Tree Physiology 27, 169–179
© 2007 Heron Publishing—Victoria, Canada
A noninvasive optical system for the measurement of xylem and
phloem sap flow in woody plants of small stem size
CAROLE HELFTER,1,2 JONATHAN D. SHEPHARD,1 JORDI MARTÍNEZ-VILALTA,3
MAURIZIO MENCUCCINI 2 and DUNCAN P. HAND1
1
Applied Optics and Photonics Group, Heriot-Watt University, Edinburgh, U.K.
2
Corresponding author ([email protected])
3
School of Geosciences, Edinburgh University, Edinburgh, U.K.
Received December 15, 2005; accepted March 1, 2006; published online November 1, 2006
Summary Over the past 70 years, heat has been widely used
as a tracer for estimating the flow of water in woody and herbaceous plants. However, most commercially available techniques for monitoring whole plant water use are invasive and
the measurements are potentially flawed because of wounding
of the xylem tissue. The study of photosynthate transport in the
phloem remains in its infancy, and little information about
phloem transport rates is available owing to the fragility of the
vascular tissue. The aim of our study was to develop a compact,
stand-alone non-invasive system allowing for direct detection
of phloem and xylem sap movement. The proposed method
uses a heat pulse as a tracer for sap flow. Heat is applied to the
surface of the stem with a near-infrared laser source, and heat
propagation is monitored externally by means of an infrared
camera. Heat pulse velocities are determined from the thermometric data and related to the more useful quantity, mass flow
rate. Simulation experiments on the xylem tissue of severed
silver birch (Betula pendula Roth.) branch segments were
performed to assess the feasibility of the proposed approach,
highlight the characteristics of the technique and outline calibration strategies. Good agreement between imposed and measured flow rates was achieved leading to experimentation with
live silver birch and oak (Quercus robur L.) saplings. It was
demonstrated that water flow through xylem vessels can be
monitored non-invasively on an intact stem with satisfactory
accuracy despite simultaneous sugar transport in the phloem.
In addition, it was demonstrated that the technique allows for
unequivocal detection of phloem flow velocities.
Keywords: heat pulse technique, single-sensor, surface measurements.
Introduction
Measurements of xylem sap flow and water use by plants have
implications in many ecological fields. The study of water use
by whole stands has led to the development of irrigation strategies (Green et al. 1997, Fernandez et al. 2001, Giorio and
Giorio 2003) as well as an understanding of interspecific com-
petition for water in mixed woody and herbaceous agroforestry systems (Dye et al. 1996, Lott et al. 1996). At the individual
level, sap flow gauges have been used to investigate how xylem sap flow is affected by both internal factors, such as water
stress (Nadezhdina 1999), and environmental factors, such as
atmospheric CO2 concentration (Dugas et al. 1994) and soil
water content (Green et al. 1997).
Several thermal methods for monitoring xylem sap flow
have been developed. Heat pulse techniques were pioneered
by Huber in the early 1930s (Huber 1932), but it was Marshall’s rigorous analysis of convective heat transfer (Marshall
1958) that led to the derivation of the equations used today for
the treatment of experimental data. Until recently, monitoring
of xylem sap flow by means of a heat-pulse technique required
drilling holes and inserting both the heating and thermometric
apparatus inside the stem. Both one-sensor (Huber 1932, Marshall 1958, Cohen et al. 1981) and two-sensor configurations
(Closs 1958, Swanson 1962) employing various heating apparatus and thermal sensor spacings have been evaluated over the
years. Working equations based on Marshall’s original analysis of heat diffusion have been adapted to each configuration,
but it is now clear that the unnatural flow conditions arising
from wounding the plant during probe implantation require
that mathematical corrections be applied to experimental data.
Calibration and correction factors for such systems are not
only unique to a given plant species, but depend also on probe
spacing, size and geometry (Swanson and Whitfield 1981,
Swanson 1994, Green et al. 2003). Alleviation of data treatment and analysis, preservation of natural flow conditions and
avoidance of instrument-specific calibration can be achieved
only by a non-invasive approach. The first step in this direction
was taken by Bauerle et al. (2002) who demonstrated that xylem sap flow in kidney bean plants, a herbaceous species, can
be measured accurately by a non-contact system.
Information about carbohydrate translocation in phloem tissues is necessary to an understanding of the biospheric carbon
cycle, although few experimental data are currently available.
Translocation of sugars into a fruit can be estimated by monitoring the fruit’s dry mass gain over a period of time because
most fruits contribute little to their own growth. The fruit sink
170
HELFTER ET AL.
method offers a long-period integration of the transport
because appreciable growth takes several days (Canny 1975).
Translocation can also be determined by monitoring the dry
mass gain per unit leaf area. Weight gain results from the positive contribution of photosynthesis less the combined losses
due to respiration and translocation. Comparison of an intact
and detached leaf in which photosynthates cannot be translocated, provides information about sugar transport rates. Although the method appears simple in principle, the gain in leaf
area due to changes in water content of the tissues constitutes a
non-negligible source of error (Thoday 1910). In addition,
translocation can be evaluated only over relatively long periods of time.
Data on the amount of sugar transported by a single sieve
tube can be obtained by severing the stylet of a feeding aphid
(Fisher and Cash-Clark 2000, Gould et al. 2004) and collecting the sap from its free extremity. Aphids feed on the sap of
plants by piercing single sieve tubes with their mouthparts.
Assumptions about the total number of sieve tubes and their
mean diameter must be made in order to evaluate the total rate
of sugar translocation. However, the formation of callose resulting from wounding to the phloem tissue may affect the
measured flow rates (Dixon 1975).
