Báo cáo khoa học: "Interpreting the variations in xylem sap flux density within the trunk of maritime pine (Pinus pinaster Ait.): application of a model for calculating water flows at tree and stand levels"

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Nội dung Text: Báo cáo khoa học: "Interpreting the variations in xylem sap flux density within the trunk of maritime pine (Pinus pinaster Ait.): application of a model for calculating water flows at tree and stand levels"

Original article Interpreting the variations in xylem sap flux density within the trunk of maritime pine (Pinus pinaster Ait.): application of a model for calculating water flows at tree and stand levels Denis Loustau Alexandre Bosc Jean-Christophe Domec, Laboratoire d’écophysiologie et nutrition, Inra-Forêts, BP 45, 33611 Gazinet, France (Received 15 January 1997; accepted 30 June 1997) Abstract - Sap flux density was measured throughout a whole growing season at different loca- tions within a 25-year-old maritime pine trunk using a continuous constant-power heating method with the aim of 1) assessing the variability of the sap flux density within a horizontal plane of the stem section and 2) interpreting the time shift in sap flow at different heights over the course of a day. Measurements were made at five height levels, from 1.3 to 15 m above ground level. At two heights (i.e. 1.30 m and beneath the lower living whorl, respectively), sap flux density was also measured at four azimuth angles. Additionally, diurnal time courses of canopy transpiration, needle transpiration, needle and trunk water potential, and trunk volume variations were measured over 4 days with differing soil moisture contents. At the single tree level, the variability of sap flux density with respect to azimuth was higher at the base of the trunk than immediately beneath the live crown. This has important implications for sampling methodologies. The observed pattern suggests that the azimuth variations observed may be attributed to sapwood heterogeneity caused by anisotropic distribution of the sapwoods hydraulic properties rather than to a sectorisation of sap flux. At the stand level, we did not find any evidence of a relationship between the tree social status and its sap flux density, and this we attributed to the high degree of homogeneity within the stand and its low LAI. An unbranched three-compartment RC-analogue model of water transfer through the tree is proposed as a rational basis for interpreting the vertical variations in water flux along the soil-tree-atmosphere continuum. Methods for determining the parameters of the model in the field are described. The model outputs are evaluated through a comparison with tree tran- spiration and needle water potential collected in the field. (© Inra/Elsevier, Paris.) sap flux / transpiration / water transfer model / Pinus pinaster Résumé - Interprétation des variations de densité de flux de sève dans le tronc d’un pin mari- time (Pinus pinaster Ait.): application d’un modèle de calcul des flux aux niveaux arbre et peuplement. La densité de flux de sève brute d’un pin maritime de 25 ans a été mesurée en * Correspondence and reprints Fax: (33) 56 68 05 46; e-mail: loustau@pierroton.inra.fr
continu à différentes positions du tronc et durant une saison de croissance complète, par une méthode à flux de chaleur constant, dans le but a) d’étudier la variabilité de la densité de flux dans la section transversale du tronc et b) d’analyser le décalage de temps du signal entre différentes hauteurs au cours de la journée. Les mesures ont été effectuées à cinq hauteurs, de 1,3 à 15 m au dessus du sol. À deux niveaux (1,3 m et sous la couronne vivante, respectivement) la densité de flux a été mesurée suivant quatre azimuts. L’évolution journalière de la transpiration du cou- vert, de la transpiration des aiguilles, du potentiel hydrique du tronc et des aiguilles et des varia- tions de volume du tronc a aussi été mesurée durant quatre journées couvrant une gamme de niveaux d’humidité du sol. Au niveau arbre, la variabilité de la densité de flux de sève dans la sec- tion horizontale de l’aubier était plus élevée à la base du tronc que sous la couronne. Ceci pour- rait s’expliquer par l’anisotropie des propriétés mécaniques et hydrauliques du bois dans le plan horizontal, classique