Limitations of a compensation heat pulse velocity system at low sap flow: implications for measurements at night and in shaded trees

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1 Tree Physiology 18, Heron Publishing----Victoria, Canada Limitations of a compensation heat pulse velocity system at low sap flow: implications for measurements at night and in shaded trees PETER BECKER Biology Department, Universiti Brunei Darussalam, Bandar Seri Begawan 2028, Brunei, SE Asia Received February 13, 1997 Summary Unlike an ideal system, the return time to thermal balance (t b ) between upstream and downstream thermistors, as measured by the (compensation) heat pulse velocity method, effectively depends on the heat input and the water content of the wood at zero and low sap flow. Even when these factors were held constant and ambient temperature was stabilized, a twofold variation in t b at zero flow was observed within and among Greenspan Technology sensors implanted in wooden posts, making it impossible to distinguish zero flow from low sap velocities (< mm s 1 ). This limitation has serious consequences because the contribution of low flow rates to water movement is important during both daytime and nighttime in tropical understory and overstory trees. Measurements in an artificial flow system showed that this technical limitation is exacerbated by erratic variation in sensor response at both zero and low flow rates. The limited sensitivity of the tested sap flow sensors may be caused by their poor thermal contact with wood. Interim procedures are suggested for estimating minimum detectable sap flow and delimiting the hydroactive zone until the sensitivity and interchangeability of sap flow probes are improved. Keywords: Greenspan Technology sensors, measurement variation, nocturnal, sap velocity, thermal balance, thermistor. Introduction The compensation method of determining sap flow is based on measuring temperature at distances above and below a pulsed source of heat (Closs 1958, Marshall 1958). The technique thus effectively removes the process of heat diffusion from the component of interest, convection. However, there are technical difficulties associated with the application of the compensation heat pulse velocity (chpv) technique under conditions of low sap flow. In particular, the equations applicable to the chpv method cannot be solved at zero sap flow and permit only poor resolution at low sap velocities. Although these limitations were discussed in the earliest theoretical treatments (Closs 1958, Marshall 1958, Swanson and Whitfield 1981) and in a recent field study (Barrett et al. 1995), they have not always been fully appreciated by researchers. A practical consequence of these limitations is the difficulty of distinguishing between zero and low sap flow at night in all trees and even during the day for poorly insolated understory trees. One commercial manufacturer of chpv equipment recommends that zero flow characteristics be assessed on the basis of measurements in a cut limb or at night in a living tree under conditions certain to produce zero sap flow (Anonymous 1995a), but this approach has proved problematic. Investigators typically fail to report how they established criteria for minimum measurable sap flow (e.g., Lopushinsky 1986), or simply disregard this matter, or exclude nocturnal measurements as unreliable (Hatton and Vertessy 1990). The objectives of this study were to: (1) determine the theoretical and instrumental constraints on measurements of low sap flow by the chpv technique; (2) illustrate the quantitative importance of low sap velocities in daily tree water movement; and (3) suggest realistic measures to deal with these circumstances. Review of theory For a point at a distance x (mm) directly above or below an instantaneous line source of heat in a nonmoving, homogeneous medium, the temperature (T) according to Marshall (1958) will be: T = (Q/4πkt)exp( x 2 /4kt), (1) where Q ( C mm 2 ) is the temperature to which the amount of heat liberated per unit length of the line would raise unit volume of the substance, k (mm 2 s 1 ) is thermal diffusivity, and t (s) is time. Figure 1a shows that thermal balance between upstream (T u ) and downstream (T d ) points is approached only asymptotically under the ideal conditions of zero sap flow specified by Equation 1 for appropriate values of Q and k. Actually, some finite temperature difference will be inferred as zero by the instrument because of the resolution limits of the electronic components. This means that, in practice, the time to thermal balance, t b, at zero flow will increase as Q (effectively heat pulse