Nuclear magnetic resonance has been used to measure
phloem and xylem sap flow velocities non-invasively (Xia et
al. 1993, Peuke et al. 2001). A pulsed magnetic field gradient
is applied along the direction of flow causing proton spin precession at a frequency directly proportional to the intensity of
the applied magnetic field. An inverse magnetic field gradient
is applied after a certain time, turning all spins back to a net
phase shift of zero. However, if the protons have moved between the respective applications of the magnetic field gradients, the phase shifts will not return to zero. These phase shifts
are proportional to flow velocity (Peuke et al. 2001). Short
time resolutions (4 min for Peuke et al. 2001) and precise
quantitative velocity measurements can be achieved non-invasively with NMR. However, the cost and dimensions of the
equipment and the complexity of data processing render NMR
unsuitable for field applications.
Indicator-dilution techniques rely on the inverse relationship between the mean concentration of a solute in a flowing
solution and flow rate. The passage of a pulse-labeled radiotracer such as 32P is monitored by a Geiger-Muller detector and
the number of counts at a given time is related to a tracer concentration. Good agreement was found between indicator-dilution mass flow rates and measurements of grain growth and
net CO2 exchange by ears of wheat (Fisher 1990), demonstrating the technique’s suitability for short-term phloem transport
rate measurements.
Use of heat as a tracer for phloem flow was first proposed by
Huber et al. (1937), who, however, failed to detect downward
heat transfer in field-grown trees over a few days at the end of
the growing season. They attributed this failure to the impact
of heat dissipation inward to the stem xylem. This concept has
permeated the botanical literature ever since and the approach
was not again tried until Ziegler and Vieweg (1961) heated isolated phloem strands from the central cavity of Heracleum
mantegazzianum Somm. & Levier and demonstrated that the
heat pulse moved from the apex toward the base of the plant at
a velocity of between 20 and 80 cm h – 1 .
We propose a noninvasive pulsed-laser-based approach for
monitoring xylem and phloem flow in woody plants. We introduce a working equation for heat pulse velocity calculations
requiring only one spatial measurement point (as opposed to
two in the case of heat compensation techniques) and compare
its performance to the one-point relationship used in conjunction with the t max method (Cohen et al. 1981). Finally, experimental xylem sap flow rates are compared with weighing
lysimetry (WL) data and phloem flow detection is demonstrated.
Materials and methods
Working equations
Using Marshall’s solution to the 1-D heat equation for combined conduction and convection in a moving wood-and-water
matrix (Equation 1; Marshall 1958), an analytically exact expression for heat pulse velocity (V ) was derived for a singlesensor configuration (Equation 2). The full derivation is provided in the Appendix:
θ=
 ( x − Vt ) 2 
Q
exp  −

4 π kt
4 kt 

 2 4 ktmax t 2  t 2  
x −
ln 

tmax t 2 
t 2 − tmax  2tmax  
1
V =
(1)
(2)
where θ denotes the temperature rise from ambient, Q is heat
input, k is apparent thermal diffusivity of the medium, x is distance downstream from the point of heating, V is heat pulse velocity and t is time. No absolute temperature measurements are
necessary for the application of Equation 2, however, knowledge of the temporal positions of the signal’s maximum amplitude (t max ) and the second occurrence of half maximum (t 2 ), k
and x are required (Figure 1).
Thermal diffusivity was determined in two separate ways.
Under zero flow condition, k can be obtained from Equation 3
(Green et al. 2003):
k=
x2
4tmax
(3)
Equation 3 is readily obtained from the tmax equation (Equation 4) (Cohen et al. 1981, Green et al. 2003) by setting the
maximum heat pulse velocity (Vmax ) = 0 and solving for k:
Vmax =
x 2 − 4 ktmax
tmax
(4)
Equation 4 was used to calculate Vmax and the results were
compared to those obtained with Equation 2 (referred to as the
TREE PHYSIOLOGY VOLUME 27, 2007
NON-INVASIVE SAP FLOW MEASUREMENTS IN WOODY PLANTS
171
Figure 1. Definition of parameters t max and t 2 in Equation 2.
Figure 2. Two-lens optical setup for imaging a laser beam onto a stem.
t2 equation hereafter) because both techniques use singlesensor configurations. For any flow rate, k can be determined
from Equation 1 through nonlinear curve fitting of the θ versus
t plot, with Q, V and k as fitting parameters.
Heat pulse velocities were related to mass flow rates by multiplying the former by the cross-sectional area of the stem at
the heating point (Equation 5):
zor blade. The bark, phloem and cambium were carefully removed with a scalpel to expose the xylem. Stripped samples
were used for measurements on the day of cutting, while the remainder of the branch was kept in water for later use.
The temperature 5 mm above and below the center of the
heating beam was monitored with K-type contact thermocouples. The spacing was chosen to achieve the optimum signal-to-noise ratio under the relatively low optical power and
laser pulse length conditions defined previously. The upstream
thermocouple was used exclusively for alignment. Overlapping of the upstream and downstream conduction signals under zero flow conditions allowed for precise positioning of the
downstream thermocouple with respect to the point of heating.
The thermometric signal was cleaned with a 1-Hz low-pass
passive filter, and displayed on a computer-controlled Gould
1604 (SPX Corp., Charlotte, NC) four channel oscilloscope.
Data acquisition by the oscilloscope was triggered by the onset
of the laser pulse. The temperature was monitored for 1000 s
(one data point per second) following the onset of the laser
pulse.
A high pressure flowmeter (HPFM-Dynamax Inc., Houston, TX) allowing precise flow rate control in the range of 1 ×
1 0 – 7 to 6 × 10 – 6 kg s – 1, was used to force ultra-filtered water
through the xylem tissue of the severed silver birch branches.
The HPFM was connected to a computer that registered the
2
d
M& = π   V
 2
(5)
where M& is mass flow rate and d is diameter of the stem at the
point of heating.
