Original article

Interpreting the variations in xylem sap fluxdensity within the trunk of maritime pine(Pinus pinaster Ait.): application of a model

for calculating water flows at tree and stand levels

Denis Loustau Jean-Christophe Domec, Alexandre Bosc

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 methodwith the aim of 1) assessing the variability of the sap flux density within a horizontal plane of thestem section and 2) interpreting the time shift in sap flow at different heights over the course ofa day. Measurements were made at five height levels, from 1.3 to 15 m above ground level. Attwo heights (i.e. 1.30 m and beneath the lower living whorl, respectively), sap flux density wasalso measured at four azimuth angles. Additionally, diurnal time courses of canopy transpiration,needle transpiration, needle and trunk water potential, and trunk volume variations were measuredover 4 days with differing soil moisture contents. At the single tree level, the variability of sap fluxdensity with respect to azimuth was higher at the base of the trunk than immediately beneath thelive crown. This has important implications for sampling methodologies. The observed patternsuggests that the azimuth variations observed may be attributed to sapwood heterogeneity causedby anisotropic distribution of the sapwoods hydraulic properties rather than to a sectorisationof sap flux. At the stand level, we did not find any evidence of a relationship between the tree socialstatus and its sap flux density, and this we attributed to the high degree of homogeneity within thestand and its low LAI. An unbranched three-compartment RC-analogue model of water transferthrough the tree is proposed as a rational basis for interpreting the vertical variations in water fluxalong the soil-tree-atmosphere continuum. Methods for determining the parameters of the modelin 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 etpeuplement. La densité de flux de sève brute d’un pin maritime de 25 ans a été mesurée en

* Correspondence and reprintsFax: (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 uneméthode à flux de chaleur constant, dans le but a) d’étudier la variabilité de la densité de flux dansla section transversale du tronc et b) d’analyser le décalage de temps du signal entre différenteshauteurs au cours de la journée. Les mesures ont été effectuées à cinq hauteurs, de 1,3 à 15 m audessus du sol. À deux niveaux (1,3 m et sous la couronne vivante, respectivement) la densité deflux 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 deniveaux 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 planhorizontal, 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 etle 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. Lesméthodes 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 modèleexplique assez bien les variations de flux observées le long du continuum sol-aiguille. Au coursde 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.)

Pinus pinaster Ait / transpiration / flux de sève / modèle de transfert hydrique

1. INTRODUCTION

Sap flow measurement is a usefulmethod for assessing the water use by for-est trees; it does not require horizontallyhomogeneous stand structure and topog-raphy and therefore can be used in situa-tions where methods such as eddy covari-ance cannot. Sap flow measurements allowone to partition the stand water fluxbetween canopy sublayers or to discrimi-nate between particular individuals in astand. Sap flow data have been used forestimating hourly transpiration and canopyconductances in a range of forest stands

[1, 10, 13, 19, 20]. The sap flow mea-surements can provide a useful investiga-tive tool for a variety of purposes, pro-viding the results can be properly upscaledto the stand level, which requires a descrip-tion of the network of resistances and

capacitances which characterise the path-way of water between the soil and the

atmosphere [18, 26]. In order to do this,we need a scheme for quantitatively inter-

preting sap flow measurements on a ratio-nal basis. Until now, the methods used for

extrapolating sap flow data to estimatestand transpiration have remained ratherempirical, with the capacitances in thewater transfer process within trees either

being ignored [1, 7, 19] or extremely sim-plified, such as being reduced to a con-stant time shift between sap flux and tran-

spiration [13]. Resistance and capacitanceto water transfer within some forest treeshave been determined for stem segments[9, 31] and for whole trees (using cut-treeexperiments). However, the extent towhich these measured values can be

applied under natural conditions is ques-tionable, since both methods rely on theanalysis of pressure-flux relationships andwater retention curves determined mainlyunder positive or slightly negative pres-sures [9]. Cohen et al. [4] proposed amethod for estimating soil-to-leaf bulkresistance in the field based on sap fluxmeasurement which avoided this ’arte-

fact’, and has been applied to different

forest species [1, 14, 23]. Using a resis-tance-capacitance analogue of the flowpathway, Wronski et al. [37] and Milne[25] derived values of stem resistance andcapacitance from field measurements ofwater potential, stem shrinkage and tran-spiration on radiata pine and sitka spruce,respectively.

