Journal of Experimental Botany, Vol. 47, No. 305, pp. 1833-1844, December 1996
Journal of
Experimental
Botany
Measurement of sap flow in plant stems
D.M. Smith and S.J. Allen1
Institute of Hydrology, Wallingford, Oxfordshire OX108BB, UK
Received 20 February 1996; Accepted 1 August 1996
Abstract
Transpiration rates for whole plants, individual
branches or tillers can be determined by techniques
which measure the rate at which sap ascends stems.
All of these methods use heat as a tracer for sap
movement, but they are fundamentally different in
their operating principles. Two methods commonly
employed, the stem heat balance and trunk sector
heat balance methods, use the heat balance principle;
the stem is heated electrically and the heat balance
is solved for the amount of heat taken up by the moving
sap stream, which is then used to calculate the mass
flow of sap in the stem. In the heat-pulse method,
rather than using continuous heating, short pulses of
heat are applied and the mass flow of sap is determined from the velocity of the heat pulses moving
along the stem. In addition, rates of sap flow can be
determined empirically, using the thermal dissipation
technique, from the temperature of sapwood near a
continuously-powered heater implanted in the stem.
Users must understand the theory underlying each of
these methods, so that they can select the method
most appropriate to their application and take precautions against potential sources of error. When
attempting to estimate transpiration by stands of
vegetation from measurements of sap flow in individual
plants, users must also select an appropriate sampling
strategy and scaling method.
Key words: Sap flow, transpiration, stem heat balance,
heat pulse velocity, review.
Introduction
Where measurements of transpiration by individual
branches, tillers or whole plants are required, sap flow
methods hold important advantages over other techniques. Sap flow methods are easily automated, so con1
tinuous records of plant water use with high time
resolution can be obtained. In contrast, determining transpiration from measurements of stomatal conductance
made with a porometer is labour intensive and provides
relatively poor time resolution (Dugas et a!., 1993); in
addition, difficulties caused by having to calculate transpiration rates for leaves from measured stomatal conductances and aggregate these over a canopy or tree crown,
while accounting for variations resulting from leaf age,
illumination and boundary layer conductances, make
porometry a relatively poor choice for measurement of
whole plant transpiration (Ansley et al., 1994). Plant
chambers can be used to measure transpiration by whole
plants, including even large trees, but they are not very
portable and, critically, they alter the microclimate of the
plant (Goulden and Field, 1994), whereas sap flow
methods can be used anywhere with very little disturbance
to the site. Deuterium tracing (Calder et al., 1992) can
also be used to measure whole plant transpiration, but
data can be difficult to interpret and the results only give
mean values over periods of several days.
Plant water use in the field can be estimated from the
soil water balance, but with temporal resolution of a few
days at best, and difficulties arise because estimates of
drainage and surface runoff are usually uncertain.
Micrometeorological methods, such as the Bowen ratio
technique and eddy covariance, can be used to measure
evapotranspiration with much better temporal resolution,
but these methods are complex, the equipment is expensive and they can only be used in large areas of flat,
uniform terrain. Both water balances and micrometeorology can provide estimates of evapotranspiration, which
includes soil evaporation and plant water use, while sap
flow techniques measure transpiration alone; thus sap
flow methods are a useful tool in studies of the water or
energy budgets of land surfaces, as they can be used to
partition evapotranspiration between plant and soil evaporation and to divide estimates of transpiration among
the component species of plant mixtures (Sakuratani,
To whom correspondence should be addressed. Fax: +44 1491 692424. E-mail: [email protected]
© Oxford University Press 1996
1834
Smith and Allen
1987; Kelliher et al., 1992; Allen and Grime, 1995).
However, when sap flow measurements are used to estimate transpiration for stands of vegetation, appropriate
methods of scaling from plant to unit area of land must
be used (Hatton and Wu, 1995; Soegaard and Boegh,
1995; Vertessy et al., 1995).
Sap flow methods have many applications in agriculture, horticulture, forestry, and ecology. Sap flow methods
have been used to quantify water use by arable crops
(Soegaard and Boegh, 1995; Senock et al., 1996), fruit
orchards (Edwards and Warwick, 1984; Cohen, 1991),
forest plantations (Cienciala et al., 1994; Hatton and
Vertessy, 1990) and natural vegetation (KSstner et al.,
1992; Allen and Grime, 1995; Senock and Ham, 1995).
They have been used to investigate genetic effects (Tan
and Buttery, 1995) and effects of CO2 enrichment (Dugas
et al., 1994; Senock et al., 1996) on crop water use, as
well as to determine how water uptake by trees influences
groundwater discharge (Cermak et al., 1984). The effect
of ozone exposure on transpiration by trees was studied
by measuring sap flow (Wiltshire et al., 1994) and sap
flow rates were used to monitor fungal colonization of
sapwood in forest trees (Yamoaka et al., 1990).
Techniques for measuring sap flow have also been used
in studies of plant water relations (Br6da et al., 1995;
Magnani and Borghetti, 1995), the energy budgets of
trees (Green, 1993; Smith, 1995) and the effects of atmospheric turbulence on transpiration by trees (Hollinger
et al., 1994). Thus, the use of sap flow methods in studies
of plant water use is becoming increasingly widespread,
so that they are likely to play a prominent role in future
efforts to devise solutions to hydrological problems encountered by farmers, foresters and conservationists.
