An alternative method to estimate zero flow temperature differences for Granier's thermal dissipation technique

Calibration of the Granier thermal dissipation technique for measuring stem sap flow in trees requires determination of the temperature difference (DeltaT) between a heated and an unheated probe when sap flow is zero (DeltaT(max)). Classically, DeltaT(max) has been estimated from the maximum predawn DeltaT, assuming that sap flow is negligible at nighttime. However, because sap flow may continue during the night, the maximum predawn DeltaT value may underestimate the true DeltaT(max). No alternative method has yet been proposed to estimate DeltaT(max) when sap flow is non-zero at night. A sensitivity analysis is presented showing that errors in DeltaT(max) may amplify through sap flux density computations in Granier's approach, such that small amounts of undetected nighttime sap flow may lead to large diurnal sap flux density errors, hence the need for a correct estimate of DeltaT(max). By rearranging Granier's original formula, an optimization method to compute DeltaT(max) from simultaneous measurements of diurnal DeltaT and micrometeorological variables, without assuming that sap flow is negligible at night, is presented. Some illustrative examples are shown for sap flow measurements carried out on individuals of Erica arborea L., which has needle-like leaves, and Myrica faya Ait., a broadleaf species. We show that, although DeltaT(max) values obtained by the proposed method may be similar in some instances to the DeltaT(max) predicted at night, in general the values differ. The procedure presented has the potential of being applied not only to Granier's method, but to other heat-based sap flow systems that require a zero flow calibration, such as the Cermák et al. (1973) heat balance method and the T-max heat pulse system of Green et al. (2003).     

热平衡茎流计在荒漠灌木植物耗水研究中的应用

首先对茎流热平衡技术测定植株茎流的基本原理进行了介绍。在此基础上,探讨了4种干旱沙区常见造林灌木的日耗水变化规律。并通过对同时观测的气象因子的分析,揭示植物耗水与太阳辐射、气温和大气湿度等因子的相关关系,建立了在西北干旱沙区,预测这4种植物蒸腾耗水的方程。     

The effect of aqueous transport of CO(2) in xylem sap on gas exchange in woody plants

The influence of CO(2) transported in the transpiration stream on measurements of leaf photosynthesis and stem respiration was investigated. Measurements were made on trees in a temperate forest in Scotland and in a tropical rain forest in Cameroon, and on shrubs in the Sahelian zone in Niger. A chamber was designed to measure the CO(2) partial pressure in the gas phase within the woody stems of trees. High CO(2) partial pressures were found, ranging from 3000 to 9200 Pa. Henry's Law was used to estimate the CO(2) concentration of xylem sap, assuming that it was in equilibrium with the measured gas phase partial pressures. The transport of CO(2) in the xylem sap was calculated by multiplying sap CO(2) concentration by transpiration rate. The magnitude of aqueous transport in the studied species ranged from 0.03 to 0.35 &mgr;mol CO(2) m(-2) s(-1), representing 0.5 to 7.1% of typical leaf photosynthetic rates. These values strongly depend on sap pH. To examine the influence of aqueous transport of CO(2) on stem gas exchange, we made simultaneous measurements of stem CO(2) efflux and sap flow on the same stem. After removing the effect of temperature, stem CO(2) efflux was positively related to sap flow. The apparent effect on measurements of stem respiration was up to 0.7 &mgr;mol m(-2) s(-1), representing ~12% of peak stem respiration rates.     

The relationship between sap flow rate and diurnal change of tangential strain on inner bark in Cryptomeria japonica saplings

The relationship between sap flow rates and diurnal fluctuation of stems was investigated in cloned 3-year-old saplings of Cryptomeria japonica D. Don grown in a phytotron with irrigation every 2 days. The improved stem heat balance method and a strain gauge were used to measure sap flow rate and diurnal fluctuation of the stem. The sap flow rate reacted to lighting conditions, increasing and decreasing immediately after lights-on and lights-off, respectively. The tangential strain on the surface of the inner bark exhibited a reaction that followed but opposed the reaction of the sap flow rate to lighting conditions. Based on the changes in sap flow rate, there seemed to be four phases in diurnal sap flow: phase A₁ began with lights-on, when the sap flow rate increased, and lasted about 2 hours. In the following phase, A₂, the sap flow rate remained almost constant at 1.3 g/min for about 10 h, and then declined for about 2 h as lights-off approached. In phase B, the early period of darkness, the sap flow declined quickly and then more slowly, for about 4 h, until the start of the second dark period, phase C, when the sap flow rate became almost constant at 0.05 g/min for about 6 h. The first derivative of each sap flow rate and the corresponding tangential strain were calculated, and the results indicated a negative correlation between the two variables in all periods. In particular, the relationship between the first derivative values exhibited a highly negative correlation in phases A₁ and B, expressed as a primary formula. Sap flow rate was found to continue for some time after lights-off, and this compensated for reduced evaporative effects, albeit at a slow rate, over 4 h. The total amount of sap flow in the dark was only about 9% of that in the light, disregarding transpiration in the dark for simplicity. Thus, the total amount of sap flow responsible for swelling of the stem was about 9% of that consumed in transpiration during the light period.     