2 178 BECKER Materials and methods Measurement of t b in wood Figure 1. Simulated difference between upstream (T u ) and downstream (T d ) sensor temperatures with time after onset of heat pulse under (a) zero sap flow: Q = 100 C mm 2 (1.6-s pulse) and k = 0.4 mm 2 s 1 (dry wood, solid line) or k = 0.14 mm 2 s 1 (water, dotted line); Q = 150 C mm 2 (2.4-s pulse) and k = 0.4 mm 2 s 1 (dry wood, dashed line) and (b) low sap flow: Q = 100 C mm 2, k = 0.25 mm 2 s 1 (wet wood), and v h = 0.022, 0.011, or mm s 1 (left to right, = 8, 4, and 2 cm h 1, respectively). The upstream and downstream sensors were taken to be 5 and 10 mm, respectively, from a line heater source. The value of Q was approximated from the measured heater wire resistance and voltage supplied to the Greenspan probes as described by Cohen et al. (1988); k is from Marshall (1958). duration) or stem water content (inversely related to k) increases. Equation 1 requires only minor modification to accommodate sap flow (Marshall 1958): T = (Q/4πkt)exp[ (x v h t) 2 /4kt], (2) where v h (mm s 1 ) is heat pulse velocity. According to Equation 2, thermal balance between upstream and downstream points will be attained at some finite t b even at extremely low sap flow. Theoretically, t b depends only on v h when there is convection; however, because of the limited sensitivity of the sensors (thermistors), t b will also depend on Q and k at low flow rates, just as it does at zero flow. For the conditions simulated in Figure 1b, this would appear to apply for v h < 0.01 mm s 1 (4 cm h 1 ) as the time to thermal balance becomes increasingly protracted. It is emphasized that Equations 1 and 2 are for an idealized system that disregards probe effects on heat transport. All measurements were made with Greenspan Technology equipment (Greenspan Technology, Warwick, Queensland, Australia). The two stainless steel sensor probes contained two pairs of thermistors spaced 10 mm apart and aligned 10 mm above and 5 mm below a central heater probe. There was some overlap in the areas of wood sensed by the two pairs of thermistors, because each thermistor detects heat from a 5+ mm radius (Swanson 1994). Heat-pulse duration was 1.6 s at 15- or 30-min intervals, and one data logger recorded the time to thermal balance for two probe sets (four sensors). Holes for the 1.8 mm-diameter probe rods were carefully drilled with 1.98-mm diameter bits aligned by a 20-mm thick jig. For insertion into cut boles, the probe rods were coated with petroleum jelly containing the fungicide benomyl, whereas they were coated with RS heat sink compound (RS Components, Corby, U.K.) for insertion into the posts. Probe rods fitted snugly or tightly in tropical hardwoods, and their looser fit in air-dried posts was compensated by the heat sink compound. To investigate the dependence of t b on k under experimental conditions, probes were implanted 0.2 m from the ends of 0.6-m lengths of boles (or a limb in one case) cut from seven tree species. The bole ends were coated with grease to reduce water gradients, and the sensors were positioned at depths of mm below the bark surface in both sapwood and heartwood (when present). Bole diameters were mm. The volume fractions of wood and water in wood cores taken midway between probe sets were determined gravimetrically by Archimedes principle, taking the density of wood tissue (cellulose and lignin) to be 1530 kg m 3. The ranges of wood and water fractions in cut boles ( and , respectively) nearly encompassed the ranges observed in 30 tree species from primary dipterocarp and tropical heath forests measured during wet and dry periods in Brunei ( and , respectively; author s unpublished data). Heat pulse velocity measurements were made in an air-conditioned room, and the probes and surrounding bole surface were insulated with foam rubber and bubble plastic. To determine whether sensors had characteristic t b values and stability, probes were implanted 0.2 m from the ends of 0.6-m sections of air-dried timber (Shorea sp., Dipterocarpaceae) cut from a single length of m post. The post was used to obtain a more homogeneous medium than cut boles while still retaining the thermal characteristics of wood. Volume fractions of wood and water ranged from 0.52 to 0.58 and from 0.24 to 0.26, respectively. Posts and probes were placed in an insulated chest filled with styrofoam chips in an air-conditioned room to minimize thermal variation. About 0.4 m of cable and the data loggers were outside the chest and uninsulated. In a subsequent experiment, the posts with probes were removed from the insulating chest, and the air conditioner was alternately turned on and off in an approximately 12-h cycle to determine whether variation in ambient temperature affected TREE PHYSIOLOGY VOLUME 18, 1998