It is therefore important that plant scientists understand
how techniques for measuring sap flow work, so that they
can select the method most appropriate to their application and take the precautions necessary to avoid errors.
Consequently, the theory underlying each of the methods
of sap flow measurement commonly encountered in the
literature have been described, giving emphasis to those
instruments that are available from commercial manufacturers. Also the circumstances in which each should be
used is discussed and sampling strategies that can be used
when scaling sap flow data from plant to stand are
reviewed.
The stem heat balance method
The stem heat balance method can be used to measure
sap flow in both woody (Steinberg et al., 1989) and
herbaceous (Baker and van Bavel, 1987) stems and has
been used on stems as small as 4 mm in diameter (Groot
and King, 1992), as well as on tree branches and the
trunks of small trees (Steinberg et al., 1990a). Stem heat
balance gauges to fit stems with diameters ranging
from 2-125 mm are commercially available (Table 1).
Individual gauges can typically be used only on stems
with diameters lying within relatively narrow limits, for
example, 2-3.5 mm for the smallest gauges and 100—
125 mm for the largest, and so a number of differentsized gauges are required when sap flow measurements
are made on stems of a variety of sizes.
Instrument description
As shown in Fig. la, a stem heat balance gauge comprises
a flexible heater, typically a few centimetres in width,
which is wrapped around the stem and enclosed in a layer
of cork, a layer of foam insulation and an aluminiumcoated PVC weather shield. Pairs of thermocouple junctions connected in series are embedded in the cork band
to form a thermopile; one junction from each pair is
positioned on the inner surface of the cork and the other
on the outer surface, so that the thermopile measures the
radial temperature gradient away from the heater (ATT)
(Steinberg et al., 1989). Gauges also contain another set
of thermocouples comprised of two pairs of thermocouple
junctions. These thermocouples are positioned against the
surface of the stem and are aligned axially along the stem,
with one junction from each pair above the heater and one
below, in a staggered arrangement (Fig. lb) (Steinberg
et al., 19906). The two thermocouple pairs measure the
temperature gradients ATt and ATb, which are used to
calculate components in the heat balance of the stem. In
the larger gauges, ATa and ATb are measured at more
than one location on the circumference of the stem, using
sets of thermocouples connected in parallel.
Theory of operation
Heat is applied to the entire circumference of the stem
encircled by the heater and the mass flow of sap obtained
from the balance of the fluxes of heat into and out of the
heated section of stem (Sakuratani, 1981; Baker and van
Bavel, 1987). The foam insulation and weather shield
surrounding the stem extend above and below the heater
sufficiently to minimize extraneous thermal gradients
across the heated section of stem and reduce solar heating
of the stem to a negligible level (Baker and van Bavel,
1987; Steinberg et al., 1989); heat input to the stem
section is thus limited to the electrical power supplied to
the heater (P) and, as shown in Fig. lc, the heat balance
of the stem is (Sakuratani, 1981; Baker and van Bavel,
1987)
P = qv + qr + q{
(1)
where qv is the rate of vertical heat loss by conduction in
the stem, qT is radial heat loss by conduction and qf is
heat uptake by the moving sap stream. The value of qf is
determined by subtracting qv and qt from P, which can
Measurement of sap flow
weather shield
(a)
air gap
(ATb-ATa)
from
1835
(Steinberget al., 19906), so that qv is obtained
foam insulation
I
(2)
thermocouple
junction
cork
thermopile
heater
heated zone
stem
OA
OH
where A,t is the cross-sectional area of the heated section
of stem, ktl is the thermal conductivity of the stem and x
is the distance between the two thermocouple junctions
on each side of the heater (Fig. lb). The value of ktl is
generally taken from the literature as 0.42 W m" 1 K " 1
for woody stems (Steinberg et al., 1989) and 0.54 W m" 1
K" 1 for herbaceous stems.
The radial component of the stem heat balance, qT, is
determined from A Tt using
qr = KlhATr
(3)
where Kth is the effective thermal conductance of the
sheath of materials surrounding the heater. The value of
K,h is unknown and depends on the thermal conductivity
of the insulating sheath and stem diameter. It usually
changes for each new installation and so must be calculated from ATr and the other components of the stem
heat balance during periods when sap flow, and therefore
qf, are known to be zero (Baker and van Bavel, 1987).
Once all other components of the stem heat balance
are known, q{ is determined by difference and the mass
flow rate of sap (/v) calculated using (Sakuratani, 1981;
Baker and van Bavel, 1987; Steinberg et al, 1990ft)
(4)
Fig. 1. (a) Vertical cross-section through a stem heat balance guage.
The dashed box in (a) is expanded in (b) to show wiring details of
thermocouples in the gauge; copper wires are shown as solid lines and
constantan wires as dotted lines For the determination of sap flow, the
temperature differentials J7*., J7*b and AT, are obtained from measurements of the voltages across AH, BH and CH, respectively, (c) The
heat balance of the length of stem heated by the gauge, where P is
heat applied to the stem, q, is the rate of vertical heat loss by
conduction, qT is radial heat loss by conduction and q, is heat uptake
by the sap stream.
all be measured; the value of P is calculated from the
electrical resistance and voltage across the heater, while
qy and qt are determined from measurements of A TB, A Tb
and ATT. Finally, q{ is converted to the mass flow rate
of sap.
