Tree Physiology 33, 986–1001
doi:10.1093/treephys/tpt070
Research paper
Inactive xylem can explain differences in calibration factors
for thermal dissipation probe sap flow measurements
Indira Paudel1, Tal Kanety1,2 and Shabtai Cohen1,3
1Institute
of Soil, Water and Environmental Sciences, A.R.O. Volcani Center, PO Box 6, Bet Dagan 50250, Israel; 2Tomato Category, Costa Exchange, 45 Elm Street, Guyra 2365,
NSW, Australia; 3Corresponding author ([email protected])
Received October 28, 2012; accepted August 2, 2013; handling Editor Nathan Phillips
Contribution from the Agricultural Research Organization, Institute of Soil, Water and Environmental Sciences, Bet Dagan, Israel, No. 607/12.
Thermal dissipation probes (TDPs) were calibrated in three diffuse porous fruit trees and one ornamental species in the field
by comparison with heat pulse probes (nectarine and persimmon), in a greenhouse on lysimeters (apple and persimmon) and
in the laboratory by pushing water through cut branches (apple, Peltophorum and nectarine). Two operational methods were
used: continuous (constant thermal dissipation, CTD) and discontinuous, or transient, heating (transient thermal dissipation,
TTD). Correction for the radial distribution of sap flux density was with an analytical function derived from a linear decrease
in flux density with depth, as measured with a multi-depth ‘Tmax’ heat pulse system. When analyzed with previous calibration
factors, the measured sap flow was <50% of actual value. The underestimations were consistent, and calibrations for each
species in the field, greenhouse and laboratory gave approximately the same factors. Reasonable values of tree water use
were obtained with the new calibration factors. Evidence is provided that even though the xylem was diffuse porous, the
underestimations were caused by contact of the probes with inactive xylem along their length. The average portion of probe
in contact with inactive xylem, measured in stained branches following laboratory calibrations, was 0.2–0.24. Using the measured fractions to correct temperature differentials between heated and unheated probes for CTD and TTD, based on
Clearwater et al. (in Potential errors in measurement of nonuniform sap flow using heat dissipation probes. Tree Physiol
1999;19:681–687) almost completely compensated for the underestimations. Calibrations are given for each species both
before and after corrections of temperature differentials, along with a multispecies calibration. These results should be an
important step in reconciling many reports of different calibration factors for TDP probes.
Keywords: Granier method, heat pulse, transpiration, tree water use.
Introduction
Thermal methods for measuring xylem sap flow can be used to
quantify the whole-plant water use and root water uptake in
woody plants (e.g., Kelliher et al. 1992, Granier et al. 1996,
Andrade et al. 1998, Ma et al. 2008, Sevanto et al. 2008 and,
for review, see Smith and Allen 1996, Lu et al. 2004,
Vandegehuchte and Steppe 2013). The method developed by
Granier (1985, 1987), based on heated probes inserted into
the active xylem, i.e., the thermal dissipation probe (TDP)
method, is one of the most frequently used (Mahjoub et al.
2009), because of its reliability, simplicity and low cost
(Andrade et al. 1998, Braun and Schmid 1999).
Thermal dissipation probe measurements have compared
well with water use estimates from other sap flow, meteorological and gravimetric methods (Diawara et al. 1991, Granier
et al. 1996, Clearwater et al. 1999, Lu et al. 2002, Ford et al.
2007, Isarangkool Na Ayutthaya et al. 2010). However, there
have also been reports of severe underestimations of sap flow
© The Author 2013. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
Inactive xylem and sap flow measurements 987
(Bush et al. 2010, Hultine et al. 2010, Steppe et al. 2010, Sun
et al. 2012). An important drawback of the method is that calibrations are empirical, since no analytical model describing the
method has been developed (Smith and Allen 1996, Clearwater
et al. 1999). The heat exchange between xylem sap, probes
and wood depends on trees species, sap flux density and trunk
diameter (Nourtier et al. 2011). A recent study used computational fluid dynamics to provide a more theoretical basis to
model and validate calibration equations (Wullschleger et al.
2011).
In the TDP method, two cylindrical probes, 2 mm in diameter
and 20 mm long, are inserted radially in the sapwood ~10 cm
vertically apart from each other. The temperature difference
between heated and unheated cylindrical probes is monitored.
In the original version, the heated probe is heated continuously
at a constant rate (constant thermal dissipation, CTD) and the
unheated probe (for reference) below, i.e., several centimeters
upstream, is assumed to be unaffected by the heating and not
to influence flow downstream. Granier (1985) found an empirical universal calibration for constant heating
Js = a × K b (1)
where a = 4.28, b = 1.2312, Js is sap flux density (l h−1 dm−2)
and K, the flux index, which normalizes the mean temperature
difference during the time interval to that measured when the
flow is zero, is defined as
K =
∆Tm − ∆T
∆T
(2)
where ΔTm is the temperature difference between the two
probes when sap velocity is zero and ΔT is the temperature difference when sap flux density is Js. The total flux, F (in l h−1), is
F = Js × A (3)
dm2.
where A is the cross-sectional area of the sapwood in
Equation (1) is applicable to many tree species when the
sensor geometry and electrical power are the same (Granier
1987, Lu et al. 2004), but subsequent work has shown that the
equation often underestimates flow (see below). Usually practitioners take the zero flow measurements late at night, when it
is assumed that sap flow is zero, and some studies restrict this
assumption to times when vapor pressure deficit is <0.1 kPa
and the night time temperature signal is stable (Kavanagh et al.
2007, Oishi et al. 2008). Although there is a possibility that
sap flow does not go to zero in irrigated agriculture or wet climates, which can introduce some error, the assumptions are
reasonable and have given good results.
One drawback of the CTD method is its relatively high power
consumption, which can be a critical issue for an experimental
design (Kostner et al. 1998, Do and Rocheteau 2002a,
Nourtier et al. 2011). Of the innate assumptions in this method,
one that has been the focus of some research is that the background wood temperature in the section of branch being measured is uniform (Do and Rocheteau 2002a). Kostner et al.
(1998) proposed the use of cyclic heating (and nonheating or
cooling) to reduce power consumption and Do and Rocheteau
(2002a, 2002b) found that cyclic, or discontinuous, heating
can compensate for thermal gradients in the stem. The transient thermal dissipation (TTD) method developed by Do and
Rocheteau (2002b) uses the same probes and configuration
as the CTD method, but applies a cyclic schedule of heating
and no heating. The cycle length, which can be a half hour or
more, determines the temporal resolution (Nourtier et al.
2011). In this method, the change in temperature during the
cycle is also measured. Do and Rocheteau (2002b) found an
empirical relationship between a re-defined flux index, Ka, and
sap flux density Js (l h−1 dm−2), i.e.,
 11.3 × K a 
Js = 

 1 − Ka 
0.707
(4)
where Ka is defined as
 ∆T − ∆Tua
K a =  oa
∆Tua




(5)
where ΔToa is the maximum temperature difference between
the heated and nonheated phases of the cycle when flux density is zero and ΔTua is the corresponding temperature difference when flux density is Js.
The temperature difference, ΔTa, is determined as
∆Ta = ∆Ton − ∆Toff (6)
where ΔTon and and ΔToff are the temperature differences
reached at the end of the heating and cooling periods,
respectively.
Do and Rocheteau (2002a, 2002b) showed that the use of
their index (Eq. (5)) can compensate for thermal gradients in
the stem, which are constant during the TTD cycle, while those
gradients cause errors in CTD measurements. In addition, their
index improves the stability of the zero flow measurements.
They found a similar response of the flux index to sap flux density with different cycles of heating and cooling, but calibration
slopes were different from those obtained with CTD. A significant difference between CTD and TTD arises from the influence of sap flux density on the rate of cooling of the heated
sensor. At high flux density, the sensor cools quickly and after
15 min sensor temperature is close to equilibrium. But, at low
flux density, sensor temperature changes slowly and after
Tree Physiology Online at http://www.treephys.oxfordjournals.org
988 Paudel et al.
15 min it may be far from equilibrium (Do and Rocheteau
2002b).
Constant thermal dissipation has been found to have similar
calibration factors for most tree species with some variation
from species to species (e.g., Cabibel and Do 1991, Lu et al.
2004). Similarly, nonspecies-specific calibrations of TTD in
artificial saw dust (Do and Rocheteau 2002a, 2002b) were
confirmed in tropical trees by Isarangkool Na Ayutthaya et al.
(2010). However, the latter found overestimations of up to 30
and 20% at low (<0.8 l dm−2 h−1) and high flux density, respectively. Based on empirical analysis, they changed Eq. (4) to a
simple linear relationship
Js = c × K a (7)
where c = 12.95.
