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A demonstration of the theoretical prediction that sap velocity is related to wood density in the conifer Dacrydium cupressinum Blackwell Publishing Ltd.

Margaret M. Barbour and David Whitehead Landcare Research, PO Box 69, Lincoln 8152, New Zealand

Summary Author for correspondence: M. M. Barbour Tel: +64 3325 6700 Fax: +64 3325 2418 Email: [email protected] Received: 24 November 2002 Accepted: 29 January 2003 doi: 10.1046/j.1469-8137.2003.00754.x

• The theoretical prediction of a close relationship between sap velocity (v) and wood density (ρb) in conifers was tested in mature Dacrydium cupressinum trees. • Thermal dissipation probes were used to measure v during summer in 12 trees of varying size and the data were analysed in relation to ρb. • Variation in (1 − ρb)2 was found to explain 94% of variation in average sap velocity for trees growing in exposed canopy positions, in support of theoretical predictions. No relationship between v and ρb was found for trees growing in sheltered canopy positions. • Differences in the relationship between v and ρb for exposed and sheltered trees are related to mixing of the air within the canopy and the response of stomatal conductance and transpiration rate to air saturation deficit. The results support the use of wood density to scale transpiration from individual trees to the stand in conifer forests. Key words: wood density, sap velocity, water transport, Dacrydium cupressinum, scaling transpiration. © New Phytologist (2003) 158: 477–488

Introduction Understanding the exchange of energy, water and carbon between vegetation and the atmosphere is critical to the success of global climate models, and to models predicting climate change effects on vegetation (Misson et al., 2002). Transpiration is an important component of this exchange. However, transpiration rates are difficult to assess at the ecosystem level because of feedback responses and complexity in scaling from foliage or whole-plant measurements to ecosystem exchange (Jarvis & McNaughton, 1986; Wullschleger et al., 2002). These scaling difficulties are magnified in forests with mixed species and complex canopy structure (Schulze et al., 1995; Meinzer et al., 2001). Whole-tree transpiration is routinely estimated using sap velocity probes, either applying a heat pulse (Marshall, 1958) or the thermal dissipation technique (Granier, 1985). Two approaches have been used to scale measurements of sap flux density from individual trees to whole-stand transpiration (E ). The most commonly used method assumes that the trees

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measured are representative of all tree sizes in the stand, so that E is the product of average sap flux density of trees measured and the ratio of stand sapwood cross-sectional area to ground area (Diawara et al., 1991; Loustau et al., 1996; van Wijk et al., 2000; Phillips & Oren, 2001; Bernier et al., 2002; Phillips et al., 2002). A number of studies have reported increasing sap flux density with increasing tree size (Meinzer et al., 1999; Tausend et al., 2000; Taylor et al., 2001), leading to the second approach to scaling in which trees are divided into classes based on size (Köstner et al., 1992, 2002; Saugier et al., 1997) or species (Wilson et al., 2001) and the class average rates of transpiration weighted according to the number of trees within each class in the stand. Finally, the position of the tree within the canopy has been found to influence sap flux density in some stands (Granier, 1987; Kelliher et al., 1992; Köstner et al., 1992). Our recent work in a stand of Dacrydium cupressinum of mixed size and age has shown widely variable sap flux densities between trees (up to sixfold differences), meaning that both the ‘average’ and the ‘size class’ approaches to scaling described

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above are inappropriate (see the Results). Thus, a new method of scaling tree transpiration to the stand is required for this complex natural ecosystem. Water use by individual trees is often considered in terms of a balance between supply and demand. Demand for water may be regulated by changes in leaf area or stomatal conductance. On the supply side, if soil water is nonlimiting, but rather the rate of water transport, increases in the crosssectional area available for transport will increase water supply. The area available for transport may be increased by either increasing the diameter of the conducting pipes (larger xylem elements) or by increasing the amount of water-conducting tissue (more sapwood). The balance between sapwood area and leaf area has been shown to be important in a number of systems (Whitehead et al., 1984; Waring & Schlesinger, 1985; Callaway et al., 1994; Margolis et al., 1995; Mencuccini & Grace, 1995; Maherali & DeLucia, 2001). However, the effects of differences in the diameter of xylem pipes on sap velocity and water flux are not well explored outside theoretical treatments (but see Hacke et al., 2001). A recent theoretical treatment relating the diameter of xylem pipes to wood density in conifers has proposed that sap velocity may be strongly related to wood density (Roderick & Berry, 2001). As such, this theoretical work highlights an important link between the structure and hydraulic properties of tree stems. In the current paper we test the theoretically predicted relationship between wood density (ρ b) and sap velocity in a stand of the conifer D. cupressinum of mixed tree age and size. The application of wood density as a scalar for stand transpiration is discussed.

E = J sLDs

Stomata respond to a number of environmental variables, including irradiance (Q ), temperature (T ), air saturation deficit, and root zone water deficit, and Jarvis (1976) introduced a useful conceptual model in which g s responds to each environmental variable in a non-linear and independent fashion. Focusing on the response of g s to Ds, Lohammar et al. (1980) suggest that g s is related to Ds by the hyperbolic function: −1

 D  Eqn 3 g s = 1 + s  D0   (D0 is a parameter describing the sensitivity of g s to D). Leuning (1995) showed that Eqn 3 is appropriate for modelling the response of g s to D. Equations 1–3 describe the demand side of the supply– demand balance. Linking supply to demand, Shinozaki et al. (1964a,b) proposed the pipe theory model, suggesting that a given unit of leaves was serviced by a continuation of conducting tissue of constant cross-sectional area, so that a linear proportionality exists between the weight of foliage and the weight of nonphotosynthetic tissue from the base of the live canopy upwards. Nygren et al. (1993) pointed out that the physiological outcome of the theory is that tree transpiration rate is proportional to leaf area and sapwood cross-sectional area. The flow rate of liquid through a pipe (q) is given by Poiseuille’s law as (Roderick & Berry, 2001): q =