The value of qv is calculated using Fourier's Law for
one-dimensional heat flow from the upward and downward gradients in temperature away from the heater
(Sakuratani, 1981; Baker and van Bavel, 1987). The
sum of these gradients is algebraically equivalent to
where c, is the specific heat capacity of sap and
(A7. + ATb)/2 is the increase in sap temperature across
the heater, assuming that heating of the sap is radially
uniform.
Some authors have found that errors in sap flow rates
measured using stem heat balance gauges can arise if
changes in the storage of heat in the heated section of
stem are neglected (Groot and King, 1992; Shackel et al.,
1992; Grime et al., 1995a). The size of these errors
increases with the diameter of the stem, but they are less
important when daily rates of transpiration are determined, as the change in heat storage over a day is usually
zero (Weibel and Boersma, 1995). A term which accounts
for changes in heat storage, q,, can be added to the heat
balance in equation 1 and quantified by measuring the
change in temperature of the stem (AT,t) over a time
interval, At (Groot and King, 1992; Grime et al., 1995a):
At
(5)
The coefficient c"tt is the volumetric heat capacity of stem
tissue, which can be taken from values in the literature
(Edwards and Warwick, 1984), and Vn is the volume of
1836
Smith and Allen
stem affected by heating, which can be reasonably
approximated as the volume of stem enclosed by the
heater (Weibel and Boersma, 1995). AT,t is evaluated
from measurements of the absolute temperature of the
stem, made by placing a thermocouple between the heater
and the surface of a small stem or by implanting a
thermocouple beneath the surface of a larger stem (Groot
and King, 1992; Grime et cil., 1995a; Weibel and
Boersma, 1995).
advantages over the conventional constant power systems:
overheating of the stem at low flow rates is avoided;
power consumption is lower, an important consideration
when operating sap flow gauges at remote sites away
from mains power; the dynamic response is improved;
and the heat storage term is reduced.
Measurements of just four voltages are required to
determine sap flow rates using stem heat balance gauges;
these are the voltage across the heater and the voltage
outputs from the radial thermopile and the thermocouples
Practical considerations
measuring ATK and ATb. When q, is included in the heat
balance, voltage output from an additional temperature
Gauges should be installed on straight sections of stem
sensor
must also be measured. These voltages are recorded
without swellings or lumps that could cause poor contact
with
an
automatic data logger and averaged, typically,
between the stem surface and the heater or thermocouples.
over
intervals
of 10-30 min to obtain a continuous record
Loose bark and any small branches or leaves sprouting
of
sap
flow
rates.
from the section to be enclosed by the gauge should be
Accurate determination of rates of sap flow using stem
carefully removed. Application of silicone-grease-based
heat
balance gauges depends critically on the correct
electrical insulating compound to the stem surface prior
evaluation
of K,h (Baker and Nieber, 1989), which must
to installation of the gauge is usually recommended for
be
done
when
sap flow is zero. For this purpose, it is
several reasons: to ensure good thermal contact between
often
assumed
that
there is no sap flow during the hours
the gauge and stem, to allow slippage of the gauge during
before dawn (Steinberg et al., 1989; Dugas et al., 1994).
installation, to prevent ingress of water and condensation,
However, sap flow can occur at night, particularly under
to prevent sensor corrosion, and to allow movement of
conditions of dry air advection (Green et al., 1989), and
the gauge during contraction and expansion of the stem.
so it can be necessary to determine Ksh in other ways.
However, Wiltshire et al. (1995) showed that, when
For example, Allen and Grime (1995) calculated K,h from
present over several months, the silicone compound suppressed radial growth in ash trees (Fraxinus excelsior L.), data obtained after heavy rainfall, when sap flow was
assumed to be zero because of low net radiation, high
resulting in stem constriction, probably as a result of
humidity and the presence of intercepted water on leaf
impaired gas exchange through the bark. Thus, users
surfaces. Alternatively, A",h can be determined after all
should monitor stems for signs of constriction, especially
foliage on a stem is wrapped in plastic to prevent transpirwhen gauges are kept on the same stem for long periods.
ation (Steinberg et al., 1989; Grime et al., 1995a) or,
After preparation of the surface, the gauge is positioned
when
practicable, A^h can be calculated from measureon the stem and fixed in place using velcro straps. It is
ments
recorded after excising the stem at the end of an
important that entry of water is prevented, as it can cause
experiment
(Baker and van Bavel, 1987; Steinberg et al.,
erratic measurements and damage the electrical compon1989).
Recently,
a novel gauge design has been proposed
ents of the gauge. Under heavy rainfall, water sometimes
(Peressotti
and
Ham,
1996) which completely eliminates
penetrates gauges by flowing down the stem surface. This
the
need
to
measure
K,h, by using dual heaters and
can be completely prevented by attaching a conical collar
variable
power.
made of heavy-duty polythene to the stem just above the
gauge and sealing the join with grafting wax.