Optical setup
Heating of the stem surface was achieved by a fiber-delivered
laser pulse of optical power directed at the sample (pulse
length 1 s at 1.5 W and wavelength 812 nm) (Coherent Fibre
Array Package, Coherent Inc., Santa Clara, CA). The beam
was filtered through a rectangular aperture and imaged onto a
3-mm high area of the stem by two bi-convex lenses each with
a focal length of 6.5 cm (Figure 2). The heated area of the sample was sprayed with black paint to enhance the optical absorption of the surface (Figure 3). Although the optical properties of the stems could not be determined, the paint was found
to increase the optical absorption of both the silver birch and
oak samples by 45%. This value was obtained by measurement
of θ directly outside the heated area. The temperature rose by
about 10 °C within the heated area upon laser illumination. No
visible damage attributable to either laser heating or use of
paint was observed.
Thermometric and flow monitoring setup
Forced flow experiment The system was first assessed
through forced flow experiments on severed silver birch
(Betula pendula Roth.) branches collected from two trees
growing on the campus of Heriot-Watt University (Edinburgh,
U.K.) between March and June 2005. Segments about 4 mm in
diameter and 5–6 cm in length were cut under water with a ra-
Figure 3. Detail of the heated area of a stem. Black paint was applied
to half the circumference of the stem, thus forming a half ring 3 mm in
height. The temperature was monitored 5 mm above and below the
point of heating (center of the heated area) with either contact thermocouples, as shown, or an infrared camera.
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
172
HELFTER ET AL.
mass flow rate every 8 s. The branch segments were allowed to
rehydrate slowly by flushing them at 5 × 10 – 7 kg s – 1 until the
flow rate measured by the HPFM became constant. The water
flow was then interrupted and the thermal diffusivity k determined according to Equation 3.
Free flow experiment The second stage of the study was concerned with the evaluation of the system in more natural flow
conditions. Potted silver birch (B. pendula) and oak (Quercus
robur L.) saplings with a mean stem diameter ranging from 0.6
to 1.2 cm were chosen to represent diffuse- and ring-porous
wood types, respectively.
An infrared (IR) camera (Electrophysics Model PV320E,
detection range 2–14 µm, 320 × 240 pixels) was chosen for
non-contact, high-precision thermometric monitoring of heat
dissipation in live saplings. High spatial and temperature resolutions (0.02 cm pixel – 1 and 0.08 °C at 25 °C, respectively)
combined with the ability to store and reload images for analysis of the temperature at different distances from the point of
heating, make the IR camera a satisfactory tool for remote
sensing of heat pulse propagation. Frame acquisition by the IR
camera was at the rate of 1 Hz. Each image saved by the computer was the result of an 8-frame averaging performed by the
camera.
Both the laser and the IR camera were piloted by the computer via a purpose-written Labview program ensuring the
synchronization of the onset of the laser pulse and the start of
frame acquisition. Analysis of the 16-bit images acquired by
the camera was performed by a second Labview program with
a graphical interface that allows the user to choose the coordinates of points for which pixel intensities are to be extracted.
These coordinates were defined following the first measurement and applied to all subsequent data within a set of measurements unless the camera was moved.
A thermal calibration of the camera was performed for each
sample using a contact K-type thermocouple positioned at a
known distance from the point of heating. Heating was applied
by the laser under continuous wave conditions for 20 s, and the
thermometric data registered by the thermocouple above the
point of heating was compared to pixel intensities at the same
distance below the point of heating. The relationship between
pixel intensity and temperature was found to be linear in the
range of temperatures tested (19–26 °C). Thus, conversion of
pixel intensity to temperature for use with Equation 2 was unnecessary.
K-type thermocouples were used with the saplings to investigate possible discrepancies between the two thermometric
approaches. Because of the presence of phloem tissue, zero
flow conditions were difficult to achieve, making probe positioning through overlapping of upstream and downstream heat
conduction signals unreliable. Consequently, the thermocouples were positioned manually by measuring the 5 mm
spacing above and below the center of the beam with a ruler.
Contrary to the forced flow configuration where only one thermocouple was used after alignment, the thermocouple located
below the point of heating in free flow experiments was active
and used for downward flow monitoring. A schematic of in-
strument hierarchy for both free and forced flow experiments
is provided in Figure 4.
The flow was varied by switching a 150 W metal-halide
lamp on or off, chosen for the similarity of its emission spectrum to that of natural light, and changing the incidence angle
of light on the canopy. Whole-plant water use was monitored
by weighing lysimetry (WL). Mass loss through transpiration
was measured every 60 s by an Ohaus Scout Pro balance
(4100 g × 0.1 g ) connected to a computer via an RS232 interface. The plant pots were wrapped in plastic bags to prevent
water loss directly from the soil.
Results
Apparent thermal diffusivity
Apparent thermal diffusivity was determined separately above
and below the point of heating by the IR camera in five oak and
five silver birch saplings; k differed slightly between the two
positions in both species (Table 1).
Measurements under zero flow conditions in seven silver
birch branch segments collected from two trees yielded an average value of 0.0019 ± 4 × 10 – 5 cm2 s – 1 for k of xylem tissue,
confirming that nonlinear curve fitting (i.e., performing a nonlinear regression of Equation 1 on temperature rise versus time
since onset of heat pulse, with Q, k and V as fitting parameters)
can be used for the determination of k under non-zero flow
conditions.
Values of k presented in Table 1 were used in all subsequent
heat pulse velocity calculations.