Theory The Penman–Monteith equation (Monteith, 1965) describes transpiration from a canopy (E ) as a function of weather variables and canopy surface properties, as: εR + Dg a E = λ ga ε +1+ g

Eqn 1

c

(R (available energy) and D (air saturation deficit, in terms of a dimensionless mole fraction) are measured at a reference height above the surface; g a and g c are bulk aerodynamic and surface conductances, respectively; λ is the latent heat of vaporization; and ε is the rate of change of the latent heat content of saturated air with a change in sensible heat). The term g c may be described as the product of mean stomatal conductance ( J a) and canopy leaf area index (L), in the simplest form (but see Whitehead, 1998, for a discussion of the assumptions inherent in this simplification). Jarvis & McNaughton (1986) suggested that if D is expressed in terms of air saturation deficit at the evaporating surface (Ds) then Eqn 1 may be reduced to:

Eqn 2

πa p4 ∆ pf 8ηl

Eqn 4

(ap is the pipe radius; ∆pf is the drop in pressure along the pipe segment due to friction; η is the dynamic viscosity of the liquid; and l is the length of the pipe). The viscosity of a solution (η) may be expressed relative to that of the solvent (η0; i.e. a relative viscosity, ηrel = η/η0). ηrel is a function of the volumetric fraction of solute molecules in the solution (φ), such that: ηrel = 1 +

5 φ 2

Eqn 5

The value of ηrel for xylem sap is usually close to unity (Roderick & Berry, 2001). The viscosity of water varies considerably with temperature, and may be described by the function: η=

1.95 × 1014 T 7w

Eqn 6

between 0°C and 50°C (Roderick & Berry, 2001), where Tw is the temperature of water in K. Combining Eqns 4–6, the laminar flow of an aqueous solution through a pipe is given by (Roderick & Berry, 2001):

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(subscripts a, u and s refer to air, water and structure). Va + Vu is the volume available for flow of water, and Roderick and Berry (2001) have shown that:

if Fp/Np is fairly constant. Thus, in conifers, sap velocity should be related strongly to wood density at constant temperature. Wood of angiosperms tends to have relatively few large conducting vessels surrounded by numerous small tracheids. In contrast to conifers, the term (1 − ε 2v ) for angiosperms will be significant, so velocity is not expected to relate to density. Equations 10, 11 and 12 imply that water temperature is an important determinant of sap velocity. At a single site, little variation in water temperature is expected between large trees accessing water well below the soil surface. As such, wood density may provide an important constraint on water velocity, and hence on transpiration.

Va + Vu ≈ 1 − ρb V

Materials and Methods

q = 2.01 × 10−15 ap4

Eqn 7

∆ pf T 7w l ηrel

However, the water-conducting cross-sectional area of wood is formed by many small ‘pipes’. Wood volume (V ) may be divided conveniently into air, water and structural volumetric components following Roderick et al. (1999): V = Va + Vu + Vs

Eqn 8

Eqn 9 cm−3).

(ρ b is wood density in g Flow rate through the population of pipes forming a stem (qp ) may be given by (Roderick & Berry, 2001): 2  ∆ pfT 7w   A 2   2  F p  s 2 q p ≈ 2.04 × 10−16  1 − ρ  1+ εv   b  η l N  rel    p 

(

)

(

(

)

)

Eqn 10 (As is the cross-sectional area of the stem; Fp is the volume fraction of available space in the stem occupied by pipes; Np is the number of pipes in the stem; εv is the coefficient of variation of the cross-sectional area of pipes). Derivation of Eqn 10 is outlined in Appendix B. However, not all pipes conduct water at any given time, so Eqn 11 is reduced to a proportionality and, by dividing through by stem cross-sectional area, velocity (v) is obtained: 2  ∆ pfT 7w   A   2  F p  s 2 v ≈∝  1 − ρ  1 + εv   b  η l N   rel   p 

(

)

(

)

Eqn 11

Eqn 11 highlights the importance of water temperature, wood density, and the statistical distribution of pipe diameters in determining sap velocity. Except for variations between early and late wood, conifers have rather uniform pipe diameters. Roderick & Berry (2001) found that εv was rather conservative in conifer species (between 0.4 and 0.6), so that variation in the (1 + ε 2v ) term had little effect on vs. As Fp and εv are both less than one, and of the same magnitude, they argue that F 2p (1 – ε 2v ) may be approximated by Fp. For conifers, Eqn 11 then becomes: 7  w 

 ∆ pfT 2  F p  As   v ≈∝      1 − ρb     Np  ηrel   l 

(

)

Eqn 12

i.e. at constant temperature: v ∝ (1 − ρb)2

Eqn 13


Field site Measurements were made in a mixed conifer–broad-leaved forest at Okarito Forest, Westland, New Zealand (43.2° S, 170.3° E, 50 m above sea level) dominated by 100- to 400year old D. cupressinum Lamb. (rimu) trees with a mean canopy top height of 20 m. Annual rainfall is high (approximately 3400 mm), resulting in a consistently high water table and an acid humic organic soil (30% organic matter), with pH 3.8–4.4 and low nutrient availability (Mew & Lee, 1981). Mean annual temperature is 11.3°C with a small range between winter and summer of 8.6°C and air saturation deficit is low (generally less than 1 kPa, but reaching 2 kPa for short periods during summer). Nutrient availability has been identified as the strongest limitation to plant growth, with annual net carbon uptake by the canopy estimated to be low at 1.1 kg C m−2 (Whitehead et al., 2002). In the experimental plot (50 × 50 m) D. cupressinum trees dominate the canopy, comprising 73% of the stand basal area of 33.2 m2 ha−1 and more than 90% of the foliage area. The contribution to stand transpiration by the broad-leaved understorey trees was considered negligible. Complexity in scaling issues results from the rather open forest structure, including gaps in the canopy, with a high degree of clumping of foliage area (Whitehead et al., 2002). The low leaf area index of 2.9 (on a projected leaf area basis) with high spatial variability (A. S. Walcroft, unpubl. data) reflects the open nature of the uneven ages of the trees in the canopy. Positional classes of trees Trees used for sap flow measurements were classified as either: (1) exposed trees, defined as those for which at least two-thirds of the crown emerged above neighbouring crowns or those growing in a significant gap within the canopy (a significant gap was defined as an absence of overtopping trees for at least twice its crown depth away from the edge of its crown for at