Thermal dissipation probe measurements, similar to several
other sap flow methods, measure only part of the stem. In
order to estimate total sap flow, assumptions must be made
about the other parts. Sap flux density can vary greatly with
radial depth and azimuth around the stem (for review, see
Gartner and Meinzer 2005 and Cohen et al. 2012) and the
azimuthal distribution of flux density is hard to predict. The
radial (or depth) distribution usually follows specific patterns,
so numerical integration can be applied to interpolate or
extrapolate the measurements of part of the radial profile to
total sap flow.
Clearwater et al. (1999) worked with the CTD method in
ring porous species where the early xylem in each new annual
ring becomes inactive after a short time. In that case, only part
of the probe is in contact with active xylem. If the fraction of
the probe in contact with active and inactive xylem, a and b
(where b = 1 − a) respectively, are known, then the measured
temperature difference, ΔT, can be expressed as the sum of
two parts, or
∆T = a∆Tsw + b∆Tm ∆T – b∆Tm
a
Correction for a linear radial distribution of sap
flux density
Sap flux density is not uniform in the radial direction (or depth
in the xylem) in which sap flow probes are usually introduced,
and the radial distribution can change from tree to tree in the
same species and can even vary during the same day. Several
equations have been proposed for fitting the distribution. In
most cases of broadleaved and coniferous trees, flux density is
high in the outer part of the xylem and decreases with depth.
This topic is further discussed in the Discussion section.
To obtain the total volume sap flux QT (l h−1) for the entire
xylem, the sap flux density measurements must be integrated for
all depths considering the radial distribution (Green et al. 2003,
Fernández et al. 2006), and for a circular stem cross section
(9)
and the value of ΔTsw is then used to compute sap flux density
for the active xylem.
Bush et al. (2010) used the same approach to correct for
known radial distributions of ring and diffuse porous species
in laboratory conditions and Lu et al. (2002) recommended
using it for cases where the probe length exceeded sapwood
depth. Although application of this correction to TTD measurements is intuitive, it has not been previously investigated
Tree Physiology Volume 33, 2013
Theory
(8)
where ΔTsw is the temperature difference for the active sapwood. Equation (8) can be rearranged to get ΔTsw, i.e.,
∆Tsw =
(Do and Rocheteau 2002a, Isarangkool Na Ayutthaya et al.
2010).
In several of our studies of tree water use using TDP sap
flow measurements, the standard calibrations gave severe
underestimations when compared with other estimates. To validate this, we conducted a series of greenhouse calibrations
with lysimeters. We hypothesize that the underestimations are
due to probe contact with nonuniform or inactive xylem and/or
differences in radial gradients among the different species. Our
investigations included both modes of heating (CTD and TTD).
Here, we report TDP calibrations for several species and two
modes of heating in greenhouse and laboratory conditions. An
analytical integral for extrapolating measurements of part of
the xylem to all radial depths is developed. We analyze the
effect of observed nonuniform and inactive xylem on sap flow
measurement and apply the Clearwater et al. (1999) correction to our findings.
QT =
∫
R
Ro
2πrVs(r ) dr
(10)
where Vs(r) is the sap flux density expressed as a function of
the depth in the stem, r, R is the total radius of the stem without
the bark and phloem, and Ro is the radius of the inner limit of
conducting sapwood, where flux density is zero.
Here we derive an analytical correction factor to account for
a linear decline in sap flux density with radial depth in the
xylem. The correction is applied to measurements of average
flux density in the first 2 cm and computes volume sap flux for
the entire sapwood, assuming a circular stem cross section
and uniform azimuthal distribution of flux density. Figure 1
shows a schematic cross-sectional area of a tree trunk along
with the linear radial distribution of sap flux density for the
outer (active) xylem. Several layers are shown, with bark and
phloem (Rp), sapwood (Rs) and heartwood (Ro), where Rp and
Inactive xylem and sap flow measurements 989
We are interested in the relationship between flux in the outer
2 cm and the total flux, i.e.
QT = KQ2 (17)
where K is the ratio of QT to Q2 or
K =
[r 2(2r − 3Ro )]RRo
[π / 3(R − Ro )][r 2(2r − 3Ro )]RRo
QT
= 2
=
2
R
Q2
[π / 3(R − Ro )][r (2r − 3Ro )]R −2 [r (2r − 3Ro )]RRo
2R 3 − 3RoR 2 + Ro3
K =
2
12R − 24R + 12Ro + 16 − 12RRo
(18)
This analytical expression (Eq. (18)), which gives a factor to
convert sap flux density measured in the first 2 cm to that for
the full stem (for the case of a linear decrease of sap flux density with depth), is quite useful and the only parameters
required are the stem radius without bark, R, and the radius at
which sap velocity is zero, Ro.
Materials and methods
Figure 1. Schematic cross section of a tree trunk and a linear distribution of relative sap velocity Vs(r) with depth in the trunk sapwood.
Ro do not participate in transporting water. R′ and R are the
total radius and radius without bark, respectively, so
R ′ = Ro + Rs + Rp
R = Ro + Rs = R – Rp
(11)
(12)
The relative sap flux density Vs(r) at depth r can be calculated
by
0 < r ≤ Ro
 0,

Vs ( r ) =  r − Ro
 R − Ro , Ro < r < R
(13)
By using Eq. (13) in Eq. (10), we get
QT = 2π
 r − Ro
r
Ro  R − R o
∫
R
2π

 dr = R − R
o

∫
R
Ro
r 2 − rRo dr
(14)
Further solving Eq. (14) for QT results in
R
QT =
2π  r 3 Ro r 2 
π
−
=
[r 2(2r − 3Ro )]RRo (15)
R − Ro  3
2 
3(R − Ro )
Ro
The volume flux in the outer 2 cm is then
Q2 =
π
[r 2(2r − 3Ro )]RR −2
3(R − Ro )
(16)
Thermal dissipation probe construction,
operation and installation
Thermal dissipation probes were constructed from 19-gauge
hypodermic needles cut to 2-cm length; with a thermocouple
placed at the center of the 2 cm. Heated probes were wrapped
with 0.13-mm-diameter coated constantan wire to obtain a
heating coil with a resistance of 10–11 ohms. Needle assemblies were dipped in thermal paste and inserted into 2.4 mm
outer diameter aluminum sleeves. Power for heating the probes
was provided by current-regulating circuits based on the 317T
integrated circuit chip, in order for probe power to be 0.2 W
each. The above conforms to instructions received from N.
Phillips and R. Oren (personal communication, Phillips et al.
1996). Probe leads were mounted on small circuit boards and
connected to thicker thermocouple or copper extension wires.
Circuit board assemblies and needle hubs were inserted in
pipette tips, molded in epoxy or polyester and equipped with
connection boxes, which enabled easy handling and field
installation. The extension wires were connected to the power
circuits and dataloggers (CR series, Campbell Scientific, Logan,
UT, USA) powered by 12 V car or deep cycle batteries. In the
field, the batteries were charged by solar panels.
Probe power circuits were connected to relay circuits to allow
turning probe power on and off by the datalogger according to
the datalogger program or user intervention. This enabled
either continuous or discontinuous heating. When heating continuously, the average temperature difference between heated
and reference probes was recorded. For discontinuous heating,
final values for the heating or cooling cycles were recorded.
For tree measurements, probes were installed in the stem
below the first branch. Bark (and phloem) was cleared around
Tree Physiology Online at http://www.treephys.oxfordjournals.org
990 Paudel et al.
the drill point, holes were drilled with 2.5 mm drill bits and
probes were again dipped in thermal paste or lanolin before
insertion to enhance contact between probe and xylem.
Reference holes (for the nonheated probes) were drilled at
least 10 cm below and usually offset from the probe azimuth,
because the reference probe can interrupt flow in the stem
10 cm above it (see Discussion). Probes and surrounding stem
were covered with polyurethane (from spray cans) inside aluminum foil wraps for insulation and to prevent thermal gradients.
Greenhouse calibrations
Calibrations of the TDP probes were in a greenhouse at The
Volcani Center, Bet Dagan. Two species were measured, persimmon (Diospyros kaki L. cv. Triumph) and apple (Malus domestica
Borkh. cv. Golden delicious). Apple (n = 10) trees were transferred to pails and allowed to adapt for several months before
measurement. Two-year-old persimmon saplings (n = 10) bought
from a commercial nursery were grown for another 2 years in a
screenhouse until the stems were thick enough for the probes.