The aim of this paper is to present asimple RC analogue of water transferwithin the soil-tree-atmosphere contin-uum in order to interpret diurnal variationsof flux and water potential observed at dif-ferent locations in the tree. Methods aredescribed that allow the determination ofboth the resistance and capacitance of thetree, based on sap flux measurement in thefield. In addition, we summarise the resultsobtained concerning the sap flux hetero-geneity within a maritime pine stand in ahorizontal plane and suggest methods for

improving the accuracy of the estimation ofwater flux at tree and stand levels.

2. AN UNBRANCHED RC MODELOF TREE WATER FLUX

The flow pathway along the soil-tree-atmosphere continuum is considered as aseries of RC units. This sort of model wasfirst applied by Landsberg et al. [22] onapple trees and solutions for estimatingthe water potential from transpiration mea-surements was given, e.g. by Powell andThorpe [28]. The present model consid-ers the tree as a three-compartment sys-tem: i) root and trunk, ii) branches andiii) needles. Such an approach has beenapplied to different coniferous trees, e.g.Pinus radiata [37], Picea sitchensis [25]and Picea abies [5]. Figure I illustrates

the electrical analogue of the model. Themain assumptions of our analysis can besummarised as follows:

- the crown is treated as a big leaf witha homogeneous temperature and transpi-ration rate;

- the resistance and capacitance ofeach compartment are independent of theflux or water potential of the compartmentand remain constant during the day (butthey can change between days);

- there is no storage resistance, that isthe water potential gradient between thereservoir and the xylem can be neglected.

In the following, all the fluxes, resis-tances and capacitances are expressed onan all-sided needle area basis. The water

potential values used in the present paperare corrected for the gravitational gradi-ent. The basic equations for each com-partment are as follows:

where

where Ji is the liquid water flux expressedin kg·m-2·s-1, Jri the storage flux, Ri(MPa·kg-1·m2·s) and Ci (kg·m-2·MPa-1)the resistance and capacitance of the com-partment and Ψi its water potential (MPa).The subscript i denotes the compartmentand can be either c for the branches of the

crown, s for the stem and root, or n for theneedles. If we assume that any change inthe water potential of the lower compart-ment during each time step can beneglected, replacing Jri and Ji in equa-tion (1) leads to the differential equation:

which can be solved for Ψi and Jri, givingthe following expressions:

Equations (1), (5) and (6) allow us toestimate iteratively the time course ofwater flux and potential from the initialvalues of a given flux, Ji, and water poten-tial, Ψi.

The parameters of the model can bederived as follows. The resistance of each

compartment is given by the slope of theregression line relating the instantaneoussap flux within the compartment, Ji, to theinstantaneous difference between the water

potentials at its upper and lower bound-aries, i.e. Ψi(t) - Ψi-1(t) [equation (3)]. Asimilar calculation has been applied pre-viously for the whole tree, e.g. by Cohenet al. [4], Granier et al. [14] and Bréda etal. [1]. This analysis must be carried outwith data covering the entire daily timecourse, where the final water content ofthe tree is equal to the initial. It does notnecessarily require that measurements bemade under steady-state conditions, i.e.Jri(t) may take positive or negative val-ues. In order to estimate the capacitance ofthe root + stem and branch compartments,

we calculate the value of exp (-Δt Ri · Ci) asthe slope of the regression line fittedbetween Jri(t) and

according to equation (6) and then extractthe value of Ci using the value of Ri cal-culated previously. For the capacitance ofthe needle compartment, we used a valueof 0.025 kg·MPa-1·m-2, assuming a bulkelastic modulus of 25 MPa [36] and asemi-cylindrical needle shape with anaverage diameter of 0.002 m.

3. MATERIALS AND METHODS

3.1. Sites

The model was parameterised and evalu-ated using data collected from two differentexperiments, at the Bray site in France(44°42N, 0°46W) and the Carrasqueira site in Portugal (38°50N, 8°51W) (table 1). Both siteswere pure even-aged stands of maritime pinewith an LAI ranging between 2.0 and 3.5. Inboth locations, the soil water retention capac-ity is rather low due to the coarse texture ofthe soil and a summer rainfall deficit thatinduces soil drought and subsequent tree waterstress, this summer drought being far moresevere at the Portuguese site. The sites wereequipped with neutron probe access tubes andscaffolding towers, enabling monitoring of thesoil moisture and micrometeorological vari-

ables. The Bray site has been extensively stud-ied since 1987 and a detailed description can befound, e.g. in Diawara et al. [6]. The Car-rasqueira site is also part of several Portugueseand European research projects and is describedby Loustau et al. [24].