chez le pin maritime, plutôt que par une sectorisation du flux liée à l’archi- tecture de la couronne. Au niveau peuplement, aucune relation entre la densité de flux de sève et le statut social de l’arbre n’a été mise en évidence, ce qui s’explique par l’homogénéité du peu- plement et son faible indice foliaire. Nous avons utilisé un modèle de transfert RC à trois com- partiments pour interpréter les variations de flux de sève le long du transfert sol-aiguille. Les méthodes de détermination des résistance et capacitance de chaque compartiment sont décrites. Les sorties du modèle ont été comparées avec les mesures de transpiration, flux de sève et de poten- tiel hydrique mesurées dans deux peuplements âgés de 25 et 65 ans respectivement.. Le modèle explique assez bien les variations de flux observées le long du continuum sol-aiguille. Au cours de la sécheresse, on observe une augmentation importante (x 10) de la résistance du comparti- ment racine-tronc. Cette augmentation est moins importante dans les branches (x 2). Les capa- citances sont peu affectées par la sécheresse. (© Inra/Elsevier, Paris.) transpiration / flux de sève / modèle de transfert hydrique Pinus pinaster Ait / preting sap flow measurements on a ratio- 1. INTRODUCTION nal basis. Until now, the methods used for flow measurement is a useful extrapolating sap flow data to estimate Sap stand transpiration have remained rather method for assessing the water use by for- empirical, with the capacitances in the est trees; it does not require horizontally water transfer process within trees either homogeneous stand structure and topog- being ignored [1, 7, 19] or extremely sim- raphy and therefore can be used in situa- plified, such as being reduced to a con- tions where methods such as eddy covari- stant time shift between sap flux and tran- ance cannot. Sap flow measurements allow spiration [13]. Resistance and capacitance one to partition the stand water flux to water transfer within some forest trees between canopy sublayers or to discrimi- nate between particular individuals in a have been determined for stem segments [9, 31]and for whole trees (using cut-tree stand. Sap flow data have been used for experiments). However, the extent to estimating hourly transpiration and canopy conductances in a range of forest stands which these measured values can be applied under natural conditions is ques- [1, 10, 13, 19, 20]. The sap flow mea- tionable, since both methods rely on the surements can provide a useful investiga- analysis of pressure-flux relationships and tive tool for a variety of purposes, pro- water retention curves determined mainly viding the results can be properly upscaled under positive or slightly negative pres- to the stand level, which requires a descrip- sures [9]. Cohen et al. [4] proposed a tion of the network of resistances and method for estimating soil-to-leaf bulk capacitances which characterise the path- resistance in the field based on sap flux way of water between the soil and the measurement which avoided this ’arte- atmosphere [18, 26]. In order to do this, fact’, and has been applied to different we need a scheme for quantitatively inter-
forest improving the accuracy of the estimation of species [1, 14, 23]. Using a resis- tance-capacitance analogue of the flow flux at tree and stand levels. water pathway, Wronski et al. [37] and Milne [25] derived values of stem resistance and capacitance from field measurements of 2. AN UNBRANCHED RC MODEL water potential, stem shrinkage and tran- OF TREE WATER FLUX spiration on radiata pine and sitka spruce, respectively. The flow pathway along the soil-tree- The aim of this paper is to present a atmosphere continuum is considered as a simple RC analogue of water transfer series of RC units. This sort of model was within the soil-tree-atmosphere contin- first applied by Landsberg et al. [22] on uum in order to interpret diurnal variations apple trees and solutions for estimating of flux and water potential observed at dif- the water potential from transpiration mea- ferent locations in the tree. Methods are surements was given, e.g. by Powell and described that allow the determination of Thorpe [28]. The present model consid- both the resistance and capacitance of the ers the tree as a three-compartment sys- tree, based on sap flux measurement in the tem: i) root and trunk, ii) branches and field. In addition, we summarise the results iii) needles. Such an approach has been obtained concerning the sap flux hetero- applied to different coniferous trees, e.g. geneity within a maritime pine stand in a Pinus radiata [37], Picea sitchensis [25] horizontal plane and suggest methods for and Picea abies [5]. Figure I illustrates