Xylem
Forced flow Heat pulse velocities versus mass flow rates imposed by the HPFM for four silver birch samples are plotted in
Figure 5. Heat pulse velocities measured at the surface of a
stem exhibited a dependency on stem diameter; higher veloci-
Figure 4. Instrumental hierarchy in (a) free flow experiments and (b)
forced flow experiments. Abbreviations: HPFM = high pressure flowmeter; and IR = infrared.
TREE PHYSIOLOGY VOLUME 27, 2007
NON-INVASIVE SAP FLOW MEASUREMENTS IN WOODY PLANTS
173
Table 1. Apparent thermal diffusivity (k; cm2 s – 1) in oak and silver
birch saplings.
Species
Apparent k for xylem
(above point of heating)
Apparent k for phloem
(below point of heating)
Oak
Silver birch
0.00196 ± 1 × 10 – 5
0.00187 ± 2.4 × 10 – 4
0.00177 ± 7 × 10 – 5
0.00215 ± 2 × 10 – 4
ties for the same mass flow rate value were observed in the two
narrowest stems. However, dependency on stem diameter disappeared when the mass flow rate was calculated as shown in
Figure 6, suggesting that the vessels contributing to the signal
measured at the outer surface of the sample are statistically representative of the velocity distribution throughout the entire
stem. Although the number of vessels contributing to the signal
is unknown, it is inherent in the technique that a measured heat
pulse velocity is a weighted average of a number of velocities.
This is illustrated in Figures 5 and 6 by the apparent slowing of
the heat pulse or change in slope at high flow rates where the
temperature rise versus time peak is relatively narrow and, consequently, more sensitive to broadening resulting from the
overlapping of heat pulses traveling at different speeds. The
heat pulse length was varied from 1 to 9 s to artificially induce
signal overlapping and illustrate the effect of peak broadening
on calculated heat pulse velocities (Figure 7).
The largest deviation from the 1:1 line (33%) occurred in
one of the 3 mm-diameter samples, whereas the minimum
deviation (1.8%) was found in the other 3 mm-diameter twig
(Figure 6), indicating no relationship with stem diameter. In
addition, there was no conclusive evidence that deviation from
the 1:1 line is a function of flow rate. One of the 3-mm samples
seemed to display a trend of increasing deviation from the 1:1
line toward lower flow rates, but no such tendency was seen in
the remaining three samples. Although 33% seems a rather
substantial uncertainty on measured values, the overall aver-
Figure 5. Heat pulse velocity versus imposed mass flow rate in four
silver birch twigs characterized by diameter and collected from two
trees. Abbreviation: HPFM = high pressure flowmeter.
Figure 6. Calculated mass flow rates versus imposed values in four silver birch twigs characterized by stem diameter. The dependency on
stem diameter apparent in Figure 5 has now disappeared. Abbreviation: HPFM = high pressure flowmeter.
age deviation between calculated and imposed flow rates was
10.9 ± 6.9%, and 80% of all data deviated from the 1:1 line by
≤ 15%. Results obtained with oak and silver birch saplings are
presented to demonstrate that the technique is applicable to
ring-porous as well as diffuse-porous species.
Free flow Weighing lysimetry data were smoothed by calculating five-point running averages. This was essential at low
flow rates because the Scout Pro balance had a resolution of
only 0.1 g per 60-s period, equating to 1.7 × 10 – 6 kg s – 1 (except
for 0 mass change). It was found, however, that averaging over
a larger number of points led to the unwanted smoothing of certain rapid fluctuations resolved by heat pulse velocity calcula-
Figure 7. Heat pulse velocity versus imposed mass flow rate as a function of heat pulse duration. The measurements were taken on a freshly
cut silver birch branch segment 3 mm in diameter. Abbreviation:
HPFM = high pressure flowmeter.
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
174
HELFTER ET AL.
tions (Figure 8).
Calculated mass flow rates versus flow rates derived from
lysimetric data for three independent measurements made on
an oak sapling 0.7 cm in diameter are shown in Figure 9. Similar data were obtained with four other oak saplings with mean
stem diameters ranging from 0.6 to 1.2 cm (data not shown).
Maximum and minimum values of deviation from the 1:1
line for each configuration (intact stem + thermocouple, intact
stem + IR camera, stripped stem + IR camera) are summarized
in Table 2. Maximum deviation from the 1:1 line was found in
data obtained with the intact stem + IR-camera configuration.
However, the presence of bark, phloem and cambium did not
seem to significantly affect xylem flow measurements taken at
the surface because the results obtained with the intact and
stripped stem were similar. Three independent sets of measurements obtained with the IR camera and the intact oak sapling were averaged and the standard deviation from the mean
calculated where applicable, i.e., data points without error bars
represent single measurements (Figure 10).
The standard deviation from the mean ranged from 1.88 ×
10– 7 to 4.96 × 10 – 7 kg s – 1. Although these values seem large
(the largest deviation represented 22% of the mean value),
four out of six points had < 4% deviation from the 1:1 line. Although more independent measurements need to be taken to
obtain a statistically reliable value for the maximum uncertainty of experimental data, the previous results suggest that,
for an intact stem, heat pulse velocities can be reliably associated with mass flow rates with no more than three sets of measurements.
Transpiration rates for one silver birch sapling with a mean
stem diameter of 0.6 cm were evaluated with the IR camera as
a thermometric probe. Four independent sets of measurements
(i.e., measurements taken daily over 8-h periods under constant illumination and resumed the following day) were carried out on consecutive days (the plant was well watered each
Figure 9. Calculated mass flow rate versus transpiration rate evaluated
by weighing lysimetry (WL) for the intact and stripped stem of an oak
sapling 7 mm in diameter. Both thermocouples and the infrared (IR)
camera were used as thermometric probes in conjunction with the intact stem, whereas the IR camera alone was used on the stripped stem.
evening); the results of this investigation are shown in Figures
11 and 12. Four additional silver birch saplings were studied
(data not shown); the relationships between calculated and
WL transpiration rates were comparable with those shown in
Figures 11 and 12.