Determination of the model parameters wascarried out for a single tree at the Bray site on4 days (days 153, 159, 229 and 243) in 1995.Table II summarises the sampling procedureapplied for each variable measured.

3.2. Azimuthal variability of sapflux density

Azimuthal variations in sap flux densityacross the sapwood horizontal section wereassessed on three trees at the Bray site. Sen-sors were inserted at a height of 1.30 m in fourazimuthal orientations. For one tree, sensorswere inserted at 1.50 and 8.50 m, just belowthe last living whorl. Sap flux densities weremonitored from May to August 1991 on twotrees, and from May to September 1995 on thetree with two measurement heights. The treeswere then cut and a cross section of stems ateach measurement height was cut, rubbeddown, polished and scanned with a high reso-lution scanner (Hewlett Packard Scanjet II cx).The number of rings crossed by each heatingprobe and the total conducting area were deter-mined together with the ratio between the ear-lywood and latewood area crossed by theprobe. We analysed only the data collectedduring clear days and considered only the nor-malised daily sums of sap flux density.

In order to analyse the between-tree vari-ability of sap flux density, we collected sapflux data from three different experiments, atthe Bray Site in 1989 and in 1994 and at theCarrasqueira site in 1994. In each experiment,one sensor was inserted into the northern faceof each stem and measurements were carriedout as described above. The data were pooledand compared on a daily summation basis withrespect to the average value of each site.

3.3. Flux measurement

The sap flux density of each compartment,ji, was measured using the linear heating sen-sor designed by Granier [ 12] and applying theempirical relationship relating sap flux den-sity to the thermal difference between theheated and reference probes. The measure-ments were carried out on a single tree, referredto here as the target tree (table III). No attemptwas made to take into account possible naturalgradients of temperature between the twoprobes [11 ]. At the Bray site, the sap flux den-sity at each measurement level was calculatedas the arithmetic mean of the values measured

by all the sensors at that height, one, two orfour according to the height (table II). At theBray site, the whole tree water flux at z = 8.5 m,Jc, was calculated on a leaf area basis by:

where Ac is the cross-sectional area of the con-ductive pathway and L the leaf area (all sided)of the tree. Ac was measured after the experi-ment on the slice of wood extracted from thetrunk at a height of 8.5 m as described above.L was estimated using the sapwood area-leafarea relationship determined by Loustau(unpublished data) from a destructive samplingof 20 trees at the same site. At Carrasqueira,only one sensor was inserted at each level. Inthis case, the stem sap flux at a height of 1.5 m,Js, and beneath the crown, Jn, was estimatedby assuming that the daily total of water flowthrough the tree was conserved. This impliesthat the daily total of water flow at any locationwithin the system is conserved and that theratio between the respective values of the sap-wood cross-sectional area and the daily sumof sap flux density at any pair of points ofheights within the tree is constant. Thus, we

estimated the sapwood cross-sectional area ofeach compartment i (i ≠ c), Ai, using the ratio

between its daily sap flux density, Σji, and

the sap flux density beneath the crown, Σjc,as follows:

3.4. Storage flux

The total storage flux of the crown andstem, Jri, were calculated as the instantaneousdifference between sap flux values measuredabove and beneath the compartment consid-ered, according to equation (1), following Lous-tau et al. [24]. For the stem storage only, theelastic storage flux into the trunk was also esti-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-ment transducers (’Colvern’) regularly spacedalong the stem (table II) and corrected for tem-perature variations. Each transducer was fixedto a PVC anchor which was attached to the

opposite side of the trunk using 5-cm-longscrews. Dead bark tissue was removed suchthat the sensor was directly in contact withexternal xylem.

3.5. Water potential measurements

Needle water potential was measured hourlyusing a pressure chamber. The branches andtrunk water potential were estimated using non-transpiring needles attached at the appropriatelocations (table II). These needles wereenclosed in waterproof aluminium-coated plas-tic bags after wetting the previous night, and itwas assumed that their water potential cameinto thorough equilibrium with the branch ortrunk xylem to which they were attached. Thesoil water potential was estimated as the aver-

age value of 15 soil psychrometric chambersused in dew-point mode (Wescor soil psy-chrometer) and buried at five depths from-10to -50 cm.