3 LIMITATIONS OF HEAT PULSE METHOD AT LOW SAP FLOW 179 measured t b values. Finally, measurements were made to determine whether t b varied diurnally under typical field conditions with zero sap flow. The posts with probes were lashed to two poles exposed to direct sun and to two tree trunks in the well-shaded understory of a 30-m tall forest. The data loggers and probe sets were covered with aluminum foil to reduce thermal variation. Measurement of t b in an artificial flow system To assess the accuracy and sensitivity of heat pulse sensor measurements of velocity, a nonbiological system with the advantages of temporal stability and spatial homogeneity was constructed (cf. Anonymous 1995b). Washed, sieved white sand ( µm) was used as the medium for water movement. The sand was contained within a vertical PVC tube (800-mm long, 103-mm inside diameter) with threaded endcaps. All seams were sealed with epoxy and silicon to prevent leaks. Probes were bent until the spacing between them was within 0.1 mm of 5 and 10 mm, and this spacing was maintained by holes drilled in the tube wall and a 15-mm thick template fastened to the outside of the tube. Two probe sets, each with two sensors (thermistor pairs), were tested in independent trials. Water entered the tube bottom under constant head pressure and exited from the top at a rate controlled by a valve. The weight of water passing through the system was measured to 0.1 g by a computerized balance at 30-s intervals, and velocity was calculated from the flow rate divided by the cross-sectional area of the tube. For each measurement of heat pulse velocity, the one or two weight measurements (depending on t b ) closest in time were used to calculate the corresponding velocity of water in the tube, which was very stable with a coefficient of variance typically < 1% for a set of measurements. Following the recommended nomenclature and symbols of Edwards et al. (1997), heat pulse velocity was calculated as: v h = (x d x u )/2t b, (3) where x d and x u are the downstream and upstream distances, respectively, of the thermistors from the heater. I assumed that the probe had no influence on the system (Anonymous 1995b); this assumption is discussed below. Sap velocity was calculated as: v s = v h (0.469F s + F w ), (4) where is calculated following the procedure of Edwards and Warwick (1984) and taking the densities of quartz and water as 2650 and 1000 kg m 3, respectively, and their heat capacities as and 4180 J kg 1 K 1, respectively (Lide 1990, cf. Anonymous 1995b). The volume fraction of water, F w, in saturated sand measured gravimetrically in a cylinder of known volume was 0.38 (n = 4), and the volume fraction of sand, F s, was determined by difference as Ten or more measurements of t b and the actual velocity were made at various velocities between and 0.08 mm s 1 to assess the accuracy of sap velocity estimates. Higher velocities characteristic of well-insolated trees could not be tested because the maximum heat pulse (2.4 s) was insufficient to produce the requisite peak temperature difference between upstream and downstream thermistors in wet sand because of its relatively high thermal diffusivity. Logged data flagged as failing to meet this (unspecified) criterion at the tested velocities were rejected. Heat pulses were typically 1.6 s at the lower velocities and 2.4 s at the higher velocities at intervals of 3 or 5 min. Sensitivity was tested by making alternate sets of 10 or more measurements at the test velocity and zero velocity and then at increasing test velocity. The effect of heat pulse duration (1.6 and 2.4 s) on t b was also tested by alternate sets of measurements. Simultaneous measurements of t b by adjacent sensors were tested for consistent differences at zero and low flows. Nonparametric statistical tests were employed because some sample distributions were bimodal and variances were often nonhomogeneous. Curve fitting The lowess smoothing employed in the figures is a robust, piecewise linear regression technique that is relatively insensitive to outliers. It produces a smoothed curve by running along the x values and finding predicted values from a weighted average of nearby y values (Wilkinson 