For the silver birch sapling, the maximum and mean deviations from the 1:1 line on averaged data were slightly larger
than for the oak (39 and 18%, respectively) even though the
standard deviations from the mean were similar (1 × 10 – 7 to
4.2 × 10 – 7 kg s – 1). The mean deviation from the 1:1 line was
18%, with 64% of points deviating by ≤ 15%.
Comparison of t max equation with t 2 equation
Figure 8. Transpiration rate evaluated by weighing lysimetry (WL)
and heat pulse velocity versus duration of heat pulse in oak saplings
with a mean stem diameter of 7 mm at the heating point. For 11-point
running averaging of WL data, some flow fluctuations visible in heat
pulse velocity data have been smoothed. The metal-halide lamp was
turned on following the acquisition of the first measurement point.
Heat pulse velocities determined by the t 2 equation (Equation 2) were compared to the values obtained with the t max
method (Equation 4). As illustrated in Figure 13, the t max equation failed to resolve some of the fluctuations observed by WL
and heat pulse velocities calculated by the t 2 equation. Most
values calculated with the t max equation were a constant value
suggesting that t max cannot be determined with sufficient precision if a temporal resolution of 1 s (or longer) is used, as was
the case for our system. Consequently, the t 2 equation was chosen and applied to all experimental data.
Figure 13 shows that calculated velocities remain high after
the lamp is turned off despite a sharp drop in measured transpiration rates, suggesting that abrupt transitions between regimes of relatively high and low photosynthetic activity do not
result in instant changes in flow rates measured in the stem despite being resolved by weighing lysimetry. This observation
does not necessarily raise questions regarding the performance
of our system, but rather indicates that the closing of stomatal
pores is a faster process than the decrease in the pressure gradient between roots and leaves. In such conditions, weighing
TREE PHYSIOLOGY VOLUME 27, 2007
NON-INVASIVE SAP FLOW MEASUREMENTS IN WOODY PLANTS
175
Table 2. Maximum and minimum deviation from the 1:1 line in the oak sapling. Abbreviations: IR = infrared; and SD = standard deviation.
Maximum deviation
from 1:1 line
Minimum deviation
from 1:1 line
Mean deviation
from 1:1 line (% ± SD)
Thermocouple
IR camera
Stripped stem
+ IR camera
Mean
(% ± SD)
17% at 1.8 × 10 – 6 kg s – 1
29% at 2.1 × 10 – 6 kg s – 1
25% at 6.7 × 10 – 7 kg s – 1
23.7 ± 6
0.11% at 1.25 × 10 – 6 kg s – 1
1.6% at 1.9 × 10 – 6 kg s – 1
1.4% at 1.6 × 10 – 6 kg s – 1
8.3 ± 5.5
14.3 ± 12
10.7 ± 7.9
lysimetry might be of limited reliability as a reference technique.
Phloem
Analysis of thermometric data collected below the point of
heating on the surface of intact stems revealed the existence of
downward convective heat propagation (Figure 14), whereas
no signal was detected once the bark, cambium and phloem
were removed (Figure 15). The behavior exhibited by the oak
sapling (Figures 14 and 15) was observed in two other saplings
(one oak and one birch). In total, three saplings were used for
qualitative verification of detection of phloem flow. These results indicate that phloem flow can be resolved by our non-invasive heat pulse technique.
Comparison of the evolution of mass flow rate and heat
pulse velocities above and below the point of heating revealed
that all three quantities exhibited similar fluctuations over time
(Figure 16), and these fluctuations were in phase for the
phloem and the xylem. Flow rate fluctuations were ahead of
the fluctuations registered in the xylem and the phloem for approximately 2 h following the beginning of illumination. All
three quantities became in phase after that.
Figure 10. Calculated mass flow rate versus weighing lysimetry (WL)
transpiration rate in an oak sapling 7 mm in diameter. The data were
acquired over three independent sets of measurements. Values with
error bars represent the mean ± standard deviation of three independent measurements obtained with the infra-red camera. Values without
error bars are single measurements.
1.0 ± 0.8
11.1 ± 3
Discussion
The feasibility of using a non-invasive single sensor laser heat
pulse technique to monitor xylem sap flow in woody plants
was demonstrated by this study. The first stage of the study
consisted of forced flow experimentation on severed silver
birch branches 3–4 mm in diameter and stripped of bark and
underlying cambium and phloem tissues. The good agreement
found between imposed and calculated mass flow rates confirmed the validity of the working equation derived for the
chosen single sensor configuration. Furthermore, the forced
flow experiments demonstrated that the heat pulse velocity
measured at the surface—although a weighted average of an
unknown number of individual flow velocities depending on
vessel sizes—can be used to determine the associated mass
flow rate by direct multiplication with the stem cross-sectional
area as previously reported for herbaceous species (Cohen and
Li 1996).
For the small silver birch and oak stems used in this study
(both under forced flow and free flow conditions), the heat
pulse velocity thus yielded a measure of the mean flow velocity within a medium with a normally unknown vessel size and
density distribution. Contrary to findings by Marshall (1958),
knowledge of the proportion of functional xylem vessels with-
Figure 11. Calculated mass flow rate versus weighing lysimetry (WL)
transpiration rate for a silver birch sapling 6 mm in diameter. The data
was obtained with the infra-red camera in four independent sets of
measurements made over four consecutive days.
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
176
HELFTER ET AL.
