13

Tree 3 15.41 5.38 50 13 35 9

Table 7. The number of sensors (r) required to determine sap flux as in Table 6. The means and standard errors (ss_) are those for the sapflow ratios

for Trees 4 and 5 given in Table 4. The degrees of freedom were 21 and 19, respectively.

Mean s_s P = 95% P = 95% P = 90% P = 90%

S = 10% S = 25% S = 10% S = 25%

Tree 4 0.876 0.235 32 5 22 4

(8)

Gambar

Table 2. Correlation matrix of sapflow velocity for Trees 1, 2, and 3 inExperiment 1. The four sensor pairs used in each tree are denoted asS1, S2, S3 and S4.
Table 3. Regression analysis of sapflow velocity for each sensor pair with average sapflow velocity for the other three sensor pairs as used inExperiment 1 and Figure 2
Table 5. Total sum of squares (s2) and sums of squares for sampling time (s2t), sensor pair (s2s) and error (s2e) for Trees 1, 2 and 3 in Experiment 1.The means and standard errors (s s_) are those for sensors S1 to S4 in Table 3; se is the standard error per observation.
Table 6. The number of sensors (r) required to determine sap flux to accuracies (S) of 10 or 25% at confidence intervals (P) of 90 or 95% for Trees1, 2 and 3 in Experiment 1

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