the electrical analogue of the model. The main assumptions of our analysis can be summarised as follows: the is treated as a big leaf with crown - homogeneous temperature and transpi- a ration rate; the resistance and capacitance of - each compartment are independent of the flux or water potential of the compartment and remain constant during the day (but they can change between days); there is no storage resistance, that is - the water potential gradient between the reservoir and the xylem can be neglected. In the following, all the fluxes, resis- and capacitances are expressed on tances an all-sided needle area basis. The water Equations (1), (5) and (6) allow us to potential values used in the present paper estimate iteratively the time course of are corrected for the gravitational gradi- water flux and potential from the initial ent. The basic equations for each com- values of a given flux, J and water poten- , i partment are as follows: . i tial, Ψ The parameters of the model can be where derived as follows. The resistance of each compartment is given by the slope of the regression line relating the instantaneous sap flux within the compartment, J to the , i instantaneous difference between the water potentials at its upper and lower bound- aries, i.e. Ψ [equation (3)]. A (t) i-1 (t) - Ψ i where J is the liquid water flux expressed i similar calculation has been applied pre- in kg·m Jr storage flux, R , -1 ·s the -2 i i viously for the whole tree, e.g. by Cohen ·s) 2 ·m -1 (MPa·kg and C (kg·m i -2 ) -1 ·MPa et al. [4], Granier et al. [14] and Bréda et the resistance and capacitance of the com- al. [1]. This analysis must be carried out partment and Ψ its water potential (MPa). i with data covering the entire daily time The subscripti denotes the compartment course, where the final water content of and can be either c for the branches of the the tree is equal to the initial. It does not crown, s for the stem and root, or n for the necessarily require that measurements be needles. If we assume that any change in made under steady-state conditions, i.e. the water potential of the lower compart- Jr may take positive or negative val- (t) i ment during each time step can be ues. In order to estimate the capacitance of neglected, replacing Jr and J in equa- i i the root + stem and branch compartments, tion (1) leads to the differential equation: ) i -Δt( exp CRas · calculate the value of we the slope of the regression line fitted which can be solved for Ψ and Jr ii giving , between Jr and (t) i the following expressions:
ables. The Bray site has been extensively stud- ied since 1987 and a detailed description can be found, e.g. in Diawara et al. [6]. The Car- rasqueira site is also part of several Portuguese and European research projects and is described according to equation (6) and then extract by Loustau et al. [24]. the value of C using the value of R cal- i i Determination of the model parameters was culated previously. For the capacitance of carried out for a single tree at the Bray site on the needle compartment, we used a value 4 days (days 153, 159, 229 and 243) in 1995. Table II summarises the sampling procedure of 0.025 kg·MPa assuming a bulk , -2 ·m -1 applied for each variable measured. elastic modulus of 25 MPa [36] and a semi-cylindrical needle shape with an average diameter of 0.002 m. 3.2. Azimuthal variability of sap flux density 3. MATERIALS AND METHODS Azimuthal variations in sap flux density the sapwood horizontal section were across assessed on three trees at the Bray site. Sen- 3.1. Sites sors were inserted at a height of 1.30 m in four azimuthal orientations. For one tree, sensors were inserted at 1.50 and 8.50 m, just below The model was parameterised and evalu- ated using data collected from two different the last living whorl. Sap flux densities were experiments, at the Bray site in France monitored from May to August 1991 on two (44°42N, 0°46W) and the Carrasqueira