Pailed trees were placed in basins on platform scales (Vishay,
Petach Tikva, Israel). Pails were wrapped in plastic to prevent soil
evaporation. Irrigation was applied by drip (2 l h−1) once a day
and controlled by an irrigation computer. Irrigation was in excess
and basins drained excess water into external collection containers. Weight data and TDP sensor output were read every 15 min
and recorded by a datalogger (CR23X, Campbell Scientific).
Field calibrations
Thermal dissipation probes were also compared with measurements of multi-depth heat pulse probes using the Tmax method
(Cohen et al. 1981, Cohen 1994) in nectarine (Prunus persica L.
cv. nectarine) and persimmon in commercial irrigated orchards
(eight trees in each case). The experimental sites were characterized by a Mediterranean semiarid climate with winter rainfall
between 500 and 700 mm. Our multi-depth Tmax equipment
and methodology is described in detail by Cohen et al. (1981,
2008). The Tmax method is considered accurate for high flux
densities but unable to measure low flux densities, and a lower
limit of 20 cm3 cm−2 h−1 has been reported (Green et al. 2003,
Vandegehuchte and Steppe 2013). However, Cohen and Li
(1998) showed that the lower limit of flux measurements (with
our equipment and a simple peak detection algorithm) is about
a third of that, and that improved peak detection lowers the limit
by an order of magnitude.
Parameters for converting heat pulse velocity to sap flux density, i.e., sapwood density and heat capacity, were determined
for stem cores taken from the trees. Values of wet and dry wood
densities were 0.996 ± 0.015 and 0.65 ± 0.014 g cm−3, respectively, for nectarine and 0.990 ± 0.009 and 0.587 ± 0.006 g cm−3
for persimmon. Heat capacity was then determined according to
these data from relationships given by Simpson and TenWolde
(2007).
Tree Physiology Volume 33, 2013
Laboratory calibrations
Plant materials
Laboratory calibrations were on branches of apple (M. domestica n = 8 from each of two varieties, Anna and Pink lady),
Peltophorum (Peltophorum dubium (spreng.) Taub.; n = 5) and
nectarine (n = 14). Branches were cut from apple and nectarine
trees in commercial orchards and Peltophorum from trees near
the laboratory. Hydraulic conductivity of branches was measured before starting the calibration and only branches whose
specific conductivity was within the range expected from previous work (e.g., Cohen et al. 2007) were used for calibrations.
Experimental setup and branch preparation
Branch sections of 4–5 cm diameter and average length of
50 cm were cut in air and immersed in a bucket of distilled
water after foliage removal. The bucket was covered with a
black plastic bag, transported and then stored in a 5 °C cold
room to prevent transpiration. Before measurement, the branch
was re-cut at both ends to a final branch size of 20–25 cm and
the cut ends were shaved with a fresh razor blade. Bark was
stripped off the top of the branch, the branch was connected to
a pipe with a pressure fitting, and the pipe was connected to a
KCl solution (20 mM) with an 11.5 m constant head (0.115 MPa,
from the building’s roof) that ran through a 2 µm filter (Cole
Parmer in-line liquid filter, El-Hamma Instruments, Kibbutz Mevo
Hamma, Israel). The branch was fastened upright to a ring
stand above a beaker, which was placed on an electronic balance with 0.01 g resolution (Shimadzu, BX4200H, Kyoto,
Japan) to measure actual flow of fluid (i.e., the KCl solution). The
balance was connected to a computer and weight values were
monitored and stored every 10 s in Microsoft Excel. The KCl
solution was prepared with de-gassed double-distilled water.
Sapwood area, thickness and sapwood depth were determined by staining with a 0.75% W/V methylene blue solution
during and after completion of the calibration measurements. The
methylene blue solution was connected to the stem and infiltrated until visible in the downstream reservoir. The branch was
then flushed with KCl solution in order to suppress the spread of
the dye to inactive parts of sapwood, and then cut at the position
of the heated probes. The pattern of staining was examined to
determine sapwood cross-sectional area and the distribution of
inactive xylem at the point of probe insertion. Images of the cross
section were taken with a digital camera and the lengths of active
and inactive xylem touching the heated probe were measured
with a ruler. Table 1 lists branch diameters and the fraction of
active sapwood in contact with each probe.
Calibration for two heating modes
Each branch segment was instrumented with a TDP pair and
azimuthal (tangential) positions of upper (heated) and lower
(nonheated) probes were offset to prevent influences of the
reference probe on flux density at the downstream heated
Inactive xylem and sap flow measurements 991
probe. Distance between heated and reference probes was
10 cm. For constant heating mode, continuous power was supplied and the average temperature difference was recorded
every 5 min. For transient heating, the final temperature differences for 15 min heating and cooling cycles were recorded.
Zero flow readings were taken at the beginning and end of the
experiment by stopping flow of the KCl solution. Generally, a
constant maximum temperature difference was observed after
1–2 h of null flow. Average maximum temperature differences
were 11.2, 11.0 and 11.6 °C for apple, peltophorum and nectarine, respectively.
Results
Field and greenhouse calibrations
First we present calibrations made in vivo, which, although not as
precise as the laboratory measurements below, demonstrate
clearly that some previous calibration factors are incorrect for
field measurements. Calibrations of the TDPs for apple and persimmon saplings on lysimeters in the greenhouse are shown in
Figure 2. Data are 15-min averages measured during a period of
several weeks. Much of the scatter is due to the lag of sap flow at
the base of the stem behind transpiration measured by the lysimeter. Sap flux density was calculated using the Granier (1985)
calibration equation (Eq. (1)). On average, the ratio between sap
flux density measured by the lysimeters and TDPs was 2.9 for
apples and 2.5 for persimmon (Figure 2). Applying these factors
to the seasonal course of sap flow measured in irrigation experiments in persimmon orchards (Kanety 2010, Kanety et al. 2013)
gave reasonable results when compared with reference evapotranspiration and orchard irrigation rates.
Comparison of heat pulse (Tmax method) to TDP measurements (in persimmon) gave a similar ratio to that obtained from
the lysimeter calibration (see above). The multi-depth heat
pulse measurements gave, for daily totals, high flux density in
the outer layer and close-to-linear decreases in flux density
with depth in the xylem, reaching null values at a depth of
~5 cm both in persimmon and nectarine (Figure 3). Changes
in the normalized radial distribution of flux density during the
day were minor. After correction with the factor found in the
lysimeter calibrations and accounting for the radial distribution
with Eq. (18), results of TDP and heat pulse measurements
were not significantly different.
Laboratory calibrations
Calibrations done in the laboratory, where sap flow in cut
branches of apple, nectarine and peltophorum branches was
measured directly, are shown in Figure 4. Figure 4a–c shows
the relationship between actual and measured flux density for
all branches measured from each of the three species with
continuous heating and flux density calculated with Eq. (1).
Figure 4d–f shows the relationship between the flux index and
flux density. For apple (Figure 4a) the ratio between actual and
measured flux density was 2.6 ± 0.1, for peltophorum
(Figure 4b) 2.6 ± 0.1 and for nectarine (Figure 4c) 2.4 ± 0.1.
Table 2 (left-hand side for CTD) gives the slopes of the calibration lines for the individual branches and for the grouped result.
The ratio of actual-to-measured flux density was not significantly different between species (P < 0.05).
Visual examination of branches that were perfused with dye
and cut at the point where the heated probe had been inserted
showed that the branches had regions with inactive xylem
adjacent to the probe. Examples of the cross sections are
shown in Figure 5. For the apple branch shown in Figure 5a,
staining was spotty in all of the annual rings, and the portion of
the probe in contact with active xylem was 75%. In the nectarine branch (Figure 5c), the two outer rings were the most
active, the inner ring was only lightly stained and the pith was
not stained. For this case, contact with active xylem was
70–74%. For peltophorum (Figure 5b) the probe was in
Figure 2. Greenhouse calibration of the CTD method in apple (a) and persimmon (b). Constant thermal dissipation values were computed with Eq.
(1) using the standard coefficients.
Tree Physiology Online at http://www.treephys.oxfordjournals.org
992 Paudel et al.
Figure 3. The radial distribution of average relative daily total sap flux
density in six persimmon (D. kaki L.) and seven nectarine (P. persica)
tree trunks in the field, measured with the heat pulse (Tmax) method.
Results are averages for summer conditions, measured continuously for
over a month. Vertical bars indicate two standard errors of the mean.
c­ ontact with the inactive pith, the inner portion of the xylem
was also spotty and contact was 72–78%.