1990). The width of the smoothing window can be controlled to reflect an appropriate scale of variation. For example, a broad window was selected to reveal diel trends and disregard short-term fluctuations. Results and discussion Sensor variation and bias in wood Under zero flow conditions, most sensors exhibited unexpectedly large variability in t b, although a few sensors were relatively stable or showed mixed behavior (Figure 2). The standard deviations of t b (ln-transformed to normalize the distributions, n = 119) measured by particular sensors implanted in posts and recorded on two occasions by different data loggers were not significantly correlated (Pearson s r = 0.12, n = 32, P = 0.50), nor were the paired readings by particular data logger channels correlated (Pearson s r = 0.06, n = 32, P = 0.75), indicating that neither sensors nor data loggers produced characteristically stable or unstable t b values. Because the baseline values were so variable, an objective criterion was used to calculate the threshold t b characteristic of zero flow (t b ). Taking the minimum observed reading would place undue emphasis on extreme results, so t b was determined as the minimum after excluding the lower 10% of records. Individual sensors had characteristic values of t b as indicated by a significant correlation between measurements for post implants on two occasions by different data loggers (Pearson s r = 0.79, n = 32, P < 0.001). Qualitatively similar results were obtained when t b was determined as the minimum after culling the lower 5% of records or calculated as the median of all records. The twofold range in t b values, from a minimum of about 100 s, even in a relatively homogeneous wood medium with a known zero flow, indicates that it would TREE PHYSIOLOGY ON-LINE at

4 180 BECKER Figure 2. Within and among sensor variability in time to thermal balance (t b (s)) as measured at 30-min intervals by probes implanted in cut boles for quiet (a), constantly noisy (b), intermittently noisy (c), and noisy/quiet (d) sensors. be difficult to define a sensor-independent threshold for zero flow in a tree implant based on field measurements. Effect of k on t b There was a significant partial correlation between t b and the volumetric fraction of water in cut boles (r = 0.537, n = 31, P < 0.01, Figure 3), but not with the wood fraction (data not shown). The observed inverse relationship was contrary to the theoretical expectation that t b should vary inversely with diffusivity, k, which in turn should vary inversely with stem water content. This deviation is probably an artifact resulting from the accidental allocation of sensors with characteristically high t b to boles with low water content before the systematic variation among sensors had been assessed. This finding demonstrates the difficulty of defining a threshold t b characteristic of zero flow without taking account of variability among sensors. If the threshold of 150 s suggested by the minimum attained by the smoothed curve in Figure 3 was adopted (t b values ranged from 84 to 322 s), about 25% of the sensors would overestimate sap flow under true zero flow conditions. Effect of ambient temperature on t b The t b values measured in posts were correlated with changes in ambient temperature, although the response varied among sensors (Figure 4). Under zero flow conditions, heat pulse velocity consistently tracked diurnal variation in temperature at a tropical latitude (5 N) in both open and forested conditions (Figure 5). As expected, v h was greatest near or a few hours after midnight when reduced temperatures were expected to depress t b (inversely related to v h ), based on the controlled temperature studies. However, different probe--data logger combinations yielded different mean v h values under similar conditions (cf. the smoothed curves in Figures 5c and 5d), indicating that the differences in characteristic t b of the four sensors were not completely averaged out between loggers. Performance in an artificial flow system Figure 3. Relationship between culled (lower 10% of 119 records excluded) minimum time to thermal balance (t b (s)) for individual sensors and volumetric fraction of water in cut boles. Line fitted by lowess with f = 0.6 (5-point window, Wilkinson 1990). Accuracy Contrary to the manufacturer s indication (Anonymous 1995b), it was not possible to test the accuracy of sap velocity measurements in a sand + water medium. The higher thermal diffusivity of the sand + water medium compared with wood resulted in t b values of about 40 to 80 s at zero velocity. Application of Equations 3 and 4 showed that these values corresponded to sap velocities of 0.04 to 0.02 mm s 1, and any measurements of velocities below these threshold values must result in overestimates, as was observed. Sap velocities, v s, typically underestimated actual velocities of mm s 1, as also reported by Anonymous (1995b). It may be that the flow of water between probes was impeded in the sand me- TREE PHYSIOLOGY VOLUME 18, 1998