site in trees, and from May to September 1995 on the tree with two measurement heights. The trees Portugal (38°50N, 8°51W) (table 1).Both sites were pure even-aged stands of maritime pine were then cut and a cross section of stems at with an LAI ranging between 2.0 and 3.5. In each measurement height was cut, rubbed both locations, the soil water retention capac- down, polished and scanned with a high reso- ity is rather low due to the coarse texture of lution scanner (Hewlett Packard Scanjet II cx). the soil and a summer rainfall deficit that The number of rings crossed by each heating induces soil drought and subsequent tree water probe and the total conducting area were deter- stress, this summer drought being far more mined together with the ratio between the ear- severe at the Portuguese site. The sites were lywood and latewood area crossed by the equipped with neutron probe access tubes and probe. We analysed only the data collected scaffolding towers, enabling monitoring of the during clear days and considered only the nor- malised daily sums of sap flux density. soil moisture and micrometeorological vari-
In order to analyse the between-tree vari- by all the sensors at that height, one, two or of sap flux density, we collected sap four according to the height (table II). At the ability flux data from three different experiments, at Bray site, the whole tree water flux at z 8.5 m, = the Bray Site in 1989 and in 1994 and at the J was calculated on a leaf area basis by: , c Carrasqueira site in 1994. In each experiment, one sensor was inserted into the northern face of each stem and measurements were carried out as described above. The data were pooled and compared on a daily summation basis with where A is the cross-sectional area of the con- c ductive pathway and L the leaf area (all sided) respect to the average value of each site. of the tree. A was measured after the experi- c ment on the slice of wood extracted from the trunk at a height of 8.5 m as described above. 3.3. Flux measurement L was estimated using the sapwood area-leaf relationship determined by Loustau area The sap flux density of each compartment, (unpublished data) from a destructive sampling j was measured using the linear heating sen- of 20 trees at the same site. At Carrasqueira, , i sor designed by Granier [ 12] and applying the only one sensor was inserted at each level. In empirical relationship relating sap flux den- this case, the stem sap flux at a height of 1.5 m, sity to the thermal difference between the J and beneath the crown, J was estimated , s , n heated and reference probes. The measure- by assuming that the daily total of water flow ments were carried out on a single tree, referred through the tree was conserved. This implies to here as the target tree (table III). No attempt that the daily total of water flow at any location within the system is conserved and that the was made to take into account possible natural gradients of temperature between the two ratio between the respective values of the sap- probes [11 ]. At the Bray site, the sap flux den- wood cross-sectional area and the daily sum sity at each measurement level was calculated of sap flux density at any pair of points of as the arithmetic mean of the values measured heights within the tree is constant. Thus, we
estimated the sapwood cross-sectional area of age value of 15 soil psychrometric chambers each compartment i (i ≠ c), A using the ratio used in dew-point mode (Wescor soil psy- , i chrometer) and buried at five depths from-10 to -50 cm. , &i and Sigma;j between its sap flux daily density, 3.6. Vapour flux measurements the sap flux , &c Sigma;j beneath the crown, density follows: The transpiration of pine canopy was esti- as mated using eddy covariance measurements of the vapour flux at two levels, above the tree crowns and in the trunkspace between the tree crown and the understorey. Fluctuations in wind speed, temperature and in water vapour concentration were measured with a 3D or 1D sonic anemometer and a Krypton hygrometer, respectively. The difference between the vapour fluxes measured above and beneath the pine crowns was assumed to give the transpi- 3.4. Storage flux ration of the pine trees only. These measure- ments were available for 14 days at the Car- rasqueira site in 1994, and for 10 