Estimating water use by sugar maple trees: considerations when using heat-pulse methods in trees with deep functional sapwood

Accurate estimates of sapwood properties (including radial depth of functional xylem and wood water content) are critical when using the heat pulse velocity (HPV) technique to estimate tree water use. Errors in estimating the volumetric water content (V(h)) of the sapwood, especially in tree species with a large proportion of sapwood, can cause significant errors in the calculations ofsap velocity and sap flow through tree boles. Scaling to the whole-stand level greatly inflates these errors. We determined the effects of season, tree size and radial wood depth on V(h) of wood cores removed from Acer saccharum Marsh. trees throughout 3 years in upstate New York. We also determined the effects of variation in V(h) on sap velocity and sap flow calculations based on HPV data collected from sap flow gauges inserted at four depths. In addition, we compared two modifications of Hatton's weighted average technique, the zero-step and zero-average methods, for determining sap velocity and sap flow at depths beyond those penetrated by the sap flow gauges. Parameter V(h) varied significantly with time of year (DOY), tree size (S), and radial wood depth (RD), and there were significant DOY x S and DOY x RD interactions. Use of a mean whole-tree V(h) value resulted in differences ranging from -6 to +47% for both sap velocity and sap flow for individual sapwood annuli compared with use of the V(h) value determined at the specific depth where a probe was placed. Whole-tree sap flow was 7% higher when calculated on the basis of the individual V(h) value compared with the mean whole-tree V(h) value. Calculated total sap flow for a tree with a DBH of 48.8 cm was 13 and 19% less using the zero-step and the zero-average velocity techniques, respectively, than the value obtained with Hatton's weighted average technique. Smaller differences among the three methods were observed for a tree with a DBH of 24.4 cm. We conclude that, for Acer saccharum: (1) mean V(h) changes significantly during the year and can range from nearly 50% during winter and early spring, to 20% during the growing season;(2) large trees have a significantly greater V(h) than small trees; (3) overall, V(h) decreases and then increases significantly with radial wood depth, suggesting that radial water movement and storage are highly dynamic; and (4) V(h) estimates can vary greatly and influence subsequent water use calculations depending on whether an average or an individual V(h) value for a wood core is used. For large diameter trees in which sapwood comprises a large fraction of total stem cross-sectional area (where sap flow gauges cannot be inserted across the entire cross-sectional area), the zero-average modification of Hatton's weighted average method reduces the potential for large errors in whole-tree and landscape water balance estimates based on the HPV method.     

胡杨蒸腾耗水的单木测定与林分转换研究

利用热脉冲技术,在黑河下游额济纳天然绿洲内测定胡杨单木边材液流在不同位点、方位的变化,结果表明:液流速率随深度的增加而增大,在15 mm处达到最大值,随后随深度增加而减小,越靠近形成层,液流启动越早,减小滞后;在4个方位上,南、西面液流速率远远高于北、东面;南面比西面液流启动较早,下降较快;西面液流速率下降滞后于南面;在北与东面,2个方位液流速率变化不大.在此基础上,采用边材面积作为纯量,对胡杨近熟林耗水量进行了推算.胡杨林边材面积与胸径之间存在较高的相关性,两者之间的关系可以用幂模型很好地拟合.通过实测标准地的胸径分布,推算出林地边材面积的分布,利用热脉冲测定单木液流通量,推算出黑河下游胡杨近熟林年生长期(4-10月)耗水量为3 172 m3·hm-2.     