5 LIMITATIONS OF HEAT PULSE METHOD AT LOW SAP FLOW 181 Figure 4. Effects of temperature (a) on time to thermal balance (t b (s)) as measured at 15-min intervals by the two most discrepant sensors (b and c) and the mean of all four sensors (d). The sensors were attached to the same monitor and implanted in a post in a room with the air conditioner switched on, off, and on again at 12-h intervals. Lines in (b--d) obtained by lowess smoothing with f = 0.3 (48-point window, Wilkinson 1990). dium, indicating that some correction analogous to the wound effect correction is necessary. Unfortunately, the wound correction calculations of Swanson and Whitfield (1981) are only applicable to material with the thermal characteristics of wet wood. Resolution In the first trial in the sand + water medium, both sensors showed statistically significant differences in t b at zero velocity and at velocities mm s 1 (Mann-Whitney U-tests, P < 0.001, n = 10 per group, data not shown). Neither sensor could statistically distinguish a velocity of 0.01 mm s 1 from zero velocity because of variances that were more than triple those observed at higher velocities. A detailed study of a second probe set confirmed the results obtained with the initial probe set except that one sensor in the second probe set statistically resolved readings at 0 and mm s 1, whereas the other sensor, making simultaneous measurements under almost identical conditions, did not. Additional trials of the second probe set showed that high variances (CV 20%) in t b could occur erratically at both zero and low (about 0.02 mm s 1 ) velocities for both 1.6- and 2.4-s heat pulses (Table 1). When variances were moderate and sample size sufficient, both sensors could statistically differentiate zero velocity from mm s 1 (Table 1, P values in bold). The detection threshold in the sand + water system occurred somewhere between 0.01 and 0.02 mm s 1, but better resolution might be achieved in a wet wood system. It has been suggested that probe sensitivity could be enhanced by increasing thermal contact between thermistor and sapwood (Swanson 1962, Barrett et al. 1995). In the Green- Figure 5. Mean heat pulse velocity (v h ) (mm s 1 ) measured at 15-min intervals by four monitors (each with two probe sets two sensors) installed in posts in the open (a and b) and in the forest (c and d). Air temperatures ranged from 28 to 35 C in the open and from 25 to 30 C in the forest. (Equipment was not available to measure temperature within the post at sensor positions.) It rained on the nights preceeding Days 1, 3, 5, and 6. Sunrise was 0610 h and sunset was 1800 h; ticks on x-axis indicate midnight (solar time). Line obtained by lowess smoothing with f = 0.2 (96-point window, Wilkinson 1990). TREE PHYSIOLOGY ON-LINE at

6 182 BECKER Table 1. Effects of heat pulse duration and sensor variation on resolution of zero and low sap velocity (about 0.02 mm s 1 ) in an artificial flow system. Abbreviations: CV (%) = coefficient of variance = 100 SD/mean; P values are for Mann-Whitney U-tests comparing t b values at zero and low sap velocity. Values of CV 20% and of P 0.05 are shown in bold. Pulse (s) Actual velocity (mm s 1 ) t b (s) of Sensor 1 t b (s) of Sensor 2 Mean CV n Mean CV n P Mean CV n P span probes, thermistors and their leads lie loosely within the approximately 1.4-mm-diameter air space inside hollow stainless steel rods. I postulate that, depending on whether the thermistor touches the wall, it will respond more or less quickly to temperature change in the surrounding wood following a heat pulse, leading to differences in t b measured under uniform conditions. An attempt to test this idea by X-raying the probe was unsuccessful because thermistor position could not be discerned, although the leads were clearly visible. However, Teflon probes with potted thermistors give stable, large t b values at zero and low sap flows, thereby affording better accuracy, precision and resolution than the stainless steel probes with unpotted thermistors used in this study (W.R.N. Edwards, DSIR Fruit and