Lengths of active and inactive xylem in contact with the
probes were determined by measuring the lengths in the
stained cross section. Results, shown in Table 1, indicate that
on the average 20–26% of the probe was in contact with inactive xylem. Clearwater et al.’s (1999) correction for inactive
xylem (Eq. (9)) was then applied and corrected calibration
points are presented in Figure 4 along with the uncorrected
values. For both cases (uncorrected and corrected) regressions were applied assuming a null intercept. The resulting
slopes, which after correction were close to unity (Table 2, left
side), indicate that application of the correction for inactive
xylem almost completely explained the underestimations found
in the laboratory (Figure 4).
This shows that for the three species TDP measurements were
low due to probe contact with inactive xylem. Regression of flux
index on flux density (with Eq. (1)) gave the results given in Table
3 (left-hand side for CTD). In apple (data from Figure 4d), the
factor ‘a’ in Eq. (1) is 10.3 ± 0.3 (± standard error of estimate)
and ‘b’ is 1.30 ± 0.06 while after correction, a = 4.9 ± 0.1 and
b = 1.18 ± 0.03. For peltophorum (Figure 4e) a = 9.7 ± 0.7 and
b = 1.10 ± 0.06
and
after
correction
a = 4.7 ± 0.3
and b = 1.01 ± 0.05. In nectarine (Figure 4f), a = 8.9 ± 0.4 and
b = 1.04 ± 0.04 and after correction a = 4.9 ± 0.2 and
b = 0.99 ± 0.03. A t-test based on the standard errors of estimate indicates that ‘a’ factors for apple and peltophorum (corrected and uncorrected) were not significantly different, but
nectarine was significantly different from the others (P < 0.05).
However, ‘b’ was significantly different in all cases. Relations
between actual and measured flux density were close to linear
(Figure 4) and a power function (Eq. (1)) adequately fit the relationship between flux index and flux density (Table 3).
Tree Physiology Volume 33, 2013
Similar analyses were done for the discontinuous TTD
method, with similar results (Tables 2 and 3 and Figure 6).
However, small and significant (P < 0.05) differences were
found in the ratio of actual-to-measured sap flux density
between TTD and CTD before correcting for contact with inactive xylem. Although application of the Clearwater et al. (1999)
correction to the TTD results is intuitive, we are not familiar
with previous reports of this.
Experimental data for TTD were analyzed with both the Do
and Rocheteau (2002b; Eq. (4)) and Isarangkool Na Ayutthaya
et al. (2010; Eq. (7)) equations. Flux density obtained from Eq.
(4) is less than that for Eq. (7) when the flux index (K) is
between 0.06 and 0.65 and exceeds that for Eq. (7) when the
flux index is higher, as shown in Figure 7. In addition, Eq. (4) is
undefined when the flux index exceeds 1, which occurs at high
flux densities, like the highest values obtained in almost all our
samples in the laboratory experiments at 0.115 MPa. For our
analyses we obtained better results with Eq. (7), and used it
for the continuation. In apple, actual flux densities measured by
TTD were 2.5 ± 0.1 greater than those measured before correction, but after correction flux densities were similar. For
­peltophorum (Figure 6b) and nectarine (Figure 6c), the ratios
for uncorrected measurements were 2.3 ± 0.1 and 2.27 ± 0.09,
and after correction the ratio was close to unity. As with CTD
(see above) the ratios for the species were not significantly
different.
For TTD the relationship between the flux index and actual
flux density was close to linear in each cut branch, as indicated
by the high r2 values in Table 3 for each species (Figure 6d–f)
and in the multispecies relation (Figure 8b). Regressions to fit
Eq. (7) to the data gave c = 32.6 ± 6, 26.6 ± 5 and 30.8 ± 4
for apple, peltophorum and nectarine before correction and
14.0 ± 4, 12.9 ± 0.7 and 13.9 ± 1.2 after correction for inactive xylem, respectively. Species differences in corrected and
uncorrected values of c were not significantly different
(P < 0.05) and values were close to the original value found by
Isarangkool Na Ayutthaya et al. (2010), 12.95 (see Table 3 for
all results).
Results of all laboratory calibrations, after correction for
inactive xylem, were combined to obtain multispecies calibration equations for the continuous and discontinuous methods
using the mathematical forms shown above. This analysis,
shown in Figure 8, yielded the following calibration equations:
CTD :
TTD:
Js = 4.86 × K 1.157
Js = 13.45 × K
(19)
(20)
The constants in Eq. (19) and (20) are close to those of Granier
(1985, 1987; Eq. (1)) and Isarangkool Na Ayutthaya et al.
Inactive xylem and sap flow measurements 993
Figure 4. Relation between actual and measured flux density for continuous heating CTD, using Granier’s calibration equation (Eq. (4)) with and
without correction for partial probe contact with inactive xylem: (a) apple, (b) peltophorum and (c) nectarine. Actual flux density vs. flux index with
and without correction: (d) apple, (e) peltophorum and (f) nectarine. Solid lines are fitted with linear (a, b and c) or power (d, e and f) functions.
Results are from laboratory calibration experiments with cut branches and points are individual measurements. Slopes and equation fits are given
in Tables 2 and 3.
(2010; Eq. (7)), but significantly different at the 95% level. The
differences in calibration factors may result from differences in
probe contact with inactive xylem and/or species differences
(see Discussion).
The results show that understimations of sap flow were
caused by probe contact with inactive xylem. Figure 9 shows
the relationship between the fraction of inactive xylem in contact with the probe and the slope of the relationship between
actual and measured sap flux density for all branches measured in our laboratory experiments. The relationship is linear
and an increase in contact with inactive xylem from 8 to 33%
increased the ratio of actual-to-measured flux density from 1.6
to 3. Correction for inactive xylem with Eq. (9) compensated
for the errors, but a significant slope still remained, so that
when contact with inactive xylem was 33% sap flux density
was underestimated by 5–10%.
Discussion
Universal or specific calibrations
Our calibrations of TDPs for four diffuse porous species using
two operational protocols (CTD and TTD), conducted in trees
in the greenhouse and field and in the laboratory with cut
branches yielded relationships significantly different from the
original equations found in the literature (Figures 2, 4 and 6
and Tables 2 and 3). The calibration results were similar to
Tree Physiology Online at http://www.treephys.oxfordjournals.org
994 Paudel et al.
c­ alibration estimates obtained by comparison with a heat pulse
(Tmax) system. There have been many reports of calibrations
of TDP sensors, some in agreement and some in disagreement
with the original calibration factors. For example, McCulloh et al.
Figure 5. Cross sections of branches used for sap flow calibration, cut
at the position of the heated probe. Branches were perfused with dye
as part of the calibration procedure. Regions of inactive xylem did not
stain. Position of the heated probe is indicated, and the portion in
­contact with inactive xylem is indicated by the red color in (c):
(a) apple, (b) peltophorum and (c) nectarine.
(2007), who measured water loss from Pseudobombax septanatum (Jacq.) Dugand and Calophyllum longifolium Willd, and
also Lu et al. (2002) in Musa sp. (banana) and Mangifera indica
L. (mango) found calibration factors in agreement with those of
Granier (1985). Cabibel and Do’s (1991) calibrations for M.
domestica, Quercus robur L., Castanea sativa Mill. and a synthetic porous material gave a similar but slightly higher calibration line (as discussed by Lu et al. 2004). However, Lu and
Chacko (1998) in Garcinia mangostana L. (mangosteen),
Gutiérrez and Santiago (2006) in Ochroma lagopus Swartz and
Hyeronima alchorneoides Allem., Steppe et al. (2010) in
Fagus grandifolia Ehrh., Hultine et al. (2010) in Tamarix ramosissima Ledeb. × chinesis Lour., Renninger and Schäfer (2012)
in several pine and oak species, Taneda and Sperry (2008) in
Quercus gambelii Nutt. and Acer grandidentatum Nutt., Sperling
et al. (2012) in date palm (Phoenix ­dactylifera L.) and Reis et al.
(2006) in papaya (Carica papaya L.) found calibration factors
significantly different. In all the latter cases, use of the Granier
(1985) calibration would have resulted in underestimations.
Smith and Allen (1996) and Sun et al. (2012) recommended
calibrating each species and each sensor set.
Reports similar to ours are those of Steppe et al. (2010) in
F. grandifolia, a 60% underestimation of actual sap flow as measured by lysimeter, Hultine et al. (2010) in excised branches of
T. ramosissima × chinesis, 50% underestimation, Sun et al.
(2012) in Populus deltoides W. Bartram ex Marshall, 34% underestimation, Taneda and Sperry (2008) in Q. gambelii and A.
grandidentatum, >50% underestimation, and Lu and Chacko
Table 1. ​​Properties of branches used in the laboratory experiments. For averages, ± standard error of the mean is given.