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least 120 azimuthal degrees); and (2) sheltered trees, which included those trees for which the crown did not emerge above neighbours, and all understorey trees not growing in gaps. Of the 12 trees measured, seven were classified as exposed and five as sheltered. Within the experimental plot 67% of the trees were classed as sheltered, forming 47% of the basal area and 49% of the projected crown area for D. cupressinum. Measurements of sap velocity The thermal dissipation technique (Granier, 1985, 1987) was used to measure the sap flow velocity in 12 trees of varying basal area within the study plot. Measurements were made over 160 d between spring (October) and late summer (March). Two probes were inserted radially into the stem to a depth of 20 or 40 mm, one 40 mm downstream of the other, at a height of 2.5 m above the ground. Probes 40 mm long (TDP-40; Dynamax, Houston, TX, USA) were installed in trees with a sapwood thickness of greater than 40 mm, and 20 mm probes (handmade, following Phillips et al., 1996) were installed in trees with narrow sapwood thickness, as measured by water content of the wood (described below). The downstream probe was heated by applying constant voltage across an insulated constantan heating wire, giving a constant power output. The temperature difference between the two probes was measured using a thermistor midway along each probe every 10 s, and a half-hourly average recorded on a data logger (21X; Campbell Scientific, Inc., Logan, UT, USA). Probes were surrounded with closed-cell insulating foam and a layer of foil-coated bubble wrap to reduce vertical temperature gradients associated with direct radiation onto the stem and temperature differences between the ground and the air. Naturally occurring temperature gradients within the stem were assessed by measuring the temperature difference between the two probes when the power to the heated probe was switched off. No significant temperature gradients were observed (i.e. the temperature difference never deviated beyond ±0.2°C). The temperature difference between the two probes (∆T ), normalized to the temperature difference with no flow (∆Tm), is related to the velocity of water movement. Granier (1985) found for three species (Pseudotsuga menziesii, Pinus nigra and Quercus pedunculata) that: v = 119 × 10−6k 1.231

Eqn 14

where v is sap flux density (in m3 m−2 s−1) or sap velocity (m s−1) and k =

∆Tm − ∆T ∆T

Eqn 15

The acceptability of Eqn 14 has recently been confirmed by Clearwater et al. (1999) for three tropical tree species (Anacardium excelsum, Bursera simaruba and Eucalyptus deglupta),

with the inclusion of a correction for the proportion of the probe in contact with non-conducting tissue. If the conducting sapwood in contact with the probe is assumed to have a relatively uniform sap velocity, then the measured ∆T is a weighted mean of ∆T in the sapwood (∆Tsw) and in the inactive tissue (∆Tm) (Clearwater et al., 1999): ∆T = (1 − a)∆Tsw + a∆Tm

Eqn 16

where a is the proportion of the probe in contact with nonconducting tissue, and assuming that the nonconducting tissue has the same thermal properties as conducting sapwood when v = 0. Eqn 15 then becomes: ∆T − a ∆Tm − ∆T 1−a k = ∆T

Eqn 17

Analysis of sapwood depth at positions where probes were inserted showed that 85–100% of the probe length was in contact with conducting sapwood in all cases, so the necessary corrections using Eqn 17 were small. The use of an empirical relationship between measured values of v and k overcomes the criticism (Roderick & Berry, 2001) that sap velocity would be overestimated because of viscosity effects when measured using thermal techniques. However, there is no mechanistic explanation for the wide applicability of Eqn 14 among species. Eqns 14 and 17 were used to calculate sap velocity in the 12 measurement trees. Sap velocities are presented in a number of ways: half-hourly measured velocity (v), average of half-hourly measurements between noon and 16:00 hours (New Zealand Standard time, NZST) for an individual tree on a single day (vm), average vm for each tree over the 160 d of measurement (vma) or for days within the specified range in average daily air saturation deficit (vmD). Sapwood density, thickness and water content Wood cores (5 mm diameter) were taken at 2 m above the ground on all measurement trees prior to probe installation in spring (October). Cores were frozen after sampling, then cut transversely into 2 mm segments. Fresh samples were weighed and the sample thickness and diameter measured with electronic callipers at four positions around the circumference of each segment. The volume of each sample could then be determined to ± 0.03 mm3. Wood samples were oven dried for 48 h at 70°C and reweighed. Wood density was determined for the wood within 14 mm of the cambium (corresponding to the last 15–20 yr of growth; Whitehead et al., 2002) by dividing the sample dry mass by its volume. Wood water content (W in Table 1) was obtained by dividing the difference between fresh and dried wood mass by fresh wood mass for each sample, and varied between 0.45 g g−1 and 0.63 g g−1 in the outer 14 mm of sapwood. Sapwood


Research Table 1 Wood and crown characteristics of each tree used for sap velocity measurements

Tree

Class

h m

d m

B m2

S m2

C m2

CV m3

C:S m2 m−2

ρb kg m−3

W g g−1

Vs m3 m−3

Vu m3 m−3

Va m3 m−3

30 38 5 12 112 116 368 18 101 39 94 126

S S S S S E E E E E E E

17.1 24.0 28.0 27.1 28.6 12.3 26.2 24.1 24.8 23.5 28.4 30.3

9.4 15.9 13.8 15.1 14.8 5.7 9.4 16.4 14.2 9.5 10.9 17.6

0.0181 0.0590 0.2884 0.2951 0.3578 0.0108 0.0611 0.0629 0.0779 0.0814 0.1134 0.2198