Potential errors in measurement of nonuniform sap flow using heat dissipation probes

The empirical calibration of Granier-type heat dissipation sap flow probes that relate temperature difference (DeltaT) to sap velocity (v) was reevaluated in stems of three tropical tree species. The original calibration was confirmed when the entire heated probe was in contact with conducting xylem, but mean v was underestimated when part of the probe was in contact with nonconducting xylem or bark. Analysis of the effects of nonuniform sap velocity profiles on heat dissipation estimates showed that errors increased as v and the proportion of the probe in nonconducting wood increased. If half of a 20-mm probe is in sapwood with a v of 0.15 mm s(-1) and the other half is in nonconducting wood, then mean v for the whole probe can be underestimated by as much as 50%. A correction was developed that can be used if the proportion of the probe in nonconducting wood is known. Even with the entire heated probe in contact with conducting xylem, v would be underestimated when radial velocity gradients are present. In this case, the error would be smaller except when velocity gradients are very steep, as can occur in species with ring-porous wood anatomy. Errors occur because the relationship between DeltaT and v is nonlinear. Mean DeltaT along the probe is therefore not a measure of mean v, and users of heat dissipation probes should not assume that v is integrated along the length of the probe. The same type of error can occur when DeltaT is averaged through time while v is changing, but the error is small unless there are sudden, step changes between zero and high sap velocity. It is recommended that relatively short probes (20 mm or less) be used and that probes longer than the depth of conducting sapwood be avoided. Multiple probes inserted to a range of depths should be used in situations where steep gradients in v are expected. If these conditions are met, heat dissipation probes remain useful and widely applicable for measuring sap flow in woody stems.     

Measurement of diurnal changes in stem and branch diameters using strain gauges

The applicability of a strain gauge for monitoring the diurnal changes of tree stem diameters and the differences in diurnal shrinkages between a stem and branches were investigated. Estimates of stem diameter changes obtained by a strain gauge were compared with changes obtained by a differential transformer. Patterns of strain changes obtained by a strain gauge were remarkably similar to the changes in the tree trunk diameter. This results demonstrated that a strain gauge is an effective technique for examining the behavior of changes in tree trunk diameter. Diurnal changes of diameter at various parts of the a tree were also measured with the help of several strain gauges. Diurnal strain changes of a stem and branches showed similar patterns of shrinkage during the day and swelling at night. However, the precise times at which the branches had their maximum and minimum strains differed from those observed in the stem, and the maximum rates of the strain changes lagged behind the stems in a day. These results lead us to believe that there is a time lag in the supply of water, which is required for compensating the water deficit between the stem and its branches. A part of this paper was presented at the 105th Annual Meeting of Japanese Forestry Society (1994).     

A model of heat transfer in sapwood and implications for sap flux density measurements using thermal dissipation probes

A variety of thermal approaches are used to estimate sap flux density in stems of woody plants. Models have proved valuable tools for interpreting the behavior of heat pulse, heat balance and heat field deformation techniques, but have seldom been used to describe heat transfer dynamics for the heat dissipation method. Therefore, to better understand the behavior of heat dissipation probes, a model was developed that takes into account the thermal properties of wood, the physical dimensions and thermal characteristics of the probes, and the conductive and convective heat transfer that occurs due to water flow in the sapwood. Probes were simulated as aluminum tubes 20 mm in length and 2 mm in diameter, whereas sapwood, heartwood and bark each had a density and water fraction that determined their thermal properties. Base simulations assumed a constant sap flux density with sapwood depth and no wounding or physical disruption of xylem beyond the 2 mm diameter hole drilled for probe installation. Simulations across a range of sap flux densities showed that the dimensionless quantity k [defined as (ΔT(m) -ΔT)/ΔT, where ΔT(m) is the temperature differential (ΔT) between the heated and unheated probe under zero-flow conditions] was dependent on the thermal conductivity of the sapwood. The relationship between sap flux density and k was also sensitive to radial gradients in sap flux density and to xylem disruption near the probe. Monte Carlo analysis in which 1000 simulations were conducted while simultaneously varying thermal conductivity and wound diameter revealed that sap flux density and k showed considerable departure from the original calibration equation used with this technique. The departure was greatest for variation in sap flux density typical of ring-porous species. Depending on the specific combination of thermal conductivity and wound diameter, use of the original calibration equation resulted in an 81% under- to 48% overestimation of sap flux density at modest flux rates. Future studies should verify these simulations and assess their utility in estimating sap flux density for this widely used technique.     