Figure 12. Calculated mass flow rate versus weighing lysimetry (WL)
transpiration rate for the four sets of measurements made on a silver
birch sapling 6 mm in diameter. Values with error bars represent the
mean ± standard deviation of four independent measurements. Values
without error bars are single measurements.
in the stem is unnecessary for flow rate calculation. The
weighted average nature of the heat pulse velocity measured at
the surface of the stem becomes especially apparent at high
flow rates where convective heat propagation yields narrow
temperature-versus-time peaks. The superposition of several
heat pulse velocities causes a broadening of the temperature-versus-time peak in the decaying part of signal, resulting
in a reduction of the measured heat pulse velocity. This observation is of critical importance because our data analysis is
based on the t2 equation. Furthermore, a low power laser (delivering optical powers in the order of a few watts) is required
for an optical system such as that described, to ensure that no
damage is caused to the plant through excessive heating. Requirements of short pulse length and low optical power lead to
a compromise of signal amplitude and signal-to-noise ratio
Figure 13. Comparison of heat pulse velocities (HPV) calculated by
the t max and t 2 methods, respectively. Abbreviation: WL = weighing
lysimetry.
Figure 14. Convective heat transfer above and below the point of heating in the intact oak sapling of mean stem diameter 7 mm (mass flow
rate 1.7 × 10 – 6 kg s – 1).
which may, in turn, dictate the resolution limit of the system.
The limitation with the optical configuration used in this study
(1.5 W of optical power, pulse length of 1 s) arose from finite
variability of the flow rate rather than insufficient signal-to-noise ratio. It is conceivable, however, that the detection
limit might diminish in larger stems.
Heat pulse velocities as low as 1 cm h – 1 were detected both
in forced and free flow regimes. The good agreement between
measured (or imposed) and calculated flow rates obtained for
such low heat pulse velocities shows that a single-sensor configuration using heat pulse velocity calculations derived from
Equation 1 is not inherently flawed as previously suggested
(Swanson and Whitfield 1981, Swanson 1994). Two-sensor
configurations have been widely used and calibration coeffi-
Figure 15. Absence of temperature rise below the point of heating after removal of bark, cambium and phloem tissues (mass flow rate 5 ×
10 – 7 kg s – 1. A 2 × 0.5 cm strip (vertical and horizontal dimensions)
of bark, phloem and cambium was removed with a scalpel; both measurement points were located inside the stripped area.
TREE PHYSIOLOGY VOLUME 27, 2007
NON-INVASIVE SAP FLOW MEASUREMENTS IN WOODY PLANTS
Figure 16. Time course of mass flow rate (transpiration rate evaluated
by weighing lysimetry (WL)) and heat pulse velocities measured
above and below the point of heating in an oak sapling. The vertical
arrow marks the start of illumination by the metal-halide lamp.
cients have been derived for various sensor spacings (Closs
1958, Swanson 1962, 1994), but the appeal of a one-probe system resides in its simplicity. The t max method was devised by
Cohen et al. (1981) as an alternative to the compensation heat
pulse technique, but despite calibration and numerical corrections for wounding, the technique was found to lose sensitivity
at velocities < 10 cm h – 1 (Cohen et al. 1988, Cohen and Li
1996, Green et al. 2003). The present study limited this loss of
sensitivity through the derivation of a working equation using
two time measurements (temporal positions of the maximum
and half-maximum temperature values), albeit at the price of
increased formula complexity. We showed that, for thermometric detection rates of 1 Hz or lower, small changes in heat
pulse velocity could be resolved with the t 2 equation (Equation 2), whereas such fluctuations were smoothed by the tmax
approach.
Proof of the feasibility of a non-contact heat compensation
system (Laser Heat Pulse Gauge (LHPG)) for the monitoring
of xylem flow rates in herbaceous species was first provided
by Bauerle et al. (2002). Underestimation of transpiration by
the LHPG was reported to vary from 4 to 20% at low and high
irradiances, respectively, and a calibration was derived allowing for correction of systematic errors.
In forced flow experiments, calculated mass flow rates were
found to deviate from imposed values by 10.9% on average
(maximum 22.5%; minimum 3.7%) for the four silver birch
samples studied. Although these values are similar to those obtained by Bauerle et al. (2002), no partition between low and
high flow rates was observed, i.e., maximum and minimum deviations from the 1:1 line were found within the same range of
flow rates. In addition, calculated flow rate values were as
likely to underestimate imposed values as to overestimate
them (50/50 splitting of under- and overestimates for the four
samples). This absence of trend (i.e., no consistent under- or
overestimation) suggests that measurements taken over a reasonably wide range of flow rates allow, in small stems, for the
177
direct determination of actual flow rates by linear regression of
the experimental data. However, data derived from measurements taken with thermocouples exhibited a tendency to lie
below the 1:1 line, especially for high flow rates, which might
be due to the presence of bark, cambium and phloem or poor
contact of the thermocouple junction with the surface of the
stem. It is also conceivable that the trend observed in connection with thermocouples is an artefact induced by the lack of
data points in the middle to low flow rate region.
No substantial differences were noted between data obtained with the IR camera on intact and stripped oak stems.
Additional trials involving more individuals are needed to
eliminate potentially abnormal effects and to determine the
true sensitivity of the system. Nevertheless, the non-contact
system based on thermal imaging has already proved that reasonable accuracy can be achieved for xylem sap flow measurement in thin silver birch and oak stems based on only a few independent sets of measurements. Although thermocouples
have the advantage of being low cost, inaccuracy in positioning and uneven contact have the potential to jeopardize the
reproducibility of a trial. Non-contact, IR thermocouples were
not evaluated because their often large field of view can induce
uncertainties about positioning. Evidence that xylem flow can
be successfully determined by both contact thermocouples and
IR camera measurements increases the versatility of our system, especially if field trials on a large scale are considered.