3.6. Vapour flux measurements

The transpiration of pine canopy was esti-mated using eddy covariance measurementsof the vapour flux at two levels, above the treecrowns and in the trunkspace between the treecrown and the understorey. Fluctuations inwind speed, temperature and in water vapourconcentration were measured with a 3D or 1Dsonic anemometer and a Krypton hygrometer,respectively. The difference between thevapour fluxes measured above and beneath the

pine crowns was assumed to give the transpi-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 theBray site in 1995. The methods used, the cor-rections applied in order to take into account thedensity effects and the absorption of UV byoxygen, energy balance closure tests and sam-

pling procedures are detailed by Berbigier et al.[2] for the Carrasqueira site and Lamaud et al.[21] for the Bray site.

4. RESULTS

4.1. Azimuthal variability of sap fluxdensity in pine stands

Figure 2 shows the time course of themeasured sap flux density at four azimuthangles and two heights in the trunk of thetarget tree at the Bray site throughout atypical spring day. There was very little, ifany, variation in sap flux density withazimuth angle immediately beneath thecrown, whilst considerable differenceswere found at the base of the trunk. This

pattern was conserved throughout thewhole measurement period, and was notaffected by soil drought (data not shown).Figure 3 summarises the results obtainedconcerning the variability of sap flux den-sity at a height of 1.30 m for three trees

at the Bray site. The relationship betweensap flux density and either the number ofrings or the proportion of earlywoodcrossed by the probe was not significant,though there was a trend for the sap flowdensity to decrease as the number of treerings measured increased in two out offour trees. Furthermore, there was no sig-nificant relationship between the varia-tion in sap flux density and the stem basalinclination, even where the excentricityof heartwood and subsequent sapwoodazimuthal anisotropy was obvious. No sig-nificant relationship was found betweenthe sap flux density measured at 1.3 mhigh and tree size in either experiment(figure 4).

4.2. Determination of the parametersof the model

Figure 5 shows the flux-water potentialgradient relationship used in calculatingthe resistance of the three compartmentsfor 2 days of contrasting soil moisture.The corresponding values of the resis-tances are given in table IV. Soil moisturereached its lowest value on days 229 and243 and the predawn water potential mea-sured for these 2 days (table IV) are typi-cal of those found during a severe droughtin this area. There was a dramatic, 8-foldincrease in the resistance of the root-trunk

compartment under these drought condi-tions, which contrasted with a very slightincrease in the resistance of the branchand needle compartments.

Figure 6 illustrates the procedure usedfor estimating the branch and stem capac-itance for day 153. We did not observeany clear change in the stem or branchcapacitance for the four sample days atthe Bray site.

4.3. Model evaluation

Figure 7 compares the water potentialvalues predicted by the model and themeasured values, for day 153 at the Braysite. There is an acceptable agreementbetween the measured and predicted data,even if a difference is observed during themorning and late afternoon for the lowercompartments. This figure also comparesthe storage flux for the stem predicted by

the model with the flux calculated from

change in the stem volume. This compar-ison shows that predicted and observeddata are the same order of magnitude butdifferences remain at certain times of the

day. Figures 8 and 9 show the model’s outputs together with measured data fortwo representative days at the Carrasqueiraand Bray sites, respectively. The parame-ter values used for implementing themodel have been derived from measure-ments made at different heights [24] andare shown in table IV. The figures com-pare the values of vapour flux predictedfrom sap flow measurements at the base ofthe crown and at the base of the trunk withthe evapotranspiration data measured by

eddy covariance for 2 days on each site.We ’upscaled’ the sap flux values fromtree to stand using optically determinedleaf area index values (table I), assumingthe needles had a semi-cylindrical shape,and calculating the sap flux as the aver-age of the measurements made at a heightof 6 m on a sample of ten trees at Car-rasqueira and at a height of 8.5 m on seventrees at the Bray site. The time course ofthe predicted values of water potential arealso shown and compared with measureddata for the days 178 and 180 at the Car-rasqueira site. The values measured byeddy covariance exhibited erratic varia-tions, particularly when the weatherregime was irregular, but the overall pat-

tem showed acceptable agreement. Waterpotential values predicted by the modelare also compared with measured data for1 d (DOY 180 Carrasqueira site) and indi-cate that the model predicts the measuredvalues reasonably well. Figure 10 showsthe relationship between the predicted andmeasured vapour flux values for both sites.