In the commercially-available system, constant power
The trunk sector heat balance method
is supplied to the gauge heater. The voltage across the
The trunk sector heat balance method of sap flow measheater must be adjustable so that it can be set between 3
urement is intended for use on tree trunks with diameters
and 10 V, depending on the size of gauge and sap flow
larger than 120 mm. Like the stem heat balance method,
rates; the voltage should be selected to maintain a measurit is based on the principle that sap flow rates can be
able increase in sap temperature (> 1.0 °C) during periods
determined from the heat balance of heated stem tissue.
of high sap flow, but without heating the stem to damHowever, in the trunk sector heat balance method, heat
aging temperatures when flow is low.
is applied internally to only a segment of the trunk, rather
Systems with a variable power supply that is controlled
than superficially to the entire circumference. The measto maintain a constant increment in stem temperature
can also be constructed (Ishida et al., 1991; Grime et al., urement system can be purchased commercially (Table 1).
19956; Weibel and Boersma, 1995), but the power control
Instrument description
requires either complex data-logger programs or additional circuitry, which is not yet available commercially.
Heat is applied to the heated sector of the trunk using
Nevertheless, variable power systems have important
five stainless steel electrode plates inserted into the wood,
Measurement of sap flow
1837
Table 1. List of manufacturers of sap flow measurement systems, showing the type and size of stem for which each system is suitable
and whether the system includes a dedicated data logger
Method
Type of stem
Stem heat balance
Woody or herbaceous
Trunk sector heat balance
Woody
>120
Heat pulse
Woody
>30
Thermal dissipation
Woody
Size range (mm)
2-125
>40
as shown in Fig. 2a, to create four segments of sapwood
bounded by electrodes. Each electrode plate is 0.9 mm
thick and 25 mm in height and they are positioned parallel
to one another, with a lateral separation of 20 mm
(Cermak et al., 1984); the length of the plates is chosen
so that they approximately span the radial width of the
sapwood. Four thermocouples, housed in metal probes
with a diameter of 1 mm, are inserted into the sapwood
of the trunk at positions level with the top of the
electrodes, with two located midway across the two
central segments of sapwood and two placed at a lateral
distance of 60 mm from the outer electrodes (Fig. 2a, b).
A further four thermocouples are installed 100 mm below
these, outside of the heated zone (Cermak and Kucera,
1981; Cermak et al., 1984). All eight thermocouples are
connected in series, giving a measurement, over the vertical distance between the two rows of thermocouples, of
the temperature increase in the heated sector that is
automatically compensated for the vertical gradient in
temperature over the same height interval outside of the
heated zone; the voltage output from the array of thermocouples gives the net increase in temperature resulting
from heating of the trunk sector (Fig. 2b) (Cermak and
Kucera, 1981). This temperature increase, AT, is used to
calculate the rate of sap flow through the two segments
at the centre of the heated sector.
Theory of operation
An alternating current (1.5 kHz), converted from a 12 V
DC supply, is applied to the five electrodes embedded in
the tree trunk, so that the electrical impedance of the
Manufacturer
Dynamax Inc.
10808 Fallstone, #350
Houston TX 77099, USA
Fa*: +1-713-564-5200
Ecological Measuring Systems
Turisticka 5, 621 00 Brno
Czech Republic
Fax: +42-(0)541-225-344
HortResearch
Private Bag 11 030, Palmerston North
New Zealand
Fax: + 64-{0)6-354-6731
Greenspan Technology Pty. Ltd.
24 Palmerin St., Warwick
Qld. 4370, Australia
Fax: +6H0)76-61-9190
UP GmbH
Ruffinstr. 12, D-80637 Mdnchen
Germany
Fax: +49-(0)89-l 165135
Dynamax Inc.
(available from late 1996)
Dedicated
data logger
No
Yes
Yes
Yes
No
No
woody tissue causes the four segments of sapwood
bounded by electrodes to be heated. The use of an AC
supply ensures that electrochemical effects in the tissue
are avoided (Kucera et al., 1977). The trunk is insulated
and shielded from radiation, so that the heat balance of
the trunk sector is (Cermak et al., 1973)
P = qv + qT + q\ + q{
(6)
Here, P is the electrical power dissipated as heat in the
trunk sector, qv is heat lost vertically by conduction, qr is
heat lost radially inwards to the non-conducting heartwood and outwards to the cambium and bark, qx is heat
lost laterally into neighbouring sapwood by conduction;
and q{ is heat loss by convection in the moving sap
stream. The mass flow rate of sap is determined from the
value of q{ for the two segments at the centre of the
heated zone, which is evaluated by accounting for all
other terms in equation 6.
Two versions of the instrument have been used (Cermak
et al., 1984); in the first, which is the version available
commercially, P is constant (Cermak et al., 1973),
whereas in the second, a constant value of A T is maintained by automatic regulation of the power supply
(Kucera et al., 1977). In both systems, P is determined
by measurement of the potential drop across the electrodes and the current supplied (Cermak et al., 1976),
while <?, is assumed to be negligible because of 'active
thermal insulation' of the two central segments. Lateral
heat losses are eliminated from the heat balance of these
segments because the adjoining segments are heated to
the same temperature, so that lateral temperature gradi-
1838
Smith and Allen
(a)
hectwod
lapvmod
•bark
where Po and AT0 are values of P and AT measured
when sap flow is zero. For the constant temperature
system, A T is constant and so qy + qT can be assumed to
be constant, with a value of Po.