Trees, Palmerston North, New Zealand, personal communication). I conclude, therefore, that probe sensitivity would be enhanced if the thermistors were potted in a substance of high thermal conductivity; however, measurement regions of the probe should be thermally insulated from adjacent regions to prevent lateral transfer of heat, as in the alternating brass and epoxy probe segments described by Jones et al. (1988). Alternatively, probe walls could be constructed of material with a heat conductivity similar to that of wood (W.R.N. Edwards, personal communication). There is apparently no advantage in insulating the external portions of probes other than to cover them with aluminum foil. Although t b was affected by thermal variation, it is impractical to shield the probes from this effect, which was detected even in a well-insulated chest (Figure 4). Further progress in understanding the limits of resolution of sap velocity by the heat pulse technique will require studies in media with thermal properties similar to those of wet wood. Taking 150 s as a typical t b for wet wood at zero flow, application of Equations 3 and 4 with parameters appropriate for wet wood indicates a resolution limit for v s of > mm s 1, using the probe spacings employed here and correcting for the wound effect. Resolution could be improved by measuring temperature changes at equal distances above and below the heater (Marshall 1958, Swanson and Whitfield 1981), or by enhancing the circuitry for detecting the return to thermal balance so that larger t b values are measured more precisely at zero flow. Sensor bias For the first probe set, Sensor 1 yielded significantly lower t b values than Sensor 2 at velocities of 0, 0.018, 0.031, and mm s 1 (Friedman tests for dependent samples, P < 0.027). There was no significant difference between Sensors 1 and 2 at 0.01 mm s 1 because of high variances. For the second probe set, t b of Sensor 1 was significantly (P < 0.005) lower than t b of Sensor 2 only at zero velocity as a result of high variances and small sample sizes at low velocities. However, the large data set in Table 1 consistently showed this difference, which was statistically significant (P < 0.046) at zero velocity for 1.6-s pulses and at zero and low velocity (0.02 mm s 1 ) for 2.4-s pulses. These results corroborate the finding of the wood post experiment that sensors have characteristic t b values and show that these sensor-specific differences persist at low velocities. The erratic but sometimes systematic variation in t b within sensors is difficult to explain. It is unlikely to be caused by irregular supply of heat in the Greenspan system. In six measurements on two data loggers at a nominal pulse of 1.6 s, a constant V was supplied to the heater for s, as measured on an oscilloscope (Tektronix TDS 520, Beaverton, OR). Random variation affecting the detection of balanced thermistor-pair resistances after the heat pulse, provided it is noncumulative, could account for only a small portion of the observed within-sensor variation in t b, which would require improbably long runs of positively or negatively biased readings. A curve fitting routine to estimate the zero intercept on the time axis of the measured resistance between upstream and downstream thermistors might help to increase the precision of t b measurements (T.J. Hatton, CSIRO Land and Water, Wembley, Australia, personal communication). Whatever the cause of systematic variation in t b among sensors, an important consequence is that probe sets are not TREE PHYSIOLOGY VOLUME 18, 1998

7 LIMITATIONS OF HEAT PULSE METHOD AT LOW SAP FLOW 183 strictly interchangeable, at least for measurements at zero and low sap flow. Systematic differences in circuitry seem unlikely, leaving the sensors themselves as the source of systematic variation. Although Swanson (1962) recommended that thermistors be closely matched in their resistances at appropriate temperatures, the Wheatstone bridge used to detect thermal balance after the heat pulse should not be affected by thermistor mismatch (W.R.N. Edwards, K.K. Lai, Universiti Brunei Darussalam Physics Department, Bandar Seri Begawan, Brunei, personal communication). Heat pulse duration For contiguous sets of measurements made at mm s 1 in the sand + water system, t b was about 14% higher for heat pulses of 2.4 s than for heat pulses of 1.6 s, the differences being statistically significant (Mann-Whitney U-tests, P < 0.001, n = 10 per group, data not shown) for two of three sensors for which sufficient data were collected. This