Trees
Branch
no.
Circumference
(2πR), cm
Radius without
bark, cm
Length
Fraction of contact
with inactive xylem
M. domestica (apple)
1
2
3
4
5
6
12.8
13.2
12.4
12.7
12.2
12.5
12.6
10.9
11.9
11.3
12.33
11.6
11.62
12.8
12.11
12.55
12.11
13.22
12.8
12.4
12.8
12.5
2.11
2.1
2.00
2.11
2.00
2.1
2.03
1.7
1.9
1.99
2.00
1.99
1.99
2.11
2.00
1.99
2.00
2.1
2.11
2.00
2.1
1.99
25
32
30
20
24
28
26.77
34
45
40
35
30
36.6
25
32
31
23
28
26
28
29
27.75
0.28
0.08
0.266
0.133
0.2
0.311
0.20 ± 0.04
0.211
0.22
0.35
0.244
0.31
0.24 ± 0.03
0.15
0.24
0.23
0.21
0.23
0.24
0.32
0.23
0.24 ± 0.16
Average
P. dubium (peltophorum)
Average
P. persica (nectarine)
Average
Tree Physiology Volume 33, 2013
1
2
3
4
5
1
2
3
4
5
6
7
8
Inactive xylem and sap flow measurements 995
Table 2.​ ​Summary of the results of the laboratory calibrations (actual flow vs. measured flow).
Species
M. domestica (apple)
Average
All data
P. dubium (peltophorum)
Average
All data
P. persica (nectarine)
Average
All data
Branch
no.
CTD (Eq. (1))
Uncorrected
R2
Corrected
R2
Uncorrected
R2
Corrected
R2
1
2
3
4
5
6
2.7
*
2.5
2.7
2.7
*
2.6 ± 0.05
2.6 ± 0.1
2.3
2.7
*
*
2.8
2.6 ± 0.15
2.6 ± 0.1
2.6
*
2.5
*
2.5
2.5
*
2.5
2.5 ± 0.03
2.4 ± 0.1
0.92
*
0.92
0.98
0.88
*
0.93
0.91
0.97
0.92
*
*
0.95
0.95
0.94
0.92
*
0.98
*
0.89
0.92
*
0.85
0.91
0.92
1.1
*
1.1
1.0
1.0
*
1.04 ± 0.02
1.05 ± 0.02
1.1
1.1
*
*
1.0
1.07 ± 0.03
1.07 ± 0.03
1.0
*
1.0
*
1.0
1.0
*
1.1
1.01 ± 0.01
1.04 ± 0.01
0.91
*
0.93
0.98
0.97
*
0.96
0.94
0.97
0.94
*
*
0.969
0.96
0.96
0.89
*
0.96
*
0.71
0.99
*
0.98
0.90
0.94
*
1.6
2.3
*
2.4
2.8
2.3 ± 0.24
2.4 ± 0.14
*
2.3
2.4
2.3
*
2.3 ± 0.03
2.3 ± 0.12
*
2.6
*
2.4
2.2
*
2.4
*
2.37 ± 0.08
2.27 ± 0.09
*
0.95
0.96
*
0.89
0.97
0.94
0.94
*
0.89
0.81
0.89
*
0.90
0.88
*
0.88
*
0.91
0.93
*
0.88
*
0.93
0.93
*
1.0
1.1
*
1.0
1.1
1.04 ± 0.03
1.04 ± 0.03
*
1.0
1.0
1.0
*
1.03 ± 0.00
1.03 ± 0.03
*
1.0
*
1.1
1.1
*
1.1
*
1.06 ± 0.02
1.06 ± 0.02
*
0.96
0.91
*
0.91
0.96
0.93
0.93
*
0.88
0.945
0.987
*
0.94
0.93
*
0.77
*
0.91
0.93
*
0.9
*
0.88
0.91
1
2
3
4
5
1
2
3
4
5
6
7
8
TTD (Eq. (7))
Numbers are the slope and r 2 for the relationship of actual to measured flux density using Eq. (1) for CTD measurements and Eq. (7) for TTD.
‘Corrected’ columns refer to the same analysis after correction for the fraction of inactive xylem in contact with the probe (from Table 1) using Eq.
(9). Averages of the branch values are given as well as regression results for pooled data for all branches (all data), ± standard error of the mean.
*Not measured.
(1998) in G. mangostana (mangosteen), 28% underestimation.
Summarizing our results in this manner, we found
­underestimations of 70% for apple in greenhouse trees and cut
branches, 55% for peltophorum cut branches and 60% for persimmon orchard trees (compared with heat pulse measurements
with the Tmax method) and greenhouse saplings, and 60% for
nectarine cut branches.
In addition, we calibrated TDP measurements using discontinuous operation (TTD) for three species in cut branches.
Analysis with Do and Rocheteau’s (2002a) and Isarangkool Na
Ayutthaya et al.’s (2010) calibration equations (Eq. (4) and (7),
respectively) gave similar but significantly different ratio of
actual-to-measured flux density.
Several studies have reported problems with Do and
Rocheteau’s (2002b) equation. Masmoudi et al. (2011) in olive
(Olea europeana L.) and Nourtier et al. (2011) in silver fir
(Abies alba Mill) did not get a good fit, and recommended
checking the calibration on each species. Reyes-Acosta et al.
(2012) reported a 25% underestimation in flux density compared with gravimetric methods in cut branches of Fagus sylvatica. Our results using Isarangkool Na Ayutthaya et al.’s
(2010) equation (Eq. (7)) gave similar calibration ratios to
those found for CTD, i.e., 50% underestimation in apple and
40% in peltophorum and nectarine. The parameter c (from Eq.
(7)) in all three species was significantly higher than Isarangkool
Na Ayutthaya et al.’s (2010), with no significant differences
between species.
Effects of inactive xylem
Underestimations of flow due to significant amounts of inactive
xylem in contact with the probe are implicated for all the ­species
we studied. The correction we used for this, Eq. (9), was originally developed for CTD measurements in ring porous stems
(Clearwater et al. 1999), where there is a regular pattern of
active and inactive xylem in the annual rings caused by differences in early and late wood or for cases where the probe is
longer than the active xylem (Lu 2002, Taneda and Sperry
2008). It is important to note that the relative underestimation
of sap flow due to inactive xylem in the profile increases with
sap flux density so that if 20% of the xylem is inactive, the error
can exceed 50% for the sap flux densities normally encountered in the field (see analysis in Clearwater et al. 1999). In the
Tree Physiology Online at http://www.treephys.oxfordjournals.org
996 Paudel et al.
Table 3. Summary of the results of laboratory calibrations (actual flux density vs. flux index).
Species
M. domestica (apple)
Average
All data
P. dubium (peltophorum)
Average
All data
P. persica (nectarine)
Branch
no.
1
2
3
4
5
6
1
2
3
4
5
1
2
3
4
5
6
7
8
Average
All data
CTD calibration results (Eq. (1))
Uncorrected
TTD calibration result (Eq. (7))
Corrected
a
b
R2
110
*
89
81
90
*
93 ± 6
103 ± 3
108
88
*
*
99
97 ± 7
97 ± 7
109
*
79
*
89
96
*
94
93 ± 5
89 ± 4
1.2
*
1.2
1.2
1.1
*
1.30 ± 0.04
1.30 ± 0.06
1.2
1.1
*
*
1
1.10 ± 0.06
1.10 ± 0.06
1.8
*
0.92
*
1.1
1.9
*
1.5
1.4 ± 0.2
1.17 ± 0.04
0.94
*
0.92
0.99
0.85
*
0.92
0.92
0.95
0.8
*
*
0.99
0.91
0.92
0.85
*
0.86
*
0.86
0.93
*
0.89
0.88
0.78
a
50
*
44
48
51
*
48 ± 2
48 ± 1
54
40
*
*
48
47 ± 4
47 ± 3
44
*
49
*
44
36
*
34
41 ± 3
49 ± 2
Uncorrected
b
R2
1.2
*
1.9
1.2
0.93
*
1.3 ± 0.2
1.15 ± 0.03
1.3
1.0
*
*
0.92
1.08 ± 0.11
1.00 ± 0.05
1.5
*
0.76
*
1.0
1.6
*
1.4
1.2 ± 0.13
1.00 ± 0.03
0.95
*
0.92
0.99
0.91
*
0.94
0.92
0.96
0.89
*
*
0.92
0.92
0.94
0.81
*
0.9
*
0.87
0.91
*
0.87
0.87
0.8
Corrected
c
R2
c
R2
*
268
263
*
313
357
300 ± 22
326 ± 65
*
330
279
288
*
299 ± 16
301 ± 64
*
273
*
297
271
*
307
*
289 ± 9
299 ± 42
*
0.96
0.99
*
0.86
0.97
0.95
0.93
*
0.98
0.86
0.81
*
0.88
0.84
*
0.91
*
0.91
0.83
*
0.92
*
0.89
0.89
*
134
142
*
142
138
139 ± 2
140 ± 35
*
144.5
134.5
133.4
*
137 ± 5
138 ± 7
*
139.8
*
133.7
148.4
*
136.9
*
140 ± 12
145 ± 12
*
0.96
0.98
*
0.86
0.96
0.97
0.96
*
0.93
0.89
0.94
*
0.02
0.97
*
0.94
*
0.94
0.87
*
0.75
*
0.87
0.87
Numbers are the regression fits and r 2 for the parameters of Eq. (1) (a and b) for CTD measurements and Eq. (7) (c) for TTD. Corrected columns
refer to the same analysis after correction for the fraction of inactive xylem in contact with the probe (from Table 1) using Eq. (9). Averages of the
branch values are given as well as regression results for pooled data for all branches (all data), ± standard error of the mean.