0.0067 0.0266 0.0594 0.0271 0.0968 0.0028 0.0087 0.0237 0.0245 0.0371 0.0304 0.0575

4.35 19.53 37.56 7.90 46.40 2.84 1.63 32.39 9.07 3.53 8.11 14.25

28 260 451 92 551 9 7 515 108 24 68 257

649 734 632 291 479 1014 187 1367 370 95 267 248

491 536 430 368 551 603 551 475 515 602 555 427

0.54 0.50 0.53 0.59 0.51 0.46 0.54 0.45 0.56 0.49 0.52 0.63

0.32 0.35 0.28 0.24 0.36 0.39 0.36 0.31 0.33 0.39 0.36 0.27

0.57 0.54 0.48 0.53 0.58 0.51 0.64 0.38 0.67 0.58 0.60 0.73

0.10 0.11 0.24 0.23 0.05 0.09 0.00 0.30 0.00 0.03 0.03 0.00

Positional class (E, exposed; S, sheltered), tree height (h), crown depth (d ), basal area (B), sapwood area (S), projected crown area (C), estimated crown volume (CV ), the ratio of crown area to sapwood area (C : S ), wood density (ρb ), water content (W ) and volume fraction of structure (Vs ), water (Vu ) and air (Va ).

thickness was determined visually in the field as the cores were removed (from the change in translucence of the wood), and confirmed in the laboratory by measuring the distance from the cambium at which there was a sudden change in water content (typically from about 0.5–0.3 g g−1 within 2 mm). Sapwood area was calculated by subtracting the nonconducting sapwood area from the total basal area for each tree. Volume fractions of structure, air and water were calculated from Eqn 9, assuming that the density of the structural component was 1530 kg m−3 (Roderick & Berry, 2001), and the density of water was 998.2 kg m−3 at 20°C (Jones, 1983). Table 1 lists the characteristics of each measured tree (crown height, depth and volume measurements and estimates for all trees in the experimental plot, including those used for sap velocity measurement, were made prior to the installation of the probes). Meteorological measurements Incident irradiance, air temperature, relative humidity and rainfall were measured above the canopy on a 30 m tower erected at the site for access to the trees. Meteorological measurements were made every 10 s and averages recorded every 30 min on a data logger (CR10; Campbell Scientific, Inc.). For comparison with sap velocities, incoming radiation is presented as a daily total, and air saturation deficit (D) as daily averages between noon and 16:00 hours (NZST). Shoot gas exchange measurements A portable gas exchange system (LI-6400; Li-Cor Inc., Lincoln, NE, USA) was used to measure stomatal conductance of shoots from two large trees (one from the ‘exposed’ and one from the ‘sheltered’ positional classes) at 18 m above the ground on a clear, sunny day in early summer. Irradiance in the chamber was provided and set to approximately external


levels, and measurements made at ambient CO2 partial pressure and air saturation deficit. D. cupressinum shoots have rather complex architecture, comprising small (2–3 mm long) overlapping, imbricate, subtrigonous leaves borne on slender, pendulous branchlets (Allan, 1961). The projected surface area of shoots was measured after the completion of gas exchange measurements using a digital camera and image analysis software (Scion Image, Scion Corporation, Frederick, MD, USA), and the half total surface leaf area estimated by multiplying the projected area by 3.69/2 (Whitehead et al., 2002).

Results The trees used for sap velocity measurement varied in size (and, by implication, age), from a basal area of 0.01–0.36 m2 (Table 1). Regression analysis (not shown, but see Table 1) revealed that variation in basal area explained just 70% of variation in sapwood area, with some large trees having just a narrow band of water-conducting sapwood around the outside of the stem. Further, trees with high basal area did not necessarily have large crowns. For example, although trees 5 and 12 had similar basal areas (at 0.29 m2), the estimated crown volume of tree 5 was more than four times greater than that of tree 12 (Table 1). Crown area and volume were related more closely to sapwood area, as predicted by the pipe theory model (Shinozaki et al., 1964a,b; Whitehead et al., 1984). Wood density varied considerably between 368 kg m−3 and 603 kg m−3, and was not related to tree size or canopy positional class. The volumetric fractions of structure, water and air also varied between trees, but again there were no clear relationships with either tree size or positional class. Typically, sap flow started 1–2 h after sunrise and reached a peak between noon and 16:00 hours (NZST). Substantial variation in velocity was observed between individual trees.

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Fig. 1 Typical daily patterns of (a) incident photosynthetically active radiation (Q, 400 –700 nm), (b) air temperature (Tair), (c) air saturation deficit (D), and (d) measured sap velocity (v) for four Dacrydium cupressinum trees during a clear, sunny day in summer. In (d) the bold solid line is tree 18, the long dashed line is tree 38, the short dashed line is tree 94, and the dotted line is tree 368.

Fig. 2 The relationships between average daily sap flux density measured between spring and late summer and (a) basal area, and (b) sapwood area for 12 Dacrydium cupressinum (rimu) trees. Open circles are exposed trees and closed circles are sheltered trees (mean ± SE).

For example, sap velocity in tree 18 peaked at about 0.055 mm s−1 on 20 January 2002, while a broad, flat peak of about 0.015 mm s−1 occurred for tree 38; more than a threefold difference (Fig. 1). Daily sap flux density, averaged over the whole measurement period, varied considerably between trees and was not related to tree basal area or sapwood area (Fig. 2). Dividing trees into ‘exposed’ or ‘sheltered’ classes separated the large trees with low sap flux densities (sheltered) from large trees with higher sap flux densities (exposed), but the relationships between tree size and sap flux density remained weak. When an average of daily maximum velocities measured between spring and summer was calculated for each tree and compared with sapwood density, separation of the two positional classes became clear. Exposed trees showed a strong relationship between average vma and (1 − ρ b)2, as predicted

by the theory (Fig. 3). As density decreased (i.e. increasing (1 − ρb)2), vma increased. Variation in (1 − ρb)2 explained 94% of variation in vma between exposed trees. However, no significant relationship between velocity and density was found for trees in the ‘sheltered’ positional class. As expected, sap velocity of individual trees was strongly regulated by D. Typically, sap velocity increased linearly with increasing D up to 1.25 kPa for both exposed and sheltered trees. In the examples presented (Fig. 4) the exposed tree had a significantly higher maximum sap velocity (at about 0.045 mm s−1) compared with the sheltered tree (at about 0.018 mm s−1). Given that velocity is strongly regulated by D, the slope of the relationship between average velocity and (1 − ρ b)2 should increase with increasing D, at least for the exposed trees. To test this hypothesis, days were divided into classes