is consistent with theoretical expectations and instrumental limitations (Figure 1), and the effect was nontrivial at low velocities in wet sand. Neither heat pulse duration yielded consistently more accurate measurements among trials. Low sap flow in trees Nighttime sap flow rates are typically much lower than daytime rates, except in understory trees that receive little or no direct solar radiation (Figure 6). Sap flow during the day and night was sometimes indistinguishable in understory trees; e.g., Days 23 and 25 in Figure 6a. Figure 6 shows that the absolute temporal variability in sap flow of the understory tree was comparable to that observed during the night in subcanopy and emergent trees (cf. Figure 6a versus Figures 6b--d). Sap flow typically declined steadily from sunset to sunrise or declined to a minimum around midnight and increased again (Figure 6). The frequently observed increase in predawn sap flow contrasted with the consistent observation of a monotonic, post-midnight decline in v h (positively related to sap flow) under zero flow conditions in the wooden posts exposed to variations in ambient temperature (Figure 5). This finding strongly suggests that the nocturnal variation in sap flow observed in trees is a real, biological phenomenon. Accordingly, a conservative estimate of minimum detectable sap flow for a particular tree implanted with a particular probe--logger combination may be taken as the minimum (T.J. Hatton, personal communication) or, still more conservatively, the median of the minimum nighttime sap flow measured during a specified period (dashed lines in Figure 6). This does not mean that sap flow rates lower than this minimum are actually zero; only that we presently have no way of verifying that these rates exceed zero. Taking values below the minimum nighttime sap flow rate as zero, nighttime sap flow accounted for 36, 16, 16, and 15% of daily total sap flow in order of increasing size of the trees in Figure 6. Based on the median detectable sap flow rate, the corresponding values were 22, 14, 10, and 10%. Thus, upward movement of water at night, especially in small trees, is apparently not trivial. It was not determined whether this movement reflects refilling or transpiration. Conclusions The theoretical constraints on the capacity of the chpv method to distinguish zero from low rates of sap flow have been experimentally verified. The chpv method provides reasonably accurate measurements of daytime sap flow (e.g., Olbrich 1991, Barrett et al. 1995); however, the method yielded unreliable measurements of the low nighttime sap velocities, which make an important contribution to daily water movement. Figure 6. Smoothed semi-hourly sap flow in Dryobalanops aromatica Gaertn. f. (Dipterocarpaceae) in a primary lowland dipterocarp forest in Brunei. Smoothing was by a 5-point running mean, and was performed twice for tree (a). Nighttime (sunset to sunrise) is shaded, ticks mark midnight (solar time), and the dashed line indicates the median of daily minimum nighttime sap flow during h. Tree sizes were (a) 93 mm, (b) 230 mm, (c) 462 mm, and (d) 753 mm in diameter at implant height. The understory tree (a) was beneath a dense canopy of leaves, the subcanopy tree (b) was overtopped by a single crown layer, and the upper portion of emergent tree crowns (c and d) was fully exposed. See Becker and Barker (1996) for details of these measurements. TREE PHYSIOLOGY ON-LINE at

8 184 BECKER Furthermore, daytime sap flow before and after the four midday hours of maximum sap flow comprised 62 and 56%, respectively, of daily daytime sap flow in the smallest and three larger trees depicted in Figure 6. During the daytime periods outside peak flow, median sap velocities, v s, were mm s 1 for the two smaller trees and mm s 1 for the two larger trees. These are velocities that, in the artificial flow system, were affected by heat pulse duration and intrinsic variation among sensors in t b, and the lower velocity was at the limit of detectability in a sand + water medium. Although the most important factor affecting accuracy of sap velocity measurements is probe spacing (Anonymous 1995a), the delimitation of the hydroactive zone (sapwood cross-sectional area) also substantially affects sap flow calculations (Hatton et al. 1995) and requires differentiating low and zero sap velocities. Until improvements in sensors and instrumental data processing are implemented, minimum detectable sap flow can be estimated as shown in Figure 6. For this procedure, it is recommended that