*Not measured.
current study, using the correction almost completely compensated for the inactive xylem when its relative length was quantified, although a small systematic error remained (i.e., the slope
of Figure 9). In addition, it appears that at least for apple, where
field, greenhouse and laboratory calibrations were in agreement
(within the accuracy of the measurements, which we estimate
to be 10%), the average relative length of inactive xylem is
more or less constant. Possible intraspecific variation in this
length may be a cause for the large variability in the lysimeter
calibrations (Figure 2).
Correcting TTD measurements for contact with inactive xylem
is new, although there is no particular reason that TTD should be
different from CTD. For TTD measurements after correction, we
found calibration coefficients close to, but significantly different
from that of Isarangkool Na Ayutthaya et al. (2010) (values of c
in Eq. (7) of 14.5 and 12.95, respectively, see Table 3). The
reason for the disagreement may be that their calibrations were
made in fully conductive cut branches (Isarangkool Na Ayutthaya
et al. 2010), while only a few of our cut branches were fully in
contact with conducting sapwood (one of six in peltophorum;
two of eight in Apple and two of 10 in nectarine; see Table 1).
Tree Physiology Volume 33, 2013
Isarangkool Na Ayutthaya et al. (2010) did not mention the frequency of fully conductive sapwood in their study.
It is not clear why inactive xylem was so prevalent in our
experiments. Perhaps there is more xylem embolism in nonnative species like agricultural trees (Eilmann and Rigling
2012). Or maybe xylem dysfunction is caused by grafting,
which disrupts the xylem in the region near the graft union. In
our field experiments (including the greenhouse measurements), we measured at least 10 cm above the graft union, but
some influence may still be present when compared with
ungrafted trees. Staining of the active xylem of apple stems on
different rootstocks, prompted by differences in hydraulic conductance of different rootstocks (Cohen et al. 2003a, 2003b)
has found that in some cases there are significant differences
in the extent of dysfunctional xylem. On the other hand, RazYaseef et al. (2012) and Taneda and Sperry (2008) reported
similar underestimation when using the same CTD method in
forest pine, oak and maple trees in semiarid conditions, and
those forest trees were not grafted. Perhaps in hot and dry
regions, where climate extremes often challenge xylem integrity, inactive xylem is more common than in other places.
Inactive xylem and sap flow measurements 997
Figure 6. Relation between actual and measured flux density for discontinuous heating TTD, using Isarangkool’s calibration equation with and
without correction for partial probe contact with inactive xylem: (a) apple, (b) peltophorum and (c) nectarine. Actual flux density vs. TTD flux index
with and without correction: (d) apple, (e) peltophorum and (f) nectarine. Solid lines are fitted with linear (a–c) or power (d–f) functions. Results
from all samples are shown (see Table 1). Results are from laboratory calibrations with cut branches and points are individual measurements.
Slopes and equation fits are given in Tables 2 and 3.
A third source of problems may be xylem disruption due to
the reference probe, which is usually installed 10 cm or more
below the heated probe. In apple, the most common vessel
length (i.e., the mode of the vessel length distribution function)
is between 5 and 9 cm (Cohen et al. 2003a), but the mean
vessel length is twice that and, therefore, exceeds the nominal
distance between the heated and reference probes. Thus, for
apple stems and 10 cm spacing, most of the xylem inactivated
by drilling at the upstream reference point will still be inactive
at the heated probe. In our experiments with staining the stem
after measurement, we noticed areas of inactive xylem in the
azimuth of the reference probe that were apparently caused by
this. These observations imply that sap flow measurements
may be significantly influenced by the distance between and
azimuthal offset of the reference and heated sensors.
Our observations raise some questions that will need attention in the future. Three of these are: (i) what thickness of inactive xylem around the probe reduces probe sensitivity to flow;
Tree Physiology Online at http://www.treephys.oxfordjournals.org
998 Paudel et al.
(ii) are there differences in the way a hole is drilled in the stem
with respect to inactivation of xylem around the probe; and (iii)
why is the TDP probe method more sensitive to inactive xylem
than the Tmax heat pulse method?
Another topic is how to determine the fraction of inactive
xylem along the probe length. In our laboratory study this was
done by staining the cut branch and visual analysis. Obviously,
that method is impractical for field studies and intact trees. It
may be possible to introduce stain into holes in the stem and
then take cores above this sometime later to determine the
fraction of inactive xylem. It is clear that this topic will need
some research in the future.
Correcting for the radial distribution of sap flux density
Sap flux density is not uniform in the radial direction (or depth
in the xylem) in which sap flow probes are usually introduced.
Figure 7. Flux density (Js) estimated from the equations of Do and
Rocheteau (2002b) (dashed line) and Isarangkool Na Ayutthaya et al.
(2010) (continuous line) vs. flux index (K).
Several methods measure the radial distribution of flux density,
and the distributions can change with soil water distribution,
stem structure, branching and root morphology (i.e., sinker and
shallow roots) (Nadezhdina et al. 2002, Steppe et al. 2010,
Čermák and Nadezhdina 2011) and can change during the
course of the day (Ford et al. 2004). However, the radial distribution often follows distinct patterns (Gartner and Meinzer
2005 for review). Agricultural trees are clones and are well irrigated, resulting in relative uniformity in tree structure and soil
water distribution. The average radial distribution for these
cases is often quite predictable (Cohen et al. 2008, 2012). One
common distribution is an increase in flux density in the first
few millimeters of xylem followed by a close-to-linear decline in
flux density with depth, which reaches zero at between 3 and
7 cm, depending on species, type of xylem, tree age and field
conditions (Gartner and Meinzer 2005, Cohen et al. 2008,
2012). Gaussian (Ford et al. 2004) and Weibull (Kubota et al.
2005) distributions have been found empirically to fit that general pattern, but they are hard to integrate analytically.
The radial distributions of sap velocity observed in persimmon and nectarine (Figure 3) fit the above description.
Describing them with a linear decline in velocity with depth
yields a convenient function (Eq. (18)), which can be used to
correct measurements of the average sap flux density in the
outer 2 cm of xylem (as usually measured with TDP probes) for
the full-depth distribution. For this correction, the only parameters needed are the radius of the tree (without bark) and the
depth at which flux density becomes zero. Errors introduced by
replacing the measured distribution function with a linear one
are evaluated here by comparing the actual distributions of sap
flux density (Figure 3) with linear decreases that reach zero at
depths of 5.2 and 4.9 cm for persimmon and nectarine, respectively, where the zero value was determined by linear regression of the data as shown in Figure 3. The analysis was done for
Figure 8. Multispecies calibration of the flux index (K) vs. actual flux density with constant heating CTD (a, n = 1773; multiple regression r 2 = 0.94)
and transient heating TTD (b, n = 311; multiple regression r 2 = 0.99), along with original calibration lines. The dashed lines are the regression line
of our multispecies calibrations and the continuous line is from the original calibration.
Tree Physiology Volume 33, 2013
Inactive xylem and sap flow measurements 999
Summary and conclusions
Figure 9. The ratio of actual-to-measured sap flux density for apple
and peltophorum branches computed without (Y = 4.1x + 1.4;
r 2 = 0.681, P = 0.02) and with (Y = 0.44x + 0.95; r 2 = 0.35, P = 0.03)
Clearwater et al.’s (1999) correction, plotted as a function of the fraction of inactive xylem in contact with the probe.