Although the discrepancies between experimental and WL
transpiration rates are far removed from predictions made by
Swanson (Swanson 1994) for single-sensor systems (underestimations of up to 75%), work remains to be done to identify
sources of errors inherent in the technique. In light of the results obtained with severed silver birch branches, it seems reasonable to infer that WL might contribute to the total error.
Although the HPFM allowed for accurate control and monitoring of the flow rate, transpiration rates determined by WL
depend on the frequency of measurements and the number of
points used to calculate a mean flow value. It is probable that
local variations resolved by heat pulse velocity calculations
are smoothed out by WL, thus creating discrepancies between
calculated and measured flow rates. Consequently, calibration
of the system based on WL data might introduce inaccurate
corrections, as would comparison with transpiration results
obtained by invasive investigation, especially in ring-porous
species such as oak that are able to withstand sometimes irreversible damage during probe implantation.
Downward convective heat flow was detected on intact
stems with the IR camera. The absence of downward flow observed after removal of the bark and underlying tissues confirmed that the downward heat transfer was not an artefact, and
indicated that phloem sap flow could be monitored by a noncontact heat pulse technique. Implementation of alternative
techniques such as isotope tracing is planned to provide a comparison for heat pulse measurements on phloem sap. Qualitative observations can already be made at this stage; downward
sap flow was found to increase dramatically as a result of exposure to a 150 W metal-halide lamp. Furthermore, fluctuations in transpiration rates observed both by WL and heat
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
178
HELFTER ET AL.
pulse velocity calculation for the xylem were found to be concurrent for phloem sap velocity.
The striking similarity in measurements obtained by these
three approaches discredits the hypothesis that their variation
results from independent factors and suggests that the opening
and closing of stomatal pores—even under constant illumination—is the cause of the variation in all three methods. Except for the investigation by NMR (Peuke et al. 2001), which
provided a time resolution of a few minutes at the price of
complex equipment and data analysis, few approaches have
provided more than gross, often non-reproducible estimates of
phloem sap rates. Stylectomy on feeding aphids results in
wounding to the tissue, and indirect techniques such as gain by
fruit sinks and loss from leaf sources offer poor temporal resolution (a few hours at best), require the destruction of the sample studied and are seasonal by nature. Above all, none of these
techniques are suited for field measurements.
Sap velocities measured in the phloem were of the same order of magnitude as those found in the xylem. In addition,
transport velocities in the phloem were monitored and quantified unequivocally without causing damage to the stem. Comparison of mass flow rates calculated for the xylem in an intact
and stripped oak sapling stem suggests that phloem flow does
not significantly affect externally monitored xylem flow rates
and it is therefore reasonable to assume that underlying xylem
tissue does not affect measured phloem flow velocities. If extrapolation of results obtained for the xylem to the phloem is
possible, the non-invasive approach evaluated in this study
may provide direct access to mean values of flow velocities allowing for straightforward calculations of volume flow rates.
However, estimations of the active phloem area in each sample
must be available for volume flow rate calculations from mean
sap velocity values (Fisher 1990), but these are less complicated to obtain than information on sieve tube density and diameter.
Although much work remains to be done to assess the reliability of a phloem flow sensor based on our non-contact,
pulsed-laser-based heat pulse system, this new approach offers
an encouraging and exciting perspective for the measurement
of both phloem and xylem sap flow.
In conclusion, xylem sap flow rates in thin stems of diffuse
porous and ring porous plants can be determined noninvasively with reasonable accuracy. We showed that both contact
thermocouples and an IR camera can be used to monitor heat
convection in the stem, increasing the versatility of the system.
Thermocouples are inexpensive and would be suitable for simultaneous measurements on a large population, but accurate
spacing and sustained contact with the stem are difficult to ensure. An IR camera, on the other hand, is portable, can be precisely focused and allows access to thermal data for a vast
number of spatial coordinates.
All saplings investigated had small diameter stems (maximum 1.2 cm) and more work is needed to evaluated the stem
diameter range over which our system is applicable. Although
no quantitative data are currently available for large trees, discrepancies between measured and actual flow velocities are
expected. Despite probable limitation of our non-contact sys-
tem to xylem flow measurements to stems of small diameter,
phloem flow measurements may be unaffected by stem diameter in the same way. Study of the effect of stem diameter on the
sensitivity of our system will be a priority for future work. Direct detection of phloem flow was achieved, but so far only sap
velocities could be determined. Thus, comparisons with alternative techniques for phloem sap flow measurement need to be
undertaken.
References
Bauerle, W.L., T.H. Whitlow, C.R. Pollock and E.A. Frongillo. 2002.
A laser-diode-based system for measuring sap flow by the heatpulse method. Agric. For. Meteorol. 110:275–284.
Canny, M. 1975. Transport in plants I. Phloem transport. In Encyclopedia of Plant Physiology. Eds. M. Zimmermann and J. Milburn.
Springer-Verlag, Berlin, pp 139–153.
Closs, R.L. 1958. The heat-pulse method for measuring sap flow in a
plant. N.Z. J. Sci. 1:281–288.
Cohen, Y. and Y. Li. 1996. Validating sap flow measurement in
field-grown sunflower and corn. J. Exp. Bot. 47:1699–1707.
Cohen, Y., M. Fuchs and G. Green. 1981. Improvement of the heat
pulse method for determining sap flow in trees. Plant Cell Environ.
4:391–397.
Cohen, Y., M. Fuchs, V. Falkenflug and S. Moreshet. 1988. Calibrated
heat pulse method for determining water-uptake in cotton. Agron.
J. 80:398–402.
Dixon, A. 1975. Transport in plants I. Phloem transport. In Encyclopedia of Plant Physiology. Eds. M. Zimmermann and J. Milburn.
Springer-Verlag, Berlin, pp 154–170.