sap flow rates be calculated with no imposed timeout value for return to thermal balance (other than the upper limit imposed by the interval between heat pulses), and that sap flow rates be first smoothed to avoid distortion by extreme values. Although this approach avoids the problems created by different sensors having different characteristic t b values at zero flow, it is not suitable for establishing the boundary between hydroactive and inactive xylem (e.g., Hatton et al. 1995). To determine this boundary, it is necessary to know t b at true zero flow. This baseline t b will have to be established for individual sensors under conditions of zero flow using tissue with the same temperature and volumetric wood and water fractions as the material under test. Alternatively, radial variation in sap velocity during periods of peak ( h) and minimum ( h) sap flow can be compared, and the sensor position where peak values cannot be statistically differentiated from minimum values can be used to define the inner boundary of the hydroactive zone (Becker 1996). Acknowledgments Research was funded by Universiti Brunei Darussalam and facilitated by the Department of Forestry. The remarks of an anonymous reviewer of another paper provided the stimulus to make the observations reported here. Discussion with Ross Edwards, Tom Hatton, K.K. Lai, Peter Reece, and Mel Tyree helped considerably in planning and interpreting the experiments. K.K. Lai made the oscilloscope and heater resistance measurements, and Mel Tyree wrote the program to process balance data. Ross Edwards and Tom Hatton commented helpfully on an initial draft. References Anonymous. 1995a. Sapflow measurement with the Greenspan sapflow sensor: theory and technique. Greenspan Technology Pty. Ltd., Warwick, Australia, 32 p. Anonymous. 1995b. Sapflow sensor calibration experiment. Greenspan Technology Pty. Ltd., Warwick, Australia, 12 p. Barrett, D.J., T.J. Hatton, J.E. Ash and M.C. Ball Evaluation of the heat pulse velocity technique for the measurement of sap flow in rainforest and eucalypt forest species of south-eastern Australia. Plant Cell Environ. 18: Becker, P Sap flow in Bornean heath and dipterocarp forest trees during wet and dry periods. Tree Physiol. 16: Becker, P. and M.G. Barker Sap flow within different-sized trees of Dryobalanops aromatica (Dipterocarpaceae) in a mixed dipterocarp forest of Brunei Darussalam. In Proc. Fifth Round Table Conf. on Dipterocarps, Chiang Mai, Thailand. Eds. S. Appanah and K.C. Khoo. For. Res. Inst. Malaysia, Kuala Lumpur, Malaysia, pp Closs, R.L The heat pulse method for measuring rate of sap flow in a plant stem. N.Z. J. Sci. 1: Cohen, Y., M. Fuchs, V. Falkenflug and S. Moreshet Calibrated heat pulse method for determining water uptake in cotton. Agron. J. 80: Edwards, W.R.N. and N.W.M. Warwick Transpiration from a kiwifruit vine as estimated by the heat pulse technique and the Penman--Monteith equation. N.Z. J. Agric. Res. 27: Edwards, W.R.N., P. Becker and J. Èermák A unified nomenclature for sap flow measurements. Tree Physiol. 17: Hatton, T.J. and R.A. Vertessy Transpiration of plantation Pinus radiata estimated by the heat pulse method and the Bowen ratio. Hydrol. Processes 4: Hatton, T.J., S.J. Moore and P.H. Reece Estimating stand transpiration in a Eucalyptus populnea woodland with the heat pulse method: measurement errors and sampling strategies. Tree Physiol. 15: Jones, H.G., P.J.C. Hamer and K.H. Higgs Evaluation of various heat-pulse methods for estimation of sap flow in orchard trees: comparison with micrometeorological estimates of evaporation. Trees 2: Lide, D.R CRC handbook of chemistry and physics, 71st Edn. CRC Press, Boca Raton, FL. Lopushinsky, W Seasonal and diurnal trends of heat pulse velocity in Douglas-fir and ponderosa pine. Can. J. For. Res. 16: Marshall, D.C Measurement of sap flow in conifers by heat transport. Plant Physiol. 33: Olbrich, B.W The verification of the heat pulse velocity technique for estimating sap flow in Eucalyptus grandis. Can J. For. Res. 21: Swanson, R.H An instrument for detecting sap movement in woody plants. USDA For. Serv., Rocky Mountain For. Range Exp. Stn., Ft. Collins, CO, Paper No. 68, 16 p. Swanson, R.H Significant historical developments in thermal methods for measuring sap flow in trees. Agric. For. Meteorol. 72: Swanson, R.H. and D.W.A. Whitfield A numerical analysis of heat pulse velocity theory and practice. J. Exp. Bot. 32: Wilkinson, L SYGRAPH: the system for graphics. SYSTAT, Inc., Evanston, IL, 547 p. TREE PHYSIOLOGY VOLUME 18, 1998