Figure 10. Hourly values of tree sap flux measured with the six depth
Tmax method and evaluated with numerical integration (full quadrature, x axis) and using only measurements in the first 2 cm corrected
with Eq. (17) (K*Q2, y axis). Measurements are averages for nectarine
and persimmon trees (eight each) and include points measured on a
number of summer days.
the hourly measurements of sap flux density at six depths. Sap
flux density at each depth was weighted by the relative flux
density and annulus area at that depth (Figure 3) for numerical
integration (quadrature), and a second computation was made
using the values of Q2 (Eq. (18)) and taking the flux density for
2 cm as an average of the first (0.4 cm), second (1.2 cm) and
half of the third (2.0 cm) depth. Comparison of the two methods, shown in Figure 10, gave r2 values of 0.98 and 0.97, with
slopes of 1.06 and 1.05, respectively, for persimmon and nectarine. These results demonstrate that the use of Eq. (18) with
average flux density in the first 2 cm of xylem is a reasonable
substitute for full integration. The error introduced, here 5 or
6%, is probably negligible relative to other assumptions and
errors, such as the assumption that the azimuthal (or tangential) distribution of velocity is uniform, or, if measured, is adequately described by a few probes, since the tangential
variability in many species is quite large and similar to the variation between trees (e.g., Cohen et al. 2008).
This study found that sap flux density measured with TDP
probes with the CTD and TTD methods in four tree species,
when analyzed with previously reported procedures, underestimated sap flow by more than 50%. These underestimations
were consistent and approximately the same calibration was
obtained for each species in the field, greenhouse or laboratory. Strong evidence is provided that the underestimations
were caused by contact of the probes with inactive xylem
along their length. Average probe fraction in contact with inactive xylem, measured in branches of three species following
laboratory calibrations, was 0.2–0.24, and use of a correction
procedure for inactive xylem explained almost all of the underestimation. Calibrations for our conditions are provided along
with a multispecies calibration.
Radial distribution of sap velocity is an additional important
factor that must be considered when measuring an average
value for the outer part of the xylem. We derived an analytical
equation to correct for a linear decline in velocity with depth. If
used routinely for the many cases where this radial distribution
is relevant, the correction should improve the accuracy of TDP
measurements.
Our results should be an important step in reconciling the
many reports of different calibration factors for TDPs. They call
for extreme caution when using the TDP method to obtain
quantitative estimates of sap flow.
Acknowledgments
The authors thank Avraham Grava for technical assistance and
Yoni Maor for help with Eq. (18).
Conflict of interest
None declared.
Funding
This research was funded by grants no. 304-0330-06, 3040469-12 and 596-0415-09 of the Chief Scientist fund of the
Israeli Ministry of Agriculture and Rural Development.
References
Andrade JA, Meinzer FC, Goldstein G, Holbrook NM, Cavelier J, Jackson P,
Silvera K (1998) Regulation of water flux through trunks, branches and
leaves in trees of a lowland tropical forest. Oecologia 115:463–471.
Braun P, Schmid J (1999) Sap flow measurements in grapevines (Vitis
vinifera L.) 2. Granier measurements. Plant Soil 215:47–55.
Bush SE, Hultine KR, Sperry SJ, Ehleringer JR (2010) Calibration of
thermal dissipation sap flow probes for ring-and diffuse-porous
trees. Tree Physiol 30:1545–1554.
Tree Physiology Online at http://www.treephys.oxfordjournals.org
1000 Paudel et al.
Cabibel B, Do F (1991) Mesures thermiques des flux de seve dans les
troncs et les racines et fonctionnement hydrique des arbres. I.
Analyse theorique des erreurs sur la mesure des flux et validation
des mesures en presence de gradients thermiques exterieurs.
Agronomie 11:669e 11.
Čermák J, Nadezhdina N (2011) Instrumental approaches for studying
tree-water relations along gradients of tree size and forest age.
Chapter 15. In: Meinzer FC, Lachenbruch B, Dawson TE (eds) Sizeand age-related changes in tree structure and function. Springer,
New York, pp 385–426.
Clearwater MJ, Meinzer FC, Andrade JL, Goldstein G, Holbrook NM
(1999) Potential errors in measurement of non-uniform sap flow
using heat dissipation probes. Tree Physiol 19:681–687.
Cohen S, Li F (1998) Heat pulse peak detection by real-time polynomial regression in sap flow measurement. In: Čermák J, Nadezhdina
N (eds) Proceedings of the 4th International Workshop on Measuring
Sap Flow in Intact Plants. Publishing House of Mendel University,
Czech Republic, pp 22–30.
Cohen S, Bennink J, Tyree M (2003a) Air method measurements of
apple vessel length distributions with improved apparatus and theory. J Exp Bot 54:1889–1897.
Cohen S, Tyree M, Naor A, Lakso A, Robinson T (2003b) Influence of
hydraulic properties of rootstocks and the rootstock-scion graft on
water use and productivity of apple trees. Final Research Report.
BARD project IS-3284–01. available from www.bard-isus.com.
Cohen S, Naor A, Bennink J, Grava A, Tyree M (2007) Hydraulic resistance components of mature apple trees on rootstocks of different
vigours. J Exp Bot 58:4213–4224.
Cohen S, Wheeler J, Holbrook M (2012) The radial and azimuthal (or
tangential) distribution of sap velocity in tree stems—why and can
we predict it? Acta Hort 951:131–137.
Cohen Y (1994) Thermoelectric methods for measurement of sap flow
in plants. In: Stanhill G (ed.) Advances in bioclimatology. Vol. 3.
Springer, Heidelberg, Germany, pp 63–88.
Cohen Y, Fuchs M, Green GC (1981) Improvement of the heat pulse
method for determining sap flow in trees. Plant Cell Environ 4:
391–397.
Cohen Y, Cohen S, Cantuarias Aviles T, Schiller G (2008) Variations in
the radial gradient of sap velocity in trunks of forest and fruit trees.
Plant Soil 305:49–59.
Diawara A, Loustau D, Berbigier P (1991) Comparison of two methods
for estimating the evaporation of a Pinus pinaster (Ait.) stand: sapflow and energy balance with sensible heat flux measurements by
an eddy covariance method. Agric For Meterol 54:49–66.
Do F, Rocheteau A (2002a) Influence of natural temperature gradients
on measurements of xylem sap flow with thermal dissipation probes.
1. Field observations and possible remedies. Tree Physiol
22:641–648.
Do F, Rocheteau A (2002b) Influence of natural temperature gradients
on measurements of xylem sap flow with thermal dissipation probes.
2. Advantages and calibration of a noncontinuous heating system.
Tree Physiol 22:649–654.
Eilmann B, Rigling A (2012) Tree-growth analysis to estimate tree species’ drought tolerance. Tree Physiol 32:173–187.
Fernández JE, Durán PJ, Palomo MJ, Diaz-espejo A, Chamorro V, Girón
IF (2006) Calibration of sap flow estimated by the compensation
heat pulse method in olive, plum and orange trees: relationships
with xylem anatomy. Tree Physiol 26:719–728.
Ford CR, McGuire MA, Mitchell RJ, Teskey RO (2004) Assessing variation in the radial profile of sap flux density in Pinus species and its
effect on daily water use. Tree Physiol 24:241–249.
Ford CR, Hunnard RM, Kloeppel BD, Lai CT (2007) A comparison of
sap flux-based evapotranspiration estimates with catchment-scale
water balance. Agric For Meterol 145:176–185.
Tree Physiology Volume 33, 2013
Gartner BL, Meinzer FC (2005) Structure–function relationships in
sapwood water transport and storage. In: Holbrook NM, Zwieniecki
MA (eds) Vascular transport in plants. Elsevier, Amsterdam. pp
307–331.
Granier A (1985) Une nouvelle méthode pour la mesure du flux de
sève brute dans le tronc des arbres. Ann For Sci 42:193–200.
Granier A (1987) Evaluation of transpiration in a Douglas-fir stands by
means of sap flow measurements. Tree Physiol 3:309–319.
Granier A, Huc R, Barigah ST (1996) Transpiration of natural rainforest
and its dependence on climatic factors. Agric For Meterol
78:115–122.
Green SR, Clothier BE, Jardine B (2003) Theory and practical application of heat pulse to measure sap flow. Agron J 95:1371–1379.
Gutiérrez MV, Santiago LS (2006) A comparison of sap flow measurements and potometry in two tropical lowland tree species with contrasting wood properties. Rev Biol Trop 54:73–81.
Hultine KR, Nagler PL, Morino K, Bush SE, Burtch KG, Dennison PE,
Glenn EP, Ehleringer JR (2010) Sap flux-scaled transpiration by tamarisk (Tamarix spp.) before, during and after episodic defoliation by
the saltcedar leaf beetle (Diarhabda carinulata). Agric For Meterol
150:1467–1475.