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Fig. 3 The relationship between average measured sap velocity between noon and 16:00 hours (NZST) over the measurement period (vma) and the square of the difference from unity of wood density ((1 − ρb)2, where ρb is wood density in g cm−3) for exposed (open circles) and sheltered (closed circles) Dacrydium cupressinum trees (mean ± SE). For exposed trees the line represents a least squares regression: vma = −0.017 + 0.153(1 − ρb)2, r2 = 0.94.

Fig. 4 The relationships between air saturation deficit (D) and sap velocity (vmc), both averaged between noon and 16:00 hours, for (a) an exposed and (b) a sheltered Dacrydium cupressinum tree. The lines represent linear least-squares regressions for data between 0 and 1.25 kPa D. (a) vm = −0.0025 + 0.045D, r2 = 0.77. (b) vm = −0.0010 + 0.017D, r2 = 0.83.

Fig. 5 The relationship between average sap velocity and the square of the difference from unity of wood density ((1 − ρb)2) for exposed (open circles) and sheltered (closed circles) Dacrydium cupressinum trees when (a) 0.1 < D < 0.4 kPa, (b) 0.6 < D < 0.7 kPa and (c) 0.8 < D < 1.0 kPa (mean ± SE). The lines represent linear least-squares regressions for exposed trees. (a) vmD = −0.004 + 0.032(1 − ρb)2, r2 = 0.78. (b) vmD = −0.021 + 0.188(1 − ρb)2, r2 = 0.94. (c) vmD = −0.025 + 0.224(1 − ρb)2, r2 = 0.95.


with narrow ranges of average daily D. The slope of the relationship between velocity and density for exposed trees increased from 0.03 at D = 0.1–0.4 kPa, to 0.19 at D = 0.6– 0.7 kPa, and to 0.22 when D = 0.8–1.0 kPa (Fig. 5). By dividing days into seven classes of differing D, the slope of the relationship between velocity and density for exposed trees was found to increase with D to a maximum of about 0.22 at about D = 0.75 kPa (Fig. 6), as would be expected from the velocity and density relationships of individual trees. No significant relationship was found between velocity and (1 − ρ b)2 for sheltered trees at any range of D. Stomatal conductance (g s ) of shoots in exposed and sheltered trees was highest in the early morning, then became fairly constant from 11:00 hours (NZST) at about 0.08 mol m−2 s−1. No significant differences in g s were observed between the trees from the two positional classes (Fig. 7). Stomatal conductance was insensitive to irradiance above a critical limit of about 300 µmol m−2 s−1, necessary for stomatal opening. However, g s was very sensitive to D (Fig. 8). The observed diurnal pattern of g s fits that typical for coniferous forest canopies with constant water supply (Whitehead, 1998): increasing irradiance in the early morning, increasing D during the day and decreasing irradiance late in the day leads to

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Fig. 6 The fitted slope of the relationship between sap velocity and the square of the difference from unity of wood density (ρb) for exposed Dacrydium cupressinum trees for days within narrow ranges of average vapour pressure deficit (D).

Fig. 7 Diurnal pattern of stomatal conductance for shoots from an exposed (open circles) and a sheltered (closed circles) Dacrydium cupressinum tree at 18 m above the ground for a clear, sunny day in early summer (mean ± SE).

maximum g s in the early morning with a gradual decline during the day.

Discussion Is sap velocity related to wood density? The theory developed by Roderick and Berry (2001) proposes that variation in sap velocity is attributable to differences in wood density (ρ b) in conifers. More precisely, sap velocity is proportional to (1 − ρ b)2. Such a relationship is demonstrated clearly in field conditions, for the first time, in the exposed conifer trees in this study. This reveals a new linkage between structural and functional properties of the water-conducting pathway and is likely to advance the understanding of hydraulic processes in trees. However, further testing of the theory for a range of species and growing conditions is needed to reveal the generality of the theory.

The observed relationship suggests that for trees in exposed canopy positions, both the proportion of pipes conducting water and the ratio of the volume fraction of stem occupied by pipes to the number of pipes in the stem (Fp/Np in Eqns 11–13) are fairly constant, or they vary in such a way that the Fp/Np ratio remains constant. Trees forming the canopy and those growing in shaded understorey positions (sheltered trees) did not show the expected relationship between density and velocity. As the temperature of xylem water is assumed to be constant between trees, this suggests that either the Fp/Np term or the proportion of non-conducting pipes must vary between individual trees (see Eqn 13). The proportion of pipes conducting water is likely to vary if the evaporative demand for water is low relative to the potential water-conducting cross-sectional area. A low demand for water may result from: (1) low ratio of leaf to sapwood, (2) low stomatal conductance due to shading, or (3) a small vapour pressure gradient between the leaf and the atmosphere (i.e. low D within the tree crown). These three possibilities will be addressed in turn. If the area of foliage is very small in relation to the sapwood water-conducting area for sheltered trees, wood density may not limit the velocity of xylem water, so the relationship between wood density and sap velocity would not be evident. To test this hypothesis, the ratio of leaf area to sapwood area should be compared between exposed and sheltered trees. In the absence of leaf area measurements, projected crown area was used. In the trees studied, the ratio of crown to sapwood area (C : S ) varied between 95 m2 m−2 and 1300 m2 m−2 (Table 1). The two positional classes were not significantly different (P = 0.40) for average C : S, suggesting the low water demand in sheltered trees is not related to low foliage area. The second explanation for the low water demand of sheltered trees is that these trees have significantly lower g s than exposed trees, resulting from shading. Measurements of stomatal conductance near the top of the canopy showed no significant differences between an exposed and a sheltered tree (Fig. 7). However, shoots of both the trees were at high incident irradiance for similar lengths of time at this height in the canopy. It may be possible that, for the whole crown, average g s is lower for sheltered compared with exposed trees owing to shading. However, Fig. 7 suggests that g s in D. cupressinum is rather insensitive to irradiance, so we consider it unlikely that shading in sheltered trees resulted in lower g s. Shoot-level gas exchange measurements highlight the sensitivity of g s to D, particularly when 0.4 < D < 1.0 kPa. To demonstrate the effects of D on both g s and E, we fitted the Lohammar function (Eqn 3) to stomatal conductance data (Fig. 8) to predict the response of g s to variation in D between 0.4 and 1.8 kPa (the range in D over which measurements were made). We suggest that D. cupressinum foliage is well coupled to the surrounding environment (reasonable, given the small, scale-like form of the shoots), assume that Ds ≈ D, and calculate E from Eqn 2 assuming L = 2.9 m2 m−2. The modelled change in g s and E with variation in D (Fig. 9) shows