不同时间尺度下兴安落叶松树干液流密度与环境因子的关系

基于连续1年的兴安落叶松树干液流密度和环境因子(光照、空气温度、空气湿度、土壤温度和土壤湿度)的测定结果,探讨不同时间尺度下树干液流密度与环境因子的关系差异.在月时间尺度上,土壤温度和土壤湿度显著影响树干液流密度变化,土壤温度单位增加引起树干液流上升0.084～0.123 L·cm-2 month-1;在天时间尺度上,显著影响因子有土壤温度、光照和空气温度,其中土壤温度为最主要的影响因子,单位增加会导致树干液流上升1.9 ～2.7 mL·cm-2 d-1;在小时时间尺度上,主要影响因子在不同季节不同,但最主要因子多是直接影响地上叶片生理指标如光照和空气湿度,二者单位上升平均分别引起树干液流上升1.239 mL·cm-2 min-1和下降0.0566 mL·cm-2 min-1.随尺度由大到小,对树干液流影响最大的因子有从地下直接与根系水分吸收相关的土壤环境因子向地上直接影响叶片蒸腾的环境因子(光照和空气湿度)转变的趋势.同时,随着尺度增大,与树干液流显著相关的环境因子数明显下降,且相关系数R2显著提高,长期监测树木耗水可以采用监测环境因子反推的方法,而在小尺度上相同方法可能导致很大误差,最好采用直接测定法.     

Estimating stand water use of large mountain ash trees and validation of the sap flow measurement technique

Mountain ash (Eucalyptus regnans F.J. Muell.) forest catchments exhibit a strong relationship between stand age and runoff, attributed inter alia to differences in tree water use. However, the tree water use component of the mountain ash forest water balance is poorly quantified. We have used the sap flow technique to obtain estimates of daily water use in large mountain ash trees. First, the sap flow technique was validated by means of an in situ cut tree experiment. Close agreement was obtained between the sap flow estimate of water use and the actual uptake of water by the tree from a reservoir. Second, we compared the variability in sap velocity between a symmetric and an asymmetric tree by using multiple sap flow loggers. In the symmetric tree, velocity was fairly uniform throughout the xylem during the day, indicating that accurate sap flow estimates can be obtained with a minimal number of sampling points. However, large variations in sap velocity were observed in the asymmetric tree, indicating that much larger sampling sizes are required in asymmetric stems for an accurate determination of mean sap velocity. Finally, we compared two procedures for scaling individual tree sap flow estimates to the stand level based on stem diameter and leaf area index measurements. The first procedure was based on a regression between stem diameter and tree water use, developed on a small sample of trees and applied to a stand-level census of stem diameter values. Inputs to the second procedure were tree water use and leaf area of a single tree and the leaf area index of the stand. The two procedures yielded similar results; however, the first procedure was more robust but it required more sampling effort than the second procedure.     

干旱区杏李树干液流时滞特征研究

为探讨树干液流速率与气象因子之间的时滞特性,采取PS-TDP8型热耗散式树干液流测定系统持续监测,以掌握树体蒸腾耗水规律,从而为杏李科学灌溉提供理论依据。研究结果表明:杏李生长季液流速率日均最大值在6月18日;决定其第1主成分大小的是温度及水气压亏缺,决定第2主成分大小的是光照强度及空气相对湿度。4—8月液流速率均与1 h前第1、2主成分相关性最大;杏李生长季液流与1 h前光照强度相关性最大,相关系数为0.810,与1 h后的气温、空气相对湿度、水汽压亏缺相关性最大,系数分别为0.757,-0.572,0.736;回归方程中液流与实时气象因子拟合决定系数最大,为0.751。杏李生长季液流速率与实时气象因子回归拟合模型效果最好,体现了杏李在长期树干液流数据模拟中,可以不用考虑液流速率与气象因子的时滞效应。     

Photosynthesis, carbohydrate storage and survival of a native and an introduced tree species in relation to light and defoliation