Dugas, W., M. Heuer, D. Hunsaker, B. Kimball, K. Lewin, J. Nagy
and M. Johnson. 1994. Sap flow measurements of transpiration
from cotton grown under ambient and enriched CO2 concentrations. Agric. For. Meteorol. 70:231–245.
Dye, P.J., S. Soko and A.G. Poulter. 1996. Evaluation of the heat pulse
velocity method for measuring sap flow in Pinus patula. J. Exp.
Bot. 47:975–981.
Fernandez, J.E., M.J. Palomo, A. Diaz-Espejo, B.E. Clothier,
S.R. Green, I.F. Giron and F. Moreno. 2001. Heat-pulse measurements of sap flow in olives for automating irrigation: tests, root
flow and diagnostics of water stress. Agric. Water Manage. 51:
99–123.
Fisher, D. 1990. Measurement of phloem transport rates by an indicator-dilution technique. Plant Physiol. 94:455–462.
Fisher, D.B. and C.E. Cash-Clark. 2000. Sieve tube unloading and
post-phloem transport of fluorescent tracers and proteins injected
into sieve tubes via severed aphid stylets. Plant Physiol. 123:
125–137.
Giorio, P. and G. Giorio. 2003. Sap flow of several olive trees estimated with the heat-pulse technique by continuous monitoring of a
single gauge. Environ. Exp. Bot. 49:9–20.
Gould, N., P.E.H. Minchin and M.R. Thorpe. 2004. Direct measurements of sieve element hydrostatic pressure reveal strong regulation after pathway blockage. Funct. Plant Biol. 31:987–993.
Green, S.R., B.E. Clothier and D.J. McLeod. 1997. The response of
sap flow in apple roots to localised irrigation. Agric. Water Manage. 33:63–78.
Green, S.R., B.E. Clothier and B. Jardine. 2003. Theory and practical
application of heat pulse to measure sap flow. Agron. J. 95:
1371–1379.
Huber, B. 1932. Beobachtung und Messung pflanzicher Sartströme.
Ber. Deut. Bot. Ges. 50:89–109.
TREE PHYSIOLOGY VOLUME 27, 2007
NON-INVASIVE SAP FLOW MEASUREMENTS IN WOODY PLANTS
Huber, B., E. Schmidt and H. Jahnel. 1937. Untersuchung über den
Assimilatstrom. Tharandter Forstliches Jahrbuch 88:1017–1050.
Lott, J.E., A.A.H. Khan, C.K. Ong and C.R. Black. 1996. Sap flow
measurements of lateral tree roots in agroforestry systems. Tree
Physiol. 16:995–1001.
Marshall, D.C. 1958. Measurement of sap flow in conifers by heat
transport. Plant Physiol. 33:385–396.
Nadezhdina, N. 1999. Sap flow index as an indicator of plant water
status. Tree Physiol. 19:885–891.
Peuke, A.D., M. Rokitta, U. Zimmermann, L. Schreiber and
A. Haase. 2001. Simultaneous measurement of water flow velocity
and solute transport in xylem and phloem of adult plants of ricinus
communis over a daily time course by nuclear magnetic resonance
spectrometry. Plant Cell Environ. 24:491–503.
Swanson, R.H. 1962. An instrument for detecting sap movement in
woody plants. Rocky Mountains Forest and Range Experiment
Station, Fort Collins, CO, Paper No. 68, 16 p.
179
Swanson, R.H. 1994. Significant historical developments in thermal
methods for measuring sap flow in trees. Agric. For. Meteorol. 72:
113–132.
Swanson, R.H. and D.W.A. Whitfield. 1981. A numerical-analysis of
heat pulse velocity theory and practice. J. Exp. Bot. 32:221–239.
Thoday, D. 1910. Experimental researches on vegetable assimilation.
V. A critical examination of sach’s method for using increase of dry
weight as a measure of carbon dioxide assimilation in leaves. Proc.
Roy. Soc. Ser. B 82:1–55.
Xia, Y., E. Sarafis, E. Campbell and P. Callaghan. 1993. Non invasive
imaging of water flow in plants by NMR microscopy. Protoplasma
173:170–176.
Ziegler, H. and G. Vieweg. 1961. Der experimentelle Nachweis einer
Massenströmung im Phloem von Heracleum mantegazzianum
somm. et lev. Planta 56:402–408.
Appendix
Full derivation of the t 2 equation (Equation 2)
Let t max and t 2 be the temporal positions of the maximum temperature rise from ambient (θmax ) and its second occurrence
(θ2) respectively. By definition of θmax and θ2:
θ 2 = 12 θmax
(A1)
 ( x − Vt 2 ) 2 ( x − Vtmax ) 2 
t2
= exp  −
+

2 tmax
4 kt 2
4 ktmax 

(A3)
 t 
1  ( x − Vt 2 ) 2 ( x − Vtmax ) 2 
+
ln  2  =
−

t2
tmax
 2 tmax  4 k 

(A4)
Inserting Equation 1 into Equation A1 yields:
Equation A4 can be reorganized and written as:
 ( x − Vt 2 ) 2 
Q
exp  −
=
4 π kt 2
4 kt 2 

 ( x − Vtmax ) 2 
1 Q
exp  −

2 4 π ktmax
4ktmax 

(A2)
 t 
1
ln  2  =
( t 2 − tmax)( x 2 − V 2 t 2 tmax)
 2 tmax  4 k t 2 tmax
(A5)
Finally:
Simplification and reorganization of Equation A2 yields:
V =
1  2 4 k t 2 tmax  t 2  
ln 

x −
t 2 tmax 
t 2 − tmax  2 tmax  
TREE PHYSIOLOGY ONLINE at http://heronpublishing.com
(A6)