days at the The total storage flux of the crown and Bray site in 1995. The methods used, the cor- stem, J were calculated as the instantaneous , ri rections applied in order to take into account the difference between sap flux values measured density effects and the absorption of UV by above and beneath the compartment consid- oxygen, energy balance closure tests and sam- ered, according to equation (1), following Lous- pling procedures are detailed by Berbigier et al. tau et al. [24]. For the stem storage only, the [2] for the Carrasqueira site and Lamaud et al. elastic storage flux into the trunk was also esti- [21]for the Bray site. mated from trunk volume variations, assum- ing these variations were due only to the trans- fer of water from the phloem into the xylem. The dendrometers used were linear displace- 4. RESULTS ment transducers (’Colvern’) regularly spaced along the stem (table II) and corrected for tem- perature variations. Each transducer was fixed 4.1. Azimuthal variability of sap flux to a PVC anchor which was attached to the opposite side of the trunk using 5-cm-long density in pine stands screws. Dead bark tissue was removed such that the sensor was directly in contact with Figure 2 shows the time course of the external xylem. measured sap flux density at four azimuth angles and two heights in the trunk of the target tree at the Bray site throughout a 3.5. Water potential measurements typical spring day. There was very little, if any, variation in sap flux density with Needle water potential was measured hourly azimuth angle immediately beneath the a pressure chamber. The branches and using crown, whilst considerable differences trunk water potential were estimated using non- were found at the base of the trunk. This transpiring needles attached at the appropriate locations (table II). These needles were pattern was conserved throughout the enclosed in waterproof aluminium-coated plas- whole measurement period, and was not tic bags after wetting the previous night, and it affected by soil drought (data not shown). was assumed that their water potential came Figure3 summarises the results obtained into thorough equilibrium with the branch or concerning the variability of sap flux den- trunk xylem to which they were attached. The sity at a height of 1.30 m for three trees soil water potential was estimated as the aver-
Bray site. The relationship between at the sap flux density and either the number of rings or the proportion of earlywood crossed by the probe was not significant, though there was a trend for the sap flow density to decrease as the number of tree rings measured increased in two out of four trees. Furthermore, there was no sig- nificant relationship between the varia- tion in sap flux density and the stem basal inclination, even where the excentricity of heartwood and subsequent sapwood azimuthal anisotropy was obvious. No sig- nificant relationship was found between the sap flux density measured at 1.3 m high and tree size in either experiment (figure 4).
4.2. Determination of the parameters Figure 6 illustrates the procedure used of the model for estimating the branch and stem capac- itance for day 153. We did not observe any clear change in the stem or branch Figure 5 shows the flux-water potential capacitance for the four sample days at used in calculating gradient relationship the Bray site. the resistance of the three compartments for 2 days of contrasting soil moisture. The corresponding values of the resis- 4.3. Model evaluation tances are given in table IV. Soil moisture reached its lowest value on days 229 and 243 and the predawn water potential mea- Figure 7 compares the water potential sured for these 2 days (table IV) are typi- values predicted by the model and the measured values, for day153 at the Bray cal of those found during a severe drought in this area. There was a dramatic, 8-fold site. There is an acceptable agreement increase in the resistance of the root-trunk between the measured and predicted data, even if a difference is observed during the compartment under these drought condi- tions, which contrasted with a very slight morning and late afternoon for the lower compartments. This figure also compares increase in the resistance of the branch the storage flux for the stem predicted by and needle compartments.