With all other components of the heat balance of the
trunk sector accounted for, q{ is calculated by difference
using equation 6 and converted to a rate of mass flow
through the central two segments of the heated zone
(Fm.c) by
F
=-*c,AT
(9)
where c, is the specific heat capacity of sap, which is
assumed equal to that of water. F m c is then multiplied
by the ratio of the width of the two central segments to
the entire stem circumference to estimate sap flow for the
whole tree (Cermak et al., 1976). Where there is substantial variation in sap flow rates around large trunks,
installations should be made at more than one location
on the circumference of the trunk in order to reduce
errors in estimates of flow for the whole tree (Cermak
et al., 1995).
AT
Practical considerations
o V
Fig. 2. Diagram of the trunk sector heat balance method, (a) Horizontal
cross section showing the system installed in a tree trunk, (b) A view
of the installation on the surface of the trunk, showing relative positions
of the heating electrodes and thermocouple junctions T[-T8, which are
connected in series by copper (solid lines) and constantan (dashed lines)
wires. The voltage across T, and T8 gives a measure of the increase in
sap temperature (AT) that is automatically compensated for underlying
thermal gradients in the trunk, as 2AT=AT43 + AT6S-ATn-AT7S,
where A T^ = Tx-Ty, the difference in temperature between the thermocouple junctions Tx and Ty.
ents do not occur and lateral heat losses by conduction
are avoided (termak et al., 1973). The remaining heat
losses by conduction, qT and qv, are accounted for
together. In the constant power system, qy + qt is found
from
qv + qI = KVTAT
(7)
where Kn is a thermal conductance coefficient which must
be evaluated during periods when there is no sap flow.
The value of Kvr accounts for the thermal conductivity
of the tissue and insulation materials surrounding the
heated zone, as well as the distance between thermocouples, so it must be evaluated for each new installation.
From equation 6,P = qv + qT when sap flow is zero (assuming qt = 0), so that K^ can be found from
ATn
(8)
Installation of the electrode plates and thermocouple
probes must be done carefully to ensure that each is
positioned correctly. The commercially-available trunk
sector heat balance system is supplied with specially
adapted tools and a template to aid installation and
wiring of the electrodes and sensors. It also has a dedicated power-supply control unit and data logger, which
records data and calculates average rates of sap flow for
desired intervals.
As with the stem heat balance method, it is critical that
data are available from periods when sap flow is zero, in
order to allow evaluation of the coefficient K^, when the
constant power system is used, or Po when the constant
temperature system is used. Enclosing the foliage of large
trees in plastic is not normally feasible, while cutting tree
trunks is not as easy as excising small stems, and so the
trunk sector heat balance method is more reliant than
the stem heat balance method on periods of zero sap flow
occurring before dawn or after rain. Thus, it may be
difficult to obtain reliable estimates of A"vr or Po under
some conditions.
The heat-pulse method
With the heat-pulse method, rates of sap flow are measured by determining the velocity of a short pulse of heat
carried by the moving sap stream, rather than the heat
balance of a heated stem. The method is suitable only for
use on woody stems. Heater and sensor probes must be
installed by drilling holes into the sapwood, so that its
Measurement of sap flow
use is limited to stems that are large enough to accommodate these, but not so large that the full depth of sapwood
cannot be accessed; generally, it can be used on stems
with diameters larger than about 30 mm. Two heat-pulse
systems are commercially available (Table 1).
Instrument description
Each set of heat-pulse probes comprises one heater probe
and two sensor probes containing miniature thermistors
approximately 1 mm in diameter. Heater probes are made
by housing a resistance wire in a stainless steel cylinder,
while sensor probes are constructed by mounting thermistors in either teflon or stainless steel tubing. Figure 3
shows a single installation, but in practice, four sets of
heat-pulse probes are typically used to measure sap flow,
one installed in each quadrant of the stem. The probes
are usually 1.8-2.0 mm in diameter and are implanted in
parallel holes drilled radially into the stem, with one
sensor probe (the upstream probe) placed 5 mm below
the heater and the other (the downstream probe) placed
10 mm above the heater. Short pulses of heat are periodically released from the heater probe and the sensor probes
are monitored continuously to measure the velocity of
each pulse as it moves with the sap stream.
1839
deploying the sensor probes at unequal distances
upstream and downstream of the heater probe, with the
upstream sensor placed nearer to the heater than the
downstream sensor (Swanson and Whitfield, 1981;
Swanson, 1994). Immediately after release of a pulse of
heat of 1-2 s duration, the temperature becomes higher
at the closer, upstream sensor than at the downstream
sensor because of conduction; but heat carried by the
moving sap then quickly warms the downstream sensor,
so that the temperature of the two sensors is again equal
after a time (re) in the order of 60 s, as shown in Fig. 4.
This is the time required for convection in the moving
sap stream to move the peak of the heat pulse from the
heater to the point midway between the two temperature
sensors, so that tc decreases as sap velocity increases. The
velocity of the heat pulse (vj is thus given by (Swanson
and Whitfield, 1981)
(10)
It,
(a)
downstream
sensor
10.0
Theory of operation
The heat-pulse technique is based on the compensation
principle; the velocity of sap ascending a stem is determined by compensation of the measured velocity of a
heat pulse for the dissipation of heat by conduction
through the matrix of wood fibres, water and gas within
the stem (for a historical review, see Swanson, 1994).