Agreement is slightly better for the Car-rasqueira where data were obtained onbright clear days than for the Bray wheredata were collected under changeableweather conditions.

DISCUSSION

An important methodological outcomeof this work is that a lower sampling errorfor mean sap flux density of a homoge-neous stand should be expected when thesap flux measurements are made imme-

diately below the crown rather than atground level. This is particularly true fortrees exhibiting basal trunk curvature andsubsequent wood excentricity and sap-wood anisotropy. We did not find any lit-erature concerning the pattern of azimuthaldistribution of sap flux density according

to the measurement height which couldfurther support this conclusion. Since it isbased on measurements made on onlythree trees, this conclusion deserves addi-tional experimental support. Sap flux den-sity variations could not be related signif-icantly to the number of rings or theearlywood/latewood ratio of the sapwoodcrossed by the heating probe. We think,however, that such a relationship couldoccur within a tree but was not observedbecause of the low number of replicates. Itmay, nevertheless, play an important rolesince Dye et al. [8] showed that growthrings and compression wood created aradial heterogeneity in sap flux densitywithin the sapwood of another pinespecies, P. patula, and that there was asubsequent heterogeneity in the azimuthaldistribution of sap flux density. Addition-ally, it has long been established that thesap flux density varies radially within thesapwood cross-sectional area [3, 15, 16,27] which could also affect the azimuthaldistribution of sap flux in anisotropicstems. The between-tree variation of sapflux density was, therefore, unsurprisingsince the data presented in figure 4 actuallyinclude the within-tree variability. In addi-

tion, only a weak between-tree variation insap flux density would be expected inthese homogeneous pine stands where theleaf area index did not exceed a value of 3.This precludes any major differencesbetween trees of differing social position.

Models based on a similar electrical

analogue, with various degrees of sophis-tication in tree architecture representationwere published by Powell and Thorpe[28], Landsberg [22], Wronski et al. [37],Milne [25] and Cruiziat et al. [5] followingthe pioneer work of Van den Honert [34],but their practical utilisation remains lim-ited owing to the large numbers of param-eters required. The merit of the presentmodel is its simplicity, which could makeit useful for routine transpiration calcula-tions from sap flow measurements, pro-vided that a proper parameterisation of theresistance and capacitance values isachieved. This would facilitate using sapflow measurements to estimate tree tran-

spiration (and consequently surface con-ductance) when other techniques areimpractical, and would allow partitioningof the vapour fluxes among canopy lay-ers on a short term basis. From this pointof view, the inadequacy of assuming thatsap flow lags with a constant time shiftbehind transpiration should be highlighted.The constant time-lag hypothesis impliesthat the water storage flux in the treewould always correspond to a constanttime fraction of the transpiration, whichis obviously erroneous. The storage fluxvaries during the day and reaches its max-imal absolute values in the morning andduring the evening, and its minimal values,close to zero, at midday.

We observed a dramatic increase in thesoil-trunk resistance under low soil mois-ture conditions, while the needle andcrown resistances were nearly unaffected.This change in resistance observed dur-ing drought dramatically increased thetime constant of the soil-trunk compart-ment, which was approximately 23 min

with wet soil and reached 348 min with

dry soil. Consequently, the estimation ofhourly transpiration values from extrapo-lating sap flow measurements made at thebase of the trunk becomes extremely dif-ficult on dry soil since a very accuratemeasurement of the water potential at thesoil-root interface becomes necessary.The major cause of this increase in theroot-trunk compartment may be attributedto the decrease in soil hydraulic conduc-tivity in the vicinity of the roots, since thetrunk and root xylem of coniferous treeshave not been reported as showing a sub-stantial reduction in hydraulic conductiv-ity caused by cavitation of tracheids atthese levels of water potential [32].Another important consequence of thisincrease in time constant under soil

drought is that, under extremely dry con-ditions, trees might not have sufficienttime overnight to restore their equilibriumwater content. During a continuous periodof drought, we can therefore hypothesisethat trees having a large time constant,such as large coniferous trees, could expe-rience a sort of ’runaway’ dehydrationresulting in them drying faster than thesoil itself.