the model with the flux calculated from eddy covariance for 2 days on each site. change in the stem volume. This compar- ’upscaled’ the sap flux values from We tree to stand using optically determined ison shows that predicted and observed data are the same order of magnitude but leaf area index values (table I), assuming differences remain certain times of the the needles had a semi-cylindrical shape, at day. Figures 8 and 9 show the model’s and calculating the sap flux as the aver- outputs together with measured data for age of the measurements made at a height of 6 m on a sample of ten trees at Car- two representative days at the Carrasqueira and Bray sites, respectively. The parame- rasqueira and at a height of 8.5 m on seven ter values used for implementing the trees at the Bray site. The time course of model have been derived from measure- the predicted values of water potential are ments made at different heights [24] and also shown and compared with measured are shown in table IV. The figures com- data for the days 178 and180 at the Car- pare the values of vapour flux predicted rasqueira site. The values measured by from sap flow measurements at the base of eddy covariance exhibited erratic varia- the crown and at the base of the trunk with tions, particularly when the weather the evapotranspiration data measured by regime was irregular, but the overall pat-
tem showed acceptable agreement. Water to the measurement height which could further support this conclusion. Since it is potential values predicted by the model are also compared with measured data for based on measurements made on only 1 d (DOY180 Carrasqueira site) and indi- three trees, this conclusion deserves addi- cate that the model predicts the measured tional experimental support. Sap flux den- values reasonably well. Figure 10 shows sity variations could not be related signif- the relationship between the predicted and icantly to the number of rings or the measured vapour flux values for both sites. earlywood/latewood ratio of the sapwood is slightly better for the Car- crossed by the heating probe. We think, Agreement rasqueira where data were obtained on however, that such a relationship could bright clear days than for the Bray where occur within a tree but was not observed data were collected under changeable because of the low number of replicates. It weather conditions. may, nevertheless, play an important role since Dye et al. [8] showed that growth rings and compression wood created a DISCUSSION radial heterogeneity in sap flux density within the sapwood of another pine species, P. patula, and that there was a An important methodological outcome of this work is that a lower sampling error subsequent heterogeneity in the azimuthal distribution of sap flux density. Addition- for mean sap flux density of a homoge- ally, it has long been established that the neous stand should be expected when the sap flux measurements are made imme- sap flux density varies radially within the sapwood cross-sectional area [3, 15, 16, diately below the crown rather than at ground level. This is particularly true for 27] which could also affect the azimuthal trees exhibiting basal trunk curvature and distribution of sap flux in anisotropic subsequent wood excentricity and sap- stems. The between-tree variation of sap wood anisotropy. We did not find any lit- flux density was, therefore, unsurprising erature concerning the pattern of azimuthal since the data presented in figure4 actually distribution of sap flux density according include the within-tree variability. In addi-
with wet soil and reached 348 min with tion, only a weak between-tree variation in dry soil. Consequently, the estimation of sap flux density would be expected in hourly transpiration values from extrapo- these homogeneous pine stands where the leaf area index did not exceed a value of 3. lating sap flow measurements made at the This precludes any major differences base of the trunk becomes extremely dif- between trees of differing social position. ficult on dry soil since a very accurate measurement of the water potential at the Models based similar electrical on a soil-root interface becomes necessary. analogue, with various degrees of sophis- The major cause of this increase in the tication in tree architecture representation root-trunk compartment may be attributed were published by Powell and Thorpe to the decrease in soil hydraulic conduc- [28], Landsberg [22], Wronski et al. [37], tivity in the vicinity of the roots, since the Milne [25] and Cruiziat et al. [5] following trunk and root xylem of coniferous trees the pioneer work of Van den Honert [34], have not been reported as showing a sub- but their practical utilisation remains lim- stantial reduction in hydraulic conductiv- ited owing to the large numbers of param- ity caused by cavitation of tracheids at eters required. The merit of the present these levels of water potential [32]. model is its simplicity, which could make Another important consequence of this it useful for routine transpiration calcula- increase in time constant under soil tions from sap flow measurements, pro- drought is that, under extremely dry con- vided that a proper parameterisation of the ditions, trees might not have sufficient resistance and capacitance values is time overnight to restore their equilibrium achieved. This would facilitate using sap water content. During a continuous period flow measurements to estimate tree tran- of drought, we can therefore hypothesise spiration (and consequently surface con- that trees having a large time constant, ductance) when other techniques are such as large coniferous