Research

relationship between velocity and density is not expected to be found in angiosperms. This is because angiosperms generally have a bimodal distribution of water-conducting element diameters, with relatively few very large vessels surrounded by many smaller tracheids. In this case, v is more strongly dependent on the diameter of the large vessels than wood density itself. Can wood density be used to scale transpiration?

Fig. 8 The relationships between stomatal conductance ( g s) and vapour pressure deficit (D) for shoots. The curves represent a fitted Lohammer function (Eqn 3). For exposed Dacrydium cupressinum trees (open circles and dashed line) D0 = 0.133, r2 = 0.72, and for sheltered trees (closed circles and solid line) D0 = 0.138, r2 = 0.71. Fitted curves for the two trees are not significantly different.

Fig. 9 The relationships between vapour pressure deficit (D) and stomatal conductance (solid line, left axis) and transpiration rate (dashed line, right axis). The relationship between D and gs was fitted to all shoot gas exchange data as presented in Figure 8, using the function given in Eqn 4 with D0 = 0.135 kPa (r2 = 0.71).

that E increases gradually with increasing D above 1.0 kPa, but decreases rapidly with decreasing D below 0.7 kPa. On this basis, we argue the most likely explanation for the low water demand of sheltered trees is that the air surrounding the crowns of the trees is not well mixed, so that the water vapour from transpiration remains within the crown, reducing D surrounding the foliage below 0.6 kPa and hence reducing E. We suggest that the observed relationship between velocity and (1 − ρ b)2 for exposed trees provides support for the model predictions for conifers by Roderick & Berry (2001). As demonstrated by the sheltered trees in this study, when other factors in Eqn 12 are not constant, wood density may be unrelated to sap velocity. It should be emphasized that the


As described in the Introduction, scaling transpiration from individual trees to the stand is difficult in natural ecosystems with trees of mixed size and age. For example, in this study the wide variability in sap flux density between trees means that scaling to whole-stand transpiration using an average of measured values would include very large errors, rendering such an approach unsuitable. Further, the absence of a relationship between sap flux density and tree size shown here also suggests that the size–class scaling approach described in the Introduction is unsuitable for this stand. The position of a tree within the canopy was found to be of some importance in determining sap flux density of these trees, as suggested by Granier (1987) (Fig. 2). Although positional class seems important in determining sap flux density in D. cupressinum, a significant level of variation was found within each class, such that taking a weighted average for each class would still result in large errors. Clearly, a new method of scaling tree transpiration is required for this stand. Variation in wood density between trees in the ‘exposed’ positional class explained 94% of variation in average sap velocity, suggesting that wood density is an important regulator of the rate of water movement in conifers. As such, measurement of wood density could be used to scale sap velocity to give transpiration rate for all exposed trees in this complex stand. In the 50 × 50 m experimental study plot just 33% of the trees were classed as ‘exposed’. However, based on sap velocity measurements, these trees would account for most (about 83%) of the daily transpirational flux. Lack of a relationship between wood density and sap velocity for the trees growing in sheltered positions means that transpiration from these trees would be poorly predicted by wood density. However, as sap velocities are low and vary to a much lesser extent in the sheltered trees, a weighted average from measured trees would introduce relatively small errors in the scaling calculation. We suggest that wood density is a suitable scalar for our study ecosystem. Specifically, a wood density distribution for the stand would allow ‘density classes’ to be defined. Daily sap velocity would be measured in sample trees selected across the range of density classes. Sap velocity for measured trees would be scaled to the stand by applying the wood density distribution to allow weighting of sap velocity by density class. Estimated stand sapwood area and measured ratio of projected crown area to plot ground area would then be used to

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express daily transpiration on the basis of stand flux density. For modelling purposes over longer time periods, daily stand flux density could be predicted from measurements of air saturation deficit alone, once the relationship is established for the stand. Such an approach will be adopted and tested for the study ecosystem in a subsequent paper.

Acknowledgements We gratefully acknowledge technical assistance from G. N. D. Rogers and T. McSeveny, and productive discussion of the work with Drs M. L. Roderick and S. L. Berry. This work was funded by the Foundation for Research, Science and Technology, and a Landcare Research Investment Postdoctoral Fellowship to M.M.B. Timberlands West Coast and the Department of Conservation provided the site and support and encouragement for the work.