Fraxinus uhdei (Wenz.) Lingelsh (tropical ash), a species introduced to Hawaii from Mexico, invades forests of the endemic tree Acacia koa A.Gray (koa). We examined physiological and morphological characteristics of koa and tropical ash to explore possible mechanisms that may facilitate invasion of koa forests by tropical ash. Seedlings of both species were grown in a greenhouse in three light treatments: 100% photosynthetic photon flux (PPF); 18% PPF; and 2% PPF inside the greenhouse. Light compensation point, maximum CO2 assimilation rate and dark respiration rate of seedlings differed significantly among light treatments, but were similar between species. A defoliation experiment indicated that tropical ash was better able to survive defoliation than koa, especially under high-light conditions. Tropical ash seedlings allocated more carbon (C) and nitrogen (N) to storage per unit PPF than koa seedlings. Total nonstructural carbohydrates were positively correlated with plant survival in both species. The patterns of C and N allocation associated with tropical ash seedlings favor their survival in high light, under intense herbivory and on sites where N availability is seasonal or highly variable. Variation in carbohydrate storage between koa and tropical ash greatly exceeded variation in photosynthetic performance at the leaf level.     

Xylem sap flow and drought stress of Fraxinus excelsior saplings

We report on diurnal and seasonal variations in sap flow rate and stem water potential of Fraxinus excelsior L. saplings growing at the edge of a Fraxino-Aceretum forest in western Germany. Because of shallow soil, the trees were subjected to drought in summer. When soil water availability was not limiting, sap flow rate was related to changes in solar radiation and vapor pressure deficit. Maximum transpiration rates per leaf area were 3.5-7.4 mmol m-2 s-1, and maximum daily totals were 1.7-3.3 kg m-2 day-1. Under drought conditions, stem water potential dropped to midday minima of -2.6 to -3.5 MPa and sap flow rate was strongly related to this parameter. After the drought period, reduced apparent (whole-plant) hydraulic conductance was observed, which was attributed to a continued reduction in stomatal conductance after the drought stress had ceased. A model was developed that linked sap flow rate directly to climatic variables and stem water potential. Good correlation between measured and simulated sap flow rates allowed the model to be used for data interpretation.     

天目山柳杉古树的液流特征研究

应用热扩散技术法,于2010年4—8月对浙江天目山自然保护区内的2株柳杉古树的树干液流进行连续观测,结合所测定的相关环境因子,分析了柳杉树干液流和耗水量的变化规律,以及液流与各环境因子的关系。结果表明:不同季节柳杉树干液流速率日变化规律基本一致,呈单峰波动曲线,但树干液流启动时间、达到峰值时间及迅速下降时间存在明显差异;树干液流密度与光合有效辐射、空气温度和水汽压差间存在极显著正相关,与空气相对湿度和CO₂浓度呈极显著负相关;液流密度随树干直径的增加,无明显变化差异,但液流速率和日均耗水量均随树干直径的增加而增大;胸径75.6 cm柳杉和胸径62.8 cm柳杉的日均耗水量季节变化过程相同,但2者变化差异较大,6月份日均耗水量最低,分别为(49.356±14.883) kg和(9.531±4.297)kg;4月份日均耗水量最高,分别为(110.022±21.890)kg和(49.352±2.629)kg。     

In situ measurement of water absorption by fine roots of three temperate trees: species differences and differential activity of superficial and deep roots

The spatial heterogeneity of water uptake by fine roots under field conditions was analyzed in situ with miniature sap flow gauges in a mature beech-oak-spruce mixed stand. Sap flow rate (J), sap flow density (Jd), and root surface-area-specific flow rate (uptake rate, Js) were measured for eight to 10 small-diameter roots (3-4 mm) per species in the organic layer (superficial roots) and in the mineral soil (30-80 cm, deep roots) during four months in summer 1999. We calculated Js by relating J to the surface area of the section of the fine root system distal to the position of the gauge on the root. When measured synchronously, roots of the three species did not differ significantly in mean Js, although oak roots tended to have lower rates. However, Jd decreased in the sequence spruce > beech > oak in most measurement periods. Microscopic investigation revealed differences in fine root anatomy that may partly explain the species differences in Jd and Js. Oak fine roots had a thicker periderm than beech and spruce roots of similar diameter and spruce roots had fewer fine branch rootlets than the other species. Synchronously recorded Jd and Js of nearby roots of the same tree species showed large differences in flow with coefficients of variation from 25 to 150% that could not be explained by patchy distribution of soil water. We hypothesize that the main cause of the large spatial heterogeneity in root water uptake is associated with differences between individual roots in morphology and ultrastructure of the root cortex that affect root radial and root-soil interface conductivities. The high intraspecific variation in Js may mask species differences in root water uptake. Superficial roots of all species typically had about five times higher Jd than deep roots of the same species. However, Js values were similar for superficial and deep roots in beech and spruce because small diameter roots of both species were more branched in the organic layer than in mineral soil. In oak, deep roots had lower Js (maximum of 100 g m(-2) day(-1)) than superficial roots (about 1000 g m(-2) day(-1)). We conclude that temperate tree species in mixed stands have different water uptake capacities. Water flow in the rhizosphere of forests appears to be a highly heterogeneous process that is influenced by both tree species and differences in uptake rates of individual roots within a species.     