With modern instrumentation, this is accomplished by
mid-point
2.5 -
8
0.0
=3 -5.0
'
heater
upstream
sensor
rl
relative temperature increase
(b)
downstream
sensor probe
heater probe
rrn
centre
heartwood
sapwood
bark + cambium
Fig. 3. Configuration of a single set of heat-pulse probes implanted
radially into a stem of radius R at the cambium and h at the heartwood
boundary. The upstream temperature sensor is installed at a distance
xu below the heater and the downstream sensor at a distance xA above
the heater.
Fig. 4. Dissipation of a heat pulse released from a line heater into a
stem containing moving sap and upstream and downstream sensor
probes in the configuration shown in Fig. 3. (a) The distribution of
relative temperature at times r,, l2 and (3 after release of the heat pulse;
the temperature of the upstream and downstream sensor probes are
equal at time (0. (b) Change with time in the temperature difference
between the upstream and downstream temperature sensors (Tu-T6)
after release of the heat pulse.
1840
Smith and Allen
where ,vu and xd are the distances between the heater
and the upstream and downstream sensors, respectively
(Fig. 3).
Marshall (1958) demonstrated analytically that vh in
woody stems is not identical to sap velocity. His analysis
of the diffusion of heat in wood containing moving sap
showed that heat ascends the stem more slowly than sap
because of the transfer of heat between the moving sap
and the stationary, interstitial tissue between xylem vessels
or tracheids. For thermally homogeneous wood, where
conducting elements are uniformly spaced and interstitial
thicknesses are sufficiently small that the time required
for equilibration of sap and woody matrix is negligible,
Marshall found that the velocity of sap (vf) is related to
vh by
flV, =
P.c.
(11)
where a is the fraction of the cross-sectional area of
conducting sapwood occupied by moving sap streams
and p and c are density and specific heat capacity, with
the subscripts s and sm referring to sap and sap plus
woody matrix (including gas), respectively. The volumetric sap flux density per unit cross-sectional area of
sapwood («v) is then given by
uv = av,
(12)
so that, theoretically, sap flux densities can be determined
from measured values of vh using equations 11 and 12
without having to quantify a, provided the condition of
thermal homogeneity is satisfied and values of p,, p, m , cs,
ctm are known.
Swanson and Whitfield (1981) used a numerical analysis of the dissipation of a heat pulse in wood to show,
however, that before sap fluxes are calculated using
equation 11, measured values of vh must be corrected to
account for the influence on heat transfer of the materials
used to construct the sensor and heater probes and
wounding caused by drilling into the wood. This correction can be made using empirical functions derived by
Swanson and Whitfield (1981) and Green and Clothier
(1988) for a variety of spacings and materials used to
construct the heater and sensor probes.
Because sap velocities in woody stems normally vary
with radial depth, sensors are usually implanted at several
depths below the cambium of a stem, so that the radial
profile of sap flux density across the sapwood can be
determined. Mass flow rates of sap through the stem (Fm)
are then calculated from the integral of the sap flux profile
over the cross-sectional area of the sapwood, which is
given by (Green and Clothier, 1988)
Mrd)drd
(13)
where u'v(ra) is sap flux density calculated from corrected
values of vh as a function of radial depth (r d ) in a stem
of radius R at the cambium and h at the heartwood
boundary. The function u^ir^) can be determined by
fitting a second-order least-squares regression equation
to the sap flux profile (Edwards and Warwick, 1984;
Green and Clothier, 1988) or, where this results in
extrapolation to unrealistically high values of sap flux
density at the cambium or heartwood boundary, from a
step function of sap flux density with depth (Hatton
et cil, 1990).
Thus, for species with sapwood that can be considered
thermally homogeneous, the heat-pulse technique can be
used to measure transpiration without calibration.
However, if the distribution of sap-conducting elements
in sapwood is markedly non-uniform, or if the interstitial
distances between elements are too large for the time
required for thermal equilibration between sap and woody
matrix to be considered negligible, transpiration rates
calculated from measurements of heat-pulse velocity using
equations 11-13 are likely to be in error (Marshall, 1958;
Swanson and Whitfield, 1981; Swanson, 1994). Swanson
(1983) concluded that interstitial distances of more than
0.4 mm are sufficient to cause thermal inhomogeneities;
the technique consequently works well in softwood species
(Swanson and Whitfield, 1981; Swanson, 1994) and in
ring-porous or diffuse-porous hardwoods with closelyspaced xylem vessels (Green and Clothier, 1988; Swanson,
1994), but in other hardwoods it may be necessary to
rely on empirical calibrations to measure transpiration
accurately. Validation of measured sap flow rates is thus
a critical step in applying the heat-pulse technique to
species for which no validation has been made, especially
if thermal homogeneity of the wood is in doubt.
Validation of the heat-pulse technique and derivation of
any required calibration functions can be accomplished
by comparing rates of sap flow determined using the
heat-pulse method with rates measured by an independent
method (Green and Clothier, 1988).
Practical considerations
It is essential that the heater and sensor probes are
correctly positioned. Accurate spacing between the probes
is achieved by using a guide jig when drilling the holes,
which must be done carefully to prevent excessive damage
to the stem. The exact position of each probe should be
carefully measured, so that errors caused by misalignment
of probes can be corrected (Olbrich, 1991). The set of
probes in each quadrant of the stem is implanted to a
different depth, so that sap velocities are sampled at four
radial depths (between 5 mm below the cambium and the
heartwood boundary) in the sapwood. Each pair of
thermistors is then connected in a Wheatstone bridge
circuit and te is measured as the time taken after the
Measurement of sap flow
application of a heat pulse for the bridge to return to the
balance point. Both of the commercially-available heatpulse systems are supplied with logging and control units
that incorporate the bridge circuitry, control pulsing of
the heaters and record tc. Measurements can be made at
intervals of 15 min or longer.