References Allan HH. 1961. Flora of New Zealand, I. Wellington, New Zealand: Government Printer. Bernier PY, Bréda N, Granier A, Rauleir F, Mathieu F. 2002. Validation of a canopy gas exchange model and derivation of a soil water modifier for transpiration for sugar maple (Acer saccharum Marsh.) using sap flow density measurements. Forest Ecology and Management 163: 185–196. Callaway RM, DeLucia EH, Schlesinger WH. 1994. Biomass allocation of montane and desert ponderosa pine: an analog for response to climate change. Ecology 75: 1474 –1481. Clearwater MJ, Meinzier FC, Andrade JL, Goldstein G, Holbrook NM. 1999. Potential errors in measurement of nonuniform sap flow using heat dissipation probes. Tree Physiology 19: 681– 687. Diawara A, Loustau D, Berbigier P. 1991. Comparison of two methods for estimating the evaporation of a Pinus pinaster (Ait.) stand: sap flow and energy balance with sensible heat flux measurements by an eddy covariance method. Agricultural and Forest Meteorology 54: 49– 66. Granier A. 1985. Une nouvelle méthode pour le mesure du flux de sève brute dans le tronc des arbres. Annales des Sciences Forestieres 42: 193 –200. Granier A. 1987. Evaluation of transpiration in a Douglas-fir stand by means of sap flow measurements. Tree Physiology 3: 309–320. Hacke UG, Sperry JS, Pockman WT, Davis SD, McCulloh KA. 2001. Trends in wood density and structure are linked to prevention of xylem implosion by negative pressure. Oecologia 126: 457– 461. Jarvis PG. 1976. The interpretation of the variation in leaf water potential and stomatal conductance found in canopies in the field. Philosophical Transactions of the Royal Society (London) B. Biological Sciences 273: 593–610. Jarvis PG, McNaughton KG. 1986. Stomatal control of transpiration: scaling up from leaf to region. Advances in Ecological Research 15: 1–19. Jones HG. 1983. Plants and Microclimate. Cambridge, UK: Cambridge University Press. Kelliher FM, Köstner BMM, Hollinger DY, Byers JN, Hunt JE, McSeveny TM, Meserth R, Weir PL, Schulze E-D. 1992. Evaporation, xylem sap flow, and tree transpiration in a New Zealand broad-leaved forest. Agricultural and Forest Meteorology 62: 53 –73. Köstner B, Falge E, Tenhunen JD. 2002. Age-related effects on leaf area/sapwood area relationships, canopy transpiration and carbon gain of Norway spruce stands (Picea abies) in the Fichtelgebirge, Germany. Tree Physiology 22: 567–574. Köstner BMM, Schulze E-D, Kelliher FM, Hollinger DY, Byers JN, Hunt JE, McSeveny TM, Meserth R, Weir PL. 1992. Transpiration and

canopy conductance in a pristine broad-leaved forest of Nothofagus : an analysis of xylem sap flow and eddy correlation measurements. Oecologia 91: 350–359. Leuning R. 1995. A critical appraisal of a combined stomatal-photosynthesis model for C3 plants. Plant, Cell & Environment 18: 339–355. Lohammar T, Larsen S, Linder S, Falk SO. 1980. FAST-simulation models of gaseous exchange in Scots pine. In: Persson T, ed. Structure and function of northern coniferous forest – an ecosystem study. Ecological Bulletin 32: 505– 523. Loustau D, Berbigier P, Roumagnac P, Arruda-Pacheco C, David JS, Ferreira MI, Pereira JS, Tavares R. 1996. Transpiration of a 64-year-old maritime pine stand in Portugal. 1. Seasonal course of water flux through maritime pine. Oecologia 107: 33. Maherali H, DeLucia EH. 2001. Influence of climate-driven shifts in biomass allocation on water transport and storage in ponderosa pine. Oecologia 129: 481–491. Margolis H, Oren R, Whitehead D, Kaufmann MR. 1995. Leaf area dynamics of conifer forests. In: Smith WK, Hinckley TM, eds. Ecophysiology of conifer forests. New York, NY, USA: Academic Press, 181–223. Marshall DC. 1958. Measurement of sap flow in conifers by heat transport. Plant Physiology 33: 385–396. Meinzer FC, Goldstein G, Andrade JL. 2001. Regulation of water flux through tropical forest canopy trees: do universal rules apply? Tree Physiology 21: 19–26. Meinzer FC, Goldstein G, Franco AC, Bustamante M, Igler E, Jackson P, Caldas L, Rundel PW. 1999. Atmospheric and hydraulic limitations on transpiration in Brazilian cerrado woody species. Functional Ecology 13: 273–282. Mencuccini M, Grace J. 1995. Climate influences the leaf area/sapwood area ratio in Scots pine. Tree Physiology 15: 1–10. Mew G, Lee R. 1981. Investigation of the properties and genesis of West Coast wet land soils, South Island, New Zealand. 1. Type localities, profile morphology, and soil chemistry. New Zealand Journal of Science 24: 1–24. Misson L, Rasse DP, Vincke C, Aubinet M, Francois L. 2002. Predicting transpiration from forest stands in Belgium for the 21st century. Agricultural and Forest Meteorology 111: 265–282. Monteith JL. 1965. Evaporation and environment. Symposia of the Society for Experimental Biology 19: 205–234. Nygren P, Rebottaro S, Chavarria R. 1993. Application of the pipe model theory to non-destructive estimation of leaf biomass and leaf area of pruned agroforestry trees. Agroforestry Systems 23: 63–77. Phillips N, Oren R. 2001. Intra- and inter-annual variation in transpiration of a pine forest. Ecological Applications 11: 385–396. Phillips N, Oren R, Zimmermann R. 1996. Radial patterns of xylem sap flow in non-, diffuse- and ring-porous tree species. Plant, Cell & Environment 19: 983–990. Phillips N, Bond BJ, McDowell NG, Ryan MG. 2002. Canopy and hydraulic conductance in young, mature and old Douglas-fir trees. Tree Physiology 22: 205–211. Roderick ML, Berry SL. 2001. Linking wood density with tree growth and environment: a theoretical analysis based on the motion of water. New Phytologist 149: 473–485. Roderick ML, Berry SL, Nobel IR, Farquhar GD. 1999. A theoretical approach to linking the composition and morphology with the function of leaves. Functional Ecology 13: 683–695. Saugier B, Granier A, Pontailler JY, Dufrêne E, Baldocchi DD. 1997. Transpiration of a boreal pine forest measured by branch bag, sap flow and micrometeorological methods. Tree Physiology 17: 511–519. Schulze E-D, Leuning R, Kelliher FM. 1995. Environmental regulation of surface conductance for evaporation from vegetation. Vegetatio 121: 79–87. Shinozaki K, Yoda K, Hozumi K, Kira T. 1964a. A quantitative analysis of plant form – the pipe model theory. I. Basic analyses. Japanese Journal of Ecology 14: 97–105.