A dynamic model for water flow in a single tree: evidence that models must account for hydraulic architecture

A model is presented for the dynamics of water flow in a single eastern white cedar tree (Thuja occidentalis L.). The model takes into account the spatial and temporal dependence of the evaporative flux from leaves in the crown. It also accounts for the quantitative hydraulic architecture of the tree, i.e., the model characterizes the tree as a branched catena of > 4000 stem segments in which account is taken of the segment length, diameter, hydraulic resistance, and the total area of leaves attached to the segment. Input values needed to run the model are measurements of evaporative flux, hydraulic conductance of stems versus stem diameter, and leaf and stem water storage capacitances. Output parameters are the spatial and temporal characterization of stem and leaf water potentials, stem and leaf water deficits, sap flow rate, and relative sap velocity. The input and output values of the branched catena model are compared and contrasted to that of an unbranched catena model. It is shown that the branched catena model fits independently measured field parameters better than an unbranched catena model. Close correspondence is found between model predictions and field measurements of shoot water potential, pressure gradients in stems, hysteresis in sap velocity between the lower and upper parts of the tree, and diurnal changes in stem and leaf water deficits. This model is discussed in terms of both the hydraulic architecture of trees and the potential application of the model to questions of tree morphology, ecology, physiology and evolution.     

Radial variation in sap flow in five laurel forest tree species in Tenerife,Canary Islands

Variations in radial patterns of xylem water content and sap flow rate were measured in five laurel forest tree species (Laurus azorica (Seub.) Franco, Persea indica (L.) Spreng., Myrica faya Ait., Erica arborea L. and Ilex perado Ait. ssp. platyphylla (Webb & Berth.) Tutin) growing in an experimental plot at Agua García, Tenerife, Canary Islands. Measurements were performed around midday during warm and sunny days by the heat field deformation method. In all species, water content was almost constant (around 35% by volume) over the whole xylem cross-sectional area. There were no differences in wood color over the whole cross-sectional area of the stem in most species with the exception of E. arborea, whose wood became darker in the inner layers. Radial patterns of sap flow were highly variable and did not show clear relationships with tree diameter or species. Sap flow occurred over the whole xylem cross-sectional area in some species, whereas it was limited to the outer xylem layers in others. Sap flow rate was either similar along the xylem radius or exhibited a peak in the outer part of the xylem area. Low sap flow rates with little variation in radial pattern were typical for shaded suppressed trees, whereas dominant trees exhibited high sap flow rates with a peak in the radial pattern. Stem damage resulted in a significant decrease in sap flow rate in the outer xylem layers. The outer xylem is more important for whole tree water supply than the inner xylem because of its larger size. We conclude that measurement of radial flow pattern provides a reliable method of integrating sap flow from individual measuring points to the whole tree.     

Radial profiles of sap flow with increasing tree size in maritime pine

We investigated the radial variation of sap flow within sapwood below the live crown in relation to tree size in 10-, 32-, 54- and 91-year-old maritime pine stands (Pinus pinaster Ait.). Radial variations were determined with two thermal dissipation sensors; one measured sap flux in the outer 20 mm of the xylem (Jref), whereas the other was moved radially across the sapwood in 20-mm increments to measure sap flux at multiple depths (Jref). For all tree sizes, sap flow ratios (Ri = JiJref (-1)) declined with increasing sapwood depth, but the decrease was steeper in trees with large diameters. Correction factors (C) were calculated to extrapolate Jref for an estimate of whole-tree sap flux. A negative linear relationship was established between stem diameter and C, the latter ranging from 0.6 to 1.0. We found that neglecting these radial corrections in 10-, 32-, 54- and 91-year-old trees would lead to overestimation of stand transpiration by 4, 14, 26 and 47%, respectively. Therefore, it is necessary to account for the differential radial profiles of sap flow in relation to tree size when comparing tree transpiration and hydraulic properties among trees differing in size.