An interesting practical issue arisingfrom the present paper is our method for

estimating the values of the bulk resis-tance and capacitance of each compart-ment under natural conditions with mini-mum disturbance to the tree. Thesemethods are consistent with the use of the

parameter values in the model. Estima-tion of the bulk resistance of a transfer

compartment through analysis of theflux-water potential relationship has beenwidely used by several authors, but hasseldom been applied to subparts of trees inthe field. Present methods rely on accu-rate determinations of the tree sap flow,which requires determination of sapwoodarea, mean sapflux density and needle areain a stand to a high degree of accuracy.Thus, application of this principle could

therefore be questionable in the case of aheterogeneous stand. Despite large scat-ter in the data, mainly caused by the rapidchanges in evaporative demand during themeasurement days, the estimated valuesof capacitance (0.078 and 0.038 kg·m-2·MPa-1) are within the expected rangeof magnitude for coniferous trees [30].The capacitances found for the stem andbranches are within the range of the valuesestimated from the measurements made

by Edwards et al. [9] on two other conif-erous species, Pinus contorta and Piceasitchensis. These capacitances were notaffected during drought, a logical conse-quence of the conservation of water poten-tial of each compartment resulting fromstomatal closure and a subsequent drop inwater flux.

We recognise that the parameterisationof the model relies on a small number of

replicates at both sites. It would be nec-

essary to enlarge the sample size of themeasurements of flux and water potentialto achieve more confidence in upscalingthe model from the tree to the stand level.

Despite this restriction, our approachallows us to investigate changes in waterflux along the soil-tree-atmosphere con-tinuum and has provided a method for pre-dicting the water potentials and waterfluxes at any point of the system whichwe have shown to be roughly consistentwith data obtained from two different sites.

Among the assumptions made a priori inthe model, two of them may restrict itsuse and deserve therefore, some criticalanalysis.

1) The capacitances of the tree com-partments were assumed to be constantover the range of water potential experi-enced. This assumption seems reasonablefrom the established relationship betweenneedle water potential and water contentbut very little is known about the waterrelations of elastic tissues such as the stem

phloem, which appears from figure 7 tobe the major component of the trunk and

branch capacitances. In the longer term,the xylem of most coniferous trees isknown to play a role as a water reservoir[35] but it appears to play an insignificantrole on a daily basis [17, 37].

2) The tree is divided into homoge-neous compartments characterised by aset of unique values of water potential,storage flux and main flux. This approxi-mation is acceptable when the modelincludes a large number of small-size com-partments and runs on a short-time reso-lution, typically seconds, which is not thecase here. Nevertheless, we feel thisassumption is still acceptable for the nee-dle and branch compartments for which

spatial variations in water potential val-ues do not exceed 0.15 MPa (Loustau,unpublished results). This simplification isquestionable for the lower compartment,which includes both the stem and root sys-tems and may exhibit spatial differences inwater potential as large as 0.5 MPa. Ignor-ing the resistance between storage tissuesand xylem may also lead to underestimatesof the time constant of the trunk andbranch compartments, even if Milne(1989) found its value negligible whencompared to the resistance of the mainpathway.

ACKNOWLEDGEMENTS

The data of vapour fluxes determined bythe eddy covariance method, and leaf areaindex values derived from optical measure-ments were measured by Paul Berbigier, YvesBrunet and Eric Lamaud during the Frenchproject AgriGES at the Bray site and the Por-tuguese STRIDE project (STRDA/C/AGR/159/92) at the Carrasqueira site. The authorsgratefully acknowledge them for providingthese data. We thank I. Ferreira-Gama and J.S.Pereira, coordinators of the STRIDE project,for giving us the opportunity to participate inthis project. The work described in this paperwas supported by the EU projects LTEEF(EV5V-CT94-0468) and EUROFLUX. Dur-ing his D.E.A. work, J.C. Domec was sup-ported by a fellowship of the Ministère de

l’Agriculture. The Carrasqueira and Bray siteswere used by courtesy of the Companhia dasLezirias and the Compagnie France-Forêts,respectively. M. Rayment provided an invalu-able help for language and style improvement.

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