Equations 11-13 show that Pt, Ptm, c,, cm, h, and R
must be determined before heat-pulse velocities are converted to rates of sap flow. In the approach of Edwards
and Warwick (1984), p, and c, are assumed to be the
same as for water, while p m and c,m are estimated by
weighting the densities and heat capacities of sap and
woody matrix by the volume fractions of each in fresh
wood. The density of woody matrix is taken to be 1530 kg
m~ 3 , a value considered to be constant between and
within species, while the heat capacity of woody matrix
is taken as 1380 J kg" 1 K" 1 (Edwards and Warwick,
1984). To measure the volume fractions of sap and woody
matrix for each stem, core samples are taken using an
increment borer after each period of measurement and
volume fractions are calculated from measurements of
the fresh mass, oven-dry mass and volume (as immersed
mass, by Archimedes' principle) of the wood samples
(Edwards and Warwick, 1984). Values of h are determined
by visually examining the same samples, while R is
determined from the stem radius less the thickness of the
bark and cambium.
In general, probe sets should be moved regularly, either
to a different part of the same stem or to a new stem,
because wound reactions in the woody tissue of the stem
often develop 14-21 d after implanting the probes. These
reactions are thought to be caused by the deposition of
resin in the xylem vessels or tracheids surrounding the
implantation site, or possibly by cavitation, with the
result that sap flow occurs further and further away from
the sensor probes as the wound reaction develops, seriously impairing the accuracy of the technique. In rare
instances, wound reactions can develop after a much
shorter period than 14 d and so it is essential that users
of the heat-pulse technique monitor their data for changes
in sensitivity to sap flow and move the probes more
frequently if necessary.
1841
change in the mass of water collected. Alternatively, the
excised-branch method can be used to test the performance of the heat-pulse technique under field conditions.
Heat-pulse probes are installed in a branch which is then
cut down, re-cut under water, and mounted in a container
of water covered with plastic to prevent loss of water by
evaporation. The container is placed on an electronic load
cell and the rate of sap flow measured using the heat-pulse
apparatus is compared to the transpiration determined
from the change in mass of the container with time.
Results from the use of both validation methods on
branches of Azadirachta indica A. Juss., a diffuse-porous
hardwood, are shown in Fig. 5. Flow rates were seriously
underestimated by the heat-pulse method, emphasizing
the importance of testing the accuracy of the method
before using it to quantify transpiration. This deviation
from heat-pulse theory was probably caused by thermal
inhomogeneity resulting from the thickness of interstitial
tissue between xylem vessels, as the mean spacing between
vessels in A. indica was 0.43±0.07 mm (Smith, 1995),
which is larger than the threshold of 0.4 mm that Swanson
(1983) found was sufficient to cause thermal inhomogeneity. The relationship between actual flow rates and those
measured with the heat-pulse technique was linear, however, so that an equation for correcting measured sap
flow rates was determined using linear regression. The
correction factor found for A. indica from the data in
Fig. 5 was 1.62 (Smith, 1995).
Green and Clothier (1988) found similar results for
kiwifruit (Actinidia deliciosa (Chev.) C.F. Liang & A.R.
Ferguson) stems and concluded that the deviation from
theory occurred because the condition of thermal homogeneity was contravened. They also demonstrated, however, that the heat-pulse technique can be used without
calibration on species with wood that satisfies the condition of thermal homogeneity; thus sap flow rates in apple
{Malm syhestris Mill.), a diffuse-porous species with
closely-spaced xylem vessels, were accurately measured.
Validation of the heat-pulse technique
Because calibration of the heat-pulse method is necessary
for species with wood that is not thermally homogeneous,
validation is an important step when using the technique.
Two methods suitable for testing the heat-pulse technique
were described by Green and Clothier (1988). In the
laboratory method, water is forced through a section of
branch in which heat-pulse probes have been implanted.
Water passing through the branch is collected in a flask
on the weighing pan of an electronic balance and the
simultaneous heat-pulse estimates of flow rate are compared to the actual flow rate, obtained from the rate of
0.2
0.4
0.6
0.8
1.0
1
actual flow (g s" )
Fig. 5. Comparison of flow rates measured using the heat pulse (HP)
technique and actual flow rates measured using the laboratory ( • ) and
field (D) methods in stems of Azadirachta indica.
1842 Smith and Allen
The thermal dissipation method
An empirical method for measuring sap flow in trees was
developed by Granier (1985). Two cylindrical probes of
2 mm diameter are inserted radially into the stem, with
one probe placed approximately 100 mm above the other.
The upper probe contains a heater element and a thermocouple junction that is referenced to another junction in
the lower probe (Granier, 1985, 1987). Constant power
is applied to the heater and the difference in temperature
between the two probes (AT) is then dependent on the
rate of sap flow around the probes; as sap flow rates
increase, heat is dissipated more rapidly and so AT
decreases. Granier (1985) found experimentally that for
Pseudotsuga menziesii (Mirb.) Franco, Pinus nigra Arnold
and Quercus pedunculata Ehrh., volumetric sap flux density (Uy, m 3 m'2 s" 1 ) is related to AT by
= 0.000119Z 1231
(14)
with Z defined as
Z =
(AT0-AT)
AT
(15)
where AT0 is the value of AT when there is no sap flow.