Research Shinozaki K, Yoda K, Hozumi K, Kira T. 1964b. A quantitative analysis of plant form – the pipe model theory. II. Further evidences of the theory and its application in forest ecology. Japanese Journal of Ecology 14: 133–139. Tausend PC, Meinzer FC, Goldstein G. 2000. Control of transpiration in three coffee cultivars: the role of hydraulic and crown architecture. Trees 14: 181–190. Taylor PJ, Nuberg IK, Hatton TJ. 2001. Enhanced transpiration in response to wind effects at the edge of a blue gum (Eucalyptus globulus) plantation. Tree Physiology 21: 403 – 408. Waring RH, Schlesinger WH. 1985. Forest ecosystems: concepts and management. New York, USA: Academic Press. Whitehead D. 1998. Regulation of stomatal conductance and transpiration in forest canopies. Tree Physiology 18: 633 – 644. Whitehead D, Edwards WRN, Jarvis PG. 1984. Relationships between conducting sapwood area, foliage area and permeability in mature Picea stichensis and Pinus contorta trees. Canadian Journal of Forest Research 14: 940–947.

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Appendix A Symbols used in this paper Symbol

Units

Description

a ap api 0p 02p As B C C:S CV d D Ds D0 ∆pf ∆T ∆Tm ∆Tsw E ε εv Fp ga gc gs 9s gsmax h η ηrel η0 l L λ Np φ ρb q qi

– m m m2 m2 m2 m2 m2 m2 m−2 m3 m kPa or mol mol−1 kPa or mol mol−1 kPa or mol mol−1 N m−2 °C °C °C mmol m−2 s−1 – m2 – mol m−2 s−1 mol m−2 s−1 mol m−2 s−1 mol m−2 s−1 mol m−2 s−1 m Ns m−2 – Ns m−2 m m2 m−2 J g−1 Number – kg m−3 or g m−3 m3 s−1 m3 s−1

Proportion of the probe in contact with nonconducting tissue Pipe radius Radius of pipe i Mean area of a population of pipes Mean square of pipe radii Cross-sectional area of the stem Basal area Projected crown area Ratio of crown area to sapwood area Estimated crown volume Crown depth Air saturation deficit Air saturation deficit at the leaf surface Fitted parameter in the Lohammar function Pressure drop due to frictional losses in a pipe Temperature difference between heated and unheated probes with sap flow Temperature difference between heated and unheated probes with no flow Temperature difference between heated and unheated probes in the sapwood with sap flow Transpiration rate Rate of change of the latent heat content of saturated air with a change in sensible heat content Coefficient of variation of the cross-sectional area of pipes Fractional volume of available space in the stem occupied by pipes Bulk aerodynamic conductance to water vapour Canopy surface conductance to water vapour Stomatal conductance Mean leaf stomatal conductance for a canopy Maximum stomatal conductance Tree height Viscosity Relative viscosity Viscosity of the solvent Length of pipe Canopy leaf area index Latent heat of vaporization Number of pipes in a stem segment Volumetric fraction of solute molecules in a solution Wood density Flow rate of liquid through a pipe Flow rate through pipe I


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Symbol

Units

Description

qp Q R S σA T Tw v vm

m3 s−1 µmol m−2 s−1 W m−2 m2 m2 °C or K °C or K m s−1 or mm s−1 mm s−1

vma vmD V Va Vu Vs W

mm s−1 mm s−1 m3 m3 m−3 m3 m−3 m3 m−3 g g−1

Flow rate through a population of pipes forming a stem Irradiance Available energy Sapwood area Standard deviation of the cross-sectional area of pipes Temperature Water temperature Sap velocity Average half-hourly measured velocity between noon and 16:00 hours (NZST) for an individual tree on a single day Average vm for each tree over the whole measurement period Average vm for each tree for days within the specified range in average daily D Volume of wood Fractional volume of air in wood Fractional volume of water in wood Fractional volume of wood structure Water content

Appendix B As described in the Theory section, wood is formed from a population of pipes of differing radii, the mean area of which (I p) may be described by (Roderick & Berry, 2001): Ip ≈

(

AsFp 1 − ρb

)

Eqn A1

Np

(As is the cross-sectional area of the stem; Fp is the volume fraction of available space in the stem occupied by pipes; and Np is the number of pipes in the stem). From Eqn 7 the flow rate through a particular pipe (qi ) of radius api is: qi =

Ba pi4

Eqn A2

I 2p = I 2p + σ 2A

Eqn A4

where σA is the standard deviation of the cross-sectional area of pipes, and the coefficient of variation (εv) is εv =

σA Ip

Eqn A5

Roderick & Berry (2001) showed that flow rate through a stem (qp ) is given by: qp =

( ) (1 + ε )

B N p Ip π2

2

2 v

Eqn A6

and combining Eqns A1, A3 and A6 gives (Roderick & Berry, 2001):

where B = 2.01 × 10−15

Using standard statistics definitions, the mean square pipe radius ( I 2p ) is given by:

∆ pf T

7 w

l ηrel

Eqn A3

2  ∆ pfTw7   A 2   2   Fp  s 2 q p ≈ 2.04 × 10−16   1 + εv     1 − ρb    Np  ηrel   l 

(

)

(

)

(

)