trees, could expe- impractical, and would allow partitioning rience a sort of ’runaway’ dehydration of the vapour fluxes among canopy lay- resulting in them drying faster than the ers on a short term basis. From this point soil itself. of view, the inadequacy of assuming that sap flow lags with a constant time shift An interesting practical issue arising behind transpiration should be highlighted. from the present paper is our method for The constant time-lag hypothesis implies estimating the values of the bulk resis- that the water storage flux in the tree tance and capacitance of each compart- would always correspond to a constant ment under natural conditions with mini- time fraction of the transpiration, which mum disturbance to the tree. These is obviously erroneous. The storage flux methods are consistent with the use of the varies during the day and reaches its max- parameter values in the model. Estima- imal absolute values in the morning and tion of the bulk resistance of a transfer during the evening, and its minimal values, compartment through analysis of the close to zero, at midday. flux-water potential relationship has been widely used by several authors, but has We observed a dramatic increase in the seldom been applied to subparts of trees in soil-trunk resistance under low soil mois- ture conditions, while the needle and the field. Present methods rely on accu- crown resistances were nearly unaffected. rate determinations of the tree sap flow, which requires determination of sapwood This change in resistance observed dur- ing drought dramatically increased the area, mean sapflux density and needle area time constant of the soil-trunk compart- in a stand to a high degree of accuracy. ment, which was approximately 23 min Thus, application of this principle could
therefore be questionable in the case of a branch capacitances. In the longer term, heterogeneous stand. Despite large scat- the xylem of most coniferous trees is ter in the data, mainly caused by the rapid known to play a role as a water reservoir changes in evaporative demand during the [35] but it appears to play an insignificant measurement days, the estimated values role on a daily basis [17, 37]. of capacitance (0.078 and 0.038 kg 2) The tree is divided into homoge- ) -1 ·MPa -2 ·m are within the expected range compartments characterised by a neous of magnitude for coniferous trees [30]. values of water of unique potential, set The capacitances found for the stem and storage flux and main flux. This approxi- branches are within the range of the values mation is acceptable when the model estimated from the measurements made includes a large number of small-size com- by Edwards et al. [9] on two other conif- partments and runs on a short-time reso- species, Pinus contorta and Picea erous lution, typically seconds, which is not the sitchensis. These capacitances were not case here. Nevertheless, we feel this affected during drought, a logical conse- assumption is still acceptable for the nee- quence of the conservation of water poten- dle and branch compartments for which tial of each compartment resulting from spatial variations in water potential val- stomatal closure and a subsequent drop in ues do not exceed 0.15 MPa (Loustau, water flux. unpublished results). This simplification is questionable for the lower compartment, We recognise that the parameterisation which includes both the stem and root sys- of the model relies on a small number of tems and may exhibit spatial differences in replicates at both sites. It would be nec- water potential as large as 0.5 MPa. Ignor- essary to enlarge the sample size of the ing the resistance between storage tissues measurements of flux and water potential and xylem may also lead to underestimates to achieve more confidence in upscaling of the time constant of the trunk and the model from the tree to the stand level. branch compartments, even if Milne Despite this restriction, our approach (1989) found its value negligible when allows us to investigate changes in water compared to the resistance of the main flux along the soil-tree-atmosphere con- pathway. tinuum and has provided a method for pre- dicting the water potentials and water fluxes at any point of the system which ACKNOWLEDGEMENTS we have shown to be roughly consistent with data obtained from two different sites. The data of vapour fluxes determined by Among the assumptions made a priori in the eddy covariance method, and leaf area the model, two of them may restrict its index values derived from optical measure- use and deserve therefore, some critical ments were measured by Paul Berbigier, Yves analysis. Brunet and Eric Lamaud during the French project AgriGES at the Bray site and the Por- 1) The capacitances of the tree com- tuguese STRIDE project (STRDA/C/AGR/ assumed to be constant partments were 159/92) at the Carrasqueira site. The authors over the range of water potential experi- gratefully acknowledge them for providing enced. This assumption seems reasonable these data. We thank I. Ferreira-Gama and J.S. Pereira, coordinators of the STRIDE project, from the established relationship between for giving us the opportunity to participate in needle water potential and water content this project. The work described in this paper but very little is known about the water was supported by the EU projects LTEEF relations of elastic tissues such as the stem (EV5V-CT94-0468) and EUROFLUX. Dur- phloem, which appears from figure 7 to ing his D.E.A. work, J.C. Domec was sup- be the major component of the trunk and ported by a fellowship of the Ministère de
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