The mass flow rate of sap is then calculated using
Fm = ptUyAm
(16)
where p, is the density of sap and A,w is the cross-sectional
area of sapwood. Granier et al. (1990) suggested that the
parameters in equation 14 do not depend on characteristics of trees or wood anatomy and so it may be possible
to utilize this method without calibration. However, their
claim is not derived from physical principles for heat
transfer and needs to be tested; hence, it is recommended
that the method should be calibrated for species on which
it has not previously been validated. The major advantages of the thermal dissipation method appear to be easy
installation, simple requirements for recording sensor
outputs, simple sap flow calculations and lower costs, so
that it will probably be more widely applied in future.
Transpiration is unlikely to vary strongly among the
members of such stands, so that sap flow can be measured
in a number of individual plants and stand transpiration
calculated from plant density (Ham et al., 1990; Dugas
and Mayeux, 1991). In thinned forest plantations with a
closed canopy, where variation in tree size is low but
spacing between plants is not uniform, Hatton and
Vertessy (1990) found that stand transpiration could be
estimated by scaling-up water use on the basis of the
ground area occupied by individual trees.
In more complex vegetation, however, such an approach
is unlikely to be satisfactory. In stands where there are
gaps in the canopy, plants of a range of sizes and a mixture
of species, as is common in natural woodland, the relationship between ground area and transpiration is likely to
vary with species and position in the canopy hierarchy.
The easiest approach in such stands is to measure sap flow
in all plants in a representative area of land, as was done
by KSstner et al. (1992), but it is unusual to have sufficient
instruments available to achieve this. Where members of
a stand population vary primarily in size, sap flow for
individual plants can be scaled to stand transpiration by
determining relationships between sap flow rates and stem
diameter, stem basal area, sapwood area or leaf area and
then extrapolating transpiration rates to unit area of land
on the basis of surveys of tree size or measurements of
leaf area index (Allen and Grime, 1995; Soegaard and
Boegh, 1995; Vertessy et al., 1995). In mixed stands or
where there is a pronounced dominance hierarchy in the
structure of the vegetation, this approach can be applied
to sub-groups of the population created by dividing the
stand into classes containing plants with similar characteristics (Granier et al., 1990). At sites where spatial and
temporal variability in plant water use is high because of
heterogeneity in the availability of resources and light
interception, scaling from plant to stand can be done using
theory developed by Hatton and Wu (1995) to account
for the dynamics of relationships between transpiration
and leaf area.
Conclusions
Sampling and scaling from plant to stand
After measuring sap flow, it is often necessary to extrapolate water use by sampled plants to an entire stand; mass
or volume flow rates for individual plants must be converted to estimates of transpiration per unit area of land
that can be used to address hydrological problems faced
by land users and managers (Hatton and Wu, 1995). It
is important, therefore, that strategies for sampling sap
flow are adopted that account for variation in transpiration within the plant stand (Cermak and Kucera, 1990).
In uniform stands, such as monoculture crops or forest
plantations with closed canopies, this is relatively simple
because most plants in the stand are of similar size and
the supply of radiant energy and soil water is uniform.
Each of the four methods of measuring sap flow reviewed
here is reported to be accurate to within 10% (Cermak
and Kucera, 1981; Diawara et al., 1991; Olbrich, 1991;
Weibel and de Vos, 1994). However, when using all
methods of sap flow measurement, users must be aware
of potential sources of error and take suitable precautions,
otherwise errors in sap flow rates can become much larger
(Baker and Neiber, 1989; Olbrich, 1991; Groot and King,
1992), particularly if assumptions in underlying theory
are contravened. Uncertainties in estimates of water use
can also occur as a result of errors made in scaling
transpiration from plant to stand (Hatton et al., 1995).
In addition, users should be aware that sap flow rates
can be out of phase with leaf transpiration because of
Measurement of sap flow
capacitance in the stem or branches resulting from the
storage of water in the tissue (Schulze et at., 1985),
although this effect is often not observed.
Sap flow methods are ideally suited to applications
requiring routine determinations of plant water use, provided that users are careful to select the method most
appropriate to their needs. These methods are also very
useful in studies of plant responses to environmental
conditions, where they can be used as one of a suite of
techniques employed in either the field or laboratory to
measure changes in the water relations, growth and water
use efficiency of plants resulting from, for example, new
management practices, environmental stress or climate
change.
Acknowledgements
We would like to thank John Roberts and an anonymous
reviewer for helpful comments on drafts of this review and
Nick Jackson for drawing Fig. 2. We are also grateful to Jiri
Kucera (Ecological Measuring Systems), Mike van Bavel
(Dynamax Inc.) and Ross Edwards (HortResearch) for informative discussions about their sap flow measurement systems,
and to Steve Bonnage (Analytical Development Company) and
Keith Parkinson (PP Systems) for equipment loans. Finally, we
thank the Society for Experimental Biology for organising the
workshop at which this paper was presented, and providing
financial support for SJA.
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