Isarangkool Na Ayutthaya S, Do FC, Pannengpetch K, Junjittakarn J,
Maeght JL, Rocheteau A, Cochard H (2010) Transient thermal
­dissipation method of xylem sap flow measurement: multi-species
calibration and field evaluation. Tree Physiol 30:139–148.
Kanety T (2010) Yield and physiological and environmental water
stress indicators of persimmon trees irrigated with different amounts
of recycled water. MSc. Thesis. Hebrew University of Jerusalem,
Rehovot, Israel (in Hebrew with English summary).
Kanety T, Naor A, Gips A, Dicken U, Lemcoff JH, Cohen S (2013)
Irrigation influences on growth, yield, and water use of persimmon
trees. Irrig Sci (in press). doi:10.1007/s00271-013-0408-y.
Kavanagh KL, Pangle P, Schotzko AD (2007) Nocturnal transpiration
causing disequilibrium between soil and stem predwawn water potentials in mixed conifer forests of Idaho. Tree Physiol 22:621–629.
Kelliher FM, Kostner BB, Hollinger JN, Byers JE, Hunt TM, McSeveny R,
Meserth R, Weir PL, Schulze ED (1992) Evaporation, xylem sap flow
and tree transpiration in a New Zealand broad-leaved forest. Agric
For Meterol 62:53–73.
Kostner B, Granier A, Cermark J (1998) Sapflow measurements in forest stands: methods and measurements. Ann Sci For 55:13–17.
Kubota M, Tenhunen J, Zimmermann R, Schmidt M, Kakubari J (2005)
Influence of environmental conditions on radial patterns of sap flux
density of a 70-year Faguscrenata trees in the Naeba Mountains,
Japan. Ann For Sci 62:289–296.
Lu P (2002) Measurement of whole-tree water use of some tropical
and subtropical tree crops and its application in irrigation management. Acta Hort 575:781–789.
Lu P, Chacko E (1998) Evaluation of Granier’s sap flux sensor in young
mango trees. Agronomie 18:461–471.
Lu P, Woo KC, Liu ZT (2002) Estimation of the whole-plant-transpiration
of bananas using sap flow measurements. J Exp Bot 53:1771–1779.
Lu P, Urban L, Ping Z (2004) Granier’s thermal dissipation probe
(TDP) method for measuring sap flow in trees: theory and practice.
Acta Bot Sin 46:631–646.
Ma L, Lu P, Roa X, Cai X, Zeng X (2008) Diurnal, daily, seasonal and
annual patterns of sap-flux-scaled transpiration from an Acacia mangium plantation in southern China. Ann For Sci 65:402.
Mahjoub I, Mohamed MM, Jean PL, Netij BM (2009) Sap flow measurement by a signal thermal dissipation probe: exploring the transient regime. Ann For Sci 66:608.
Masmoudi CC, Masmoudi M, Abid-Karray J, Mechilia NB (2011) Sap
flow measurements in young olives (Olea europaea L.) CV. Chetoui
under Tunisian conditions. Sci Hortic 129:520–527.
Inactive xylem and sap flow measurements 1001
McCulloh KA, Winter K, Meinzer FC, Garcia M, Aranda J, Lachenbruch
B (2007) A comparison of daily water use estimates derived from
constant-heat sap-flow probe values and gravimetric measurements
in pot-grown saplings. Tree Physiol 27:1355–1360.
Nadezhdina N, Čermák J, Ceulemans R (2002) Radial pattern of sap
flow in woody stems related to positioning of sensors and scaling
errors in dominant and understorey species. Tree Physiol
22:907–918.
Nourtier M, Chanzy A, Granier G, Huc R (2011) Sap flow measurements by thermal dissipation method using cyclic heating: a processing method accounting for the non-stationary regime. Ann For
Sci 68:1255–1264.
Oishi AC, Oren R, Stoy PC (2008) Estimating components of forest
evapotranspiration: a footprint approach for scaling sap flux measurements. Agric For Meteorol 148:1719–1732.
Phillips N, Oren R, Zimmermann R (1996) Radial patterns of xylem sap
flow in non-, diffuse- and ring-porous tree species. Plant Cell Environ
19:983–990.
Raz-Yaseef N, Yakir D, Schiller GD, Cohen S (2012) Dynamics of
evapotranspiration partitioning in a semi-arid forest as affected by
temporal rainfall patterns. Agric For Meterol 157:77–85.
Renninger HJ, Schäfer KVR (2012) Comparison of tissue heat balanceand thermal dissipation-derived sap flow measurements in ringporous oaks and a pine. Front Funct Plant Ecol 3:doi:10.3389/
fpls.2012.00103.
Reyes-Acosta JL, Vandegehuchte MW, Steppe K, Lubczynski MW
(2012) Novel, cyclic heat dissipation method for the correction of
natural temperature gradients in sap flow measurements. Part 2.
Laboratory validation. Tree Physiol 32:913–929.
Reis FD, Campostrini E, De Sousa EF, Silva MG (2006) Sap flow in
papaya plants: laboratory calibrations and the relationships with gas
exchange under field conditions. Sci Hortic 110:254–259.
Sevanto S, Nikinmaa E, Riikonen A, Deley M, Pettyjohn JC, Mikkelsen
TN, Phillips N, Holbrook NM (2008) Linking xylem diameter variation with sap flow measurements. Plant Soil 305:77–90.
Simpson W, TenWolde A (2007) Physical properties and moisture relations of wood. Chapter 3. In The Encyclopedia of Wood. U.S.
Department of Agriculture. Skyhorse Publishing, New York. http://
www.fs.fed.us/ccrc/topics/urban-forests/docs/physical%20properties%20and%20moisture%20relations%20of%20wood.pdf.
Smith DM, Allen SJ (1996) Measurement of sap flow in plant stems.
J Exp Bot 47:1833–1844.
Sperling O, Shapira O, Cohen S, Tripler AE, Schwartz A, Lazarovitch N
(2012) Estimating sap flux densities in date palm trees using the
heat dissipation method and weighing lysimeters. Tree Physiol
32:1171–1178.
Steppe K, Pauw DJW, Doody MT, Teskey RO (2010) A comparison of
sap flux density using thermal dissipation, heat pulse velocity and
heat field deformation methods. Agric For Meterol 150: 1046–1056.
Sun H, Aubrey DP, Teskey RO (2012) A simple calibration improved
the accuracy of the thermal dissipation techniques for sap flow measurements in juvenile trees of six species. Trees 26:0631–0640.
Taneda H, Sperry JS (2008) A case-study of water transport in
­co-occurring ring- versus diffuse-porous trees: contrasts in
­ ater-status, conducting capacity, cavitation and vessel refilling.
w
Tree Physiol 28:1641–1651.
Vandegehuchte MW, Steppe K (2013) Sap-flux density measurement
methods: working principles and applicability. Funct Plant Biol
40:213–223.
Wullschleger SD, Childs KW, King AW, Hanson PJ, Phillips N (2011) A
model of heat transfer in sapwood and implications for sap flux density measurements using thermal dissipation probes. Tree Physiol
31:669–679.
Appendix
Symbols and units
Symbol
Meaning
Units
ΔT
Temperature signal, difference between two
thermocouples, for constant heating method
Temperature signal for transient heating method
Maximum temperature signal, for zero flow
Temperature signal for inactive xylem
Temperature signal at the end of the cooling
phase
Temperature signal at the end of the heating
phase
Temperature signal for active sapwood
Cross-sectional area
Regression constants used in calibration
equations
Circumference
Continuous (or constant) thermal dissipation
Sap flux density
Flux index for CTD
Flux index for TTD
Number of measurement
Flux density in the outer two cm of xylem
Total flux density
Radius without bark
Total radius
Radius of heartwood
Radius of the phloem layer
Radius of sapwood
Thermal dissipation probe
Multi-depth heat pulse system using the Tmax
method
Transient (or discontinuous) thermal
dissipation
Sap velocity
Weight per volume
mV
ΔTa
ΔTau/max
ΔTm
ΔToff
ΔTon
ΔTsw
A
a, b, c
Circum
CTD
Js
K
Ka
N
Q2
QT
R
R′
Ro
Rp
Rs
TDP
T-max
TTD
Vs(r)
W/V
mV
mV
mV
mV
mV
mV
dm2
cm
g cm−2 h−1
g cm−2 h−1
g cm−2 h−1
cm
cm
cm
cm
cm
g cm−2 h−1
g cm−3
Tree Physiology Online at http://www.treephys.oxfordjournals.org