• 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.
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).
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 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 cross-sectional 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 (ρb) 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.
The Penman–Monteith equation (Monteith, 1965) describes transpiration from a canopy (E) as a function of weather variables and canopy surface properties, as:
(R (available energy) and D (air saturation deficit, in terms of a dimensionless mole fraction) are measured at a reference height above the surface; ga and gc are bulk aerodynamic and surface conductances, respectively; λ is the latent heat of vaporization; and ɛ is the rate of change of the latent heat content of saturated air with a change in sensible heat). The term gc may be described as the product of mean stomatal conductance (ḡa) 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:
E = ḡsLDs(Eqn 2)
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 gs responds to each environmental variable in a non-linear and independent fashion. Focusing on the response of gs to Ds, Lohammar et al. (1980) suggest that gs is related to Ds by the hyperbolic function:
(D0 is a parameter describing the sensitivity of gs to D). Leuning (1995) showed that Eqn 3 is appropriate for modelling the response of gs 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.
(ap is the pipe radius; Δpf 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:
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)
(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:
(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; ɛv 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:
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 ɛv was rather conservative in conifer species (between 0.4 and 0.6), so that variation in the () term had little effect on vs. As Fp and ɛv are both less than one, and of the same magnitude, they argue that may be approximated by Fp. For conifers, Eqn 11 then becomes:
i.e. at constant temperature:
v ∝ (1 − ρb)2(Eqn 13)
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 () 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.
Materials and Methods
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 400-year 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 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 (ΔT), normalized to the temperature difference with no flow (ΔTm), is related to the velocity of water movement. Granier (1985) found for three species (Pseudotsuga menziesii, Pinus nigra and Quercus pedunculata) that:
v = 119 × 10−6k1.231(Eqn 14)
where v is sap flux density (in m3 m−2 s−1) or sap velocity (m s−1) and
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 ΔT is a weighted mean of ΔT in the sapwood (ΔTsw) and in the inactive tissue (ΔTm) (Clearwater et al., 1999):
ΔT = (1 − a)ΔTsw + aΔTm(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:
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 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).
Table 1. Wood and crown characteristics of each tree used for sap velocity measurements
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
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).
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).
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. 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 − ρb)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 − ρb)2 should increase with increasing D, at least for the exposed trees. To test this hypothesis, days were divided into classes 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 − ρb)2 for sheltered trees at any range of D.
Stomatal conductance (gs) 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 gs 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, gs was very sensitive to D (Fig. 8). The observed diurnal pattern of gs 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 maximum gs in the early morning with a gradual decline during the day.
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 (ρb) in conifers. More precisely, sap velocity is proportional to (1 − ρb)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 gs 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 gs is lower for sheltered compared with exposed trees owing to shading. However, Fig. 7 suggests that gs in D. cupressinum is rather insensitive to irradiance, so we consider it unlikely that shading in sheltered trees resulted in lower gs.
Shoot-level gas exchange measurements highlight the sensitivity of gs to D, particularly when 0.4 < D < 1.0 kPa. To demonstrate the effects of D on both gs and E, we fitted the Lohammar function (Eqn 3) to stomatal conductance data (Fig. 8) to predict the response of gs 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 gs and E with variation in D (Fig. 9) shows 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 − ρb)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 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?
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 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.
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.
Symbols used in this paper
Proportion of the probe in contact with nonconducting tissue
Radius of pipe i
Mean area of a population of pipes
Mean square of pipe radii
Cross-sectional area of the stem
Projected crown area
C : S
Ratio of crown area to sapwood area
Estimated crown volume
kPa or mol mol−1
Air saturation deficit
kPa or mol mol−1
Air saturation deficit at the leaf surface
kPa or mol mol−1
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
mmol m−2 s−1
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
mol m−2 s−1
Bulk aerodynamic conductance to water vapour
mol m−2 s−1
Canopy surface conductance to water vapour
mol m−2 s−1
mol m−2 s−1
Mean leaf stomatal conductance for a canopy
mol m−2 s−1
Maximum stomatal conductance
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
kg m−3 or g m−3
Flow rate of liquid through a pipe
Flow rate through pipe I
Flow rate through a population of pipes forming a stem
µmol m−2 s−1
Standard deviation of the cross-sectional area of pipes
°C or K
°C or K
m s−1 or mm s−1
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
As described in the Theory section, wood is formed from a population of pipes of differing radii, the mean area of which (Āp) may be described by (Roderick & Berry, 2001):
(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:
Using standard statistics definitions, the mean square pipe radius () is given by:
where σA is the standard deviation of the cross-sectional area of pipes, and the coefficient of variation (ɛv) is