The Stem Heat Balance Method for Measuring
Sap Flow
in the Stems of Intact Plants
Tetsuo
SAKURATANI
The use of
thermic techniques to measure sap flow in the stems and roots of
plants is widespread in studies of plant-water relations.
Commonly used methods include heat pulse methods, first proposed
by Huber in 1932, and heat balance methods, which were developed
in the latter half of the twentieth century. The two types of
heat balance methods are the tree-trunk heat balance method and
the stem heat balance (SHB) method. The former was developed to
measure the mass flow rate of sap in large trees (e.g., Cermak et
al., 1973), and the latter was originally proposed by Sakuratani
(1981) to measure the mass flow rate of the sap stream in
herbaceous plants. The SHB method is based on the energy balance
of a stem segment to which heat energy is supplied by an external
annular heater.
This short note outlines the stem heat balance method.
1.
Theory
Consider a stem segment of a plant to which a constant
heat flux (Q W) is applied through an external annular
heater (Fig. 1). In steady state conditions, the supplied heat
should be balanced by the heat loss, as in Eq. (1).
where qf is the energy transported in the sap flow from the heated segment (W), qu and qd are the energies transferred upward and downward, respectively, by thermal conduction along the stem (W), and qr is the energy lost radially (W). The heat energy (Q) is represented by Q = IEp, where I and Ep are the electric current (A) and voltage (V) supplied to the heater. The energy transported by the mass flow of the sap (qf W) is given by
where c is the specific heat of water (4.18 J g-1 ºC-1), F is the rate of flow of the sap in the stem (g s-1), Tu is the mean temperature (ºC) of sap flowing out of the segment, and Td is the mean temperature of sap streaming into the segment (ºC). Assuming that the temperature is uniform in the radial direction in each cross-section of the stem segment, Tu and Td can be assumed to be equal to the surface temperatures measured at the uppermost and lowest points of the heated segment, respectively. qu and qd can be approximated by the following equations:
where l is the thermal conductivity of the stem, assumed to be 0.54 W m-1ºC-1 for herbaceous plants, and A is the cross-sectional area of the heated segment (m2). Tu’ is the temperature of the stem at the point Dx (m) above where Tu is measured, and Td’ is the temperature at the point Dx below where Td is measured. qr is estimated from the following equation, using a cylindrical heat flow sensing element that is attached to the surface of the heater:
where k is a coefficient related to the thermal conductivity, shape and size of the element (W V-1). E is the voltage of the thermopile construction of the element (V). Combining Eqs. (1)-(5) yields the following relation for the sap flow rate, equivalent to the amount of sap moving up through a cross-section of the stem per unit time:
Assuming that F = 0, k is determined from the relationship:
It is usually assumed that F = 0 during the predawn period. To estimate k without assuming F = 0, another method has been proposed (Sakuratani et al., 1999).
2.
Sensor design and measurement
Our sap flow sensor, constructed based on the SHB
method, consists of a flexible heater, a thermopile to sense the
radial heat loss, and thermocouples to sense the temperature
differences Tu-Tu', Td-Td'
and Tu-Td, as shown in Fig.
2. Once the sensor is installed on the stem surface, both the
sensor and the stem sections above and below the sensor are
completely covered by a heat insulator to minimize thermal
perturbations caused by the ambient environment. Power is
supplied continuously to the heater from a DC electric source.
Sensor signals are usually logged using a data logger.
The original design of the sensor has been modified by several
researchers (Baker and van Bavel; 1987; Ham and Heilman, 1990;
Steinberg et al., 1990).
3.
Accuracy of the sensor
The sap flow in stems of soybean, sunflower, tomato and
rice plants was determined with the sap flow sensor and compared
with the transpiration rates measured directly with a balance.
These measurements showed that the accuracy of the sap flow
sensor is generally ±10%.
However, the sap flow in roots of Sesbania rostrata was
overestimated by the sap flow sensor by 30-50% in comparison to
the water uptake by the roots determined using a potometric
method. Since the root xylem vessels in this plant tend to be
distributed toward the center of the root rather than near the
surface, this overestimation probably resulted from a lack of
thermal equilibrium between the xylem fluid and the sensor on the
root surface.
In conclusion, the SHB method measures mass flow rates of sap in
plant stems with 10% accuracy without calibration, with the
exception of stems and roots in which the xylem vessels tend to
be distributed toward the center of the stem or root.
4.
Applications of the sensor
The SHB method has been found to be applicable to stems
and trunks of about 2-150 mm in diameter (van Bavel, 2002).
Listed below are major studies in which the authors used the SHB
method for stems and/or roots.
- Estimation of water consumption at different levels of a
soybean canopy (Ref. 3).
- Diurnal changes in the sap flow of field-grown sugarcane plants
(Ref. 5).
- Separate estimations of transpiration and evaporation from a soybean
field (Ref. 7).
- Comparison of remote and stem flow gauge methods in soybean
canopies (Ref. 11).
- Relationship between the transpiration rate of soybean plants
and soil water content (Ref. 12).
- Water dynamics in the peduncle of the mango inflorescence (Ref. 13, Ref.
19), and in mango fruit (Ref. 20).
- Sap flow in the roots, trunk and shoots of an apple tree using
the heat pulse and heat balance methods (Ref. 14).
- Water dynamics in citrus trees (Ref. 15).
- Reverse flow in roots of Sesbania rostrata (Ref. 16).
- Effects of hydraulic lift by Markhamia lutea on
neighboring crops (Ref. 18).
References (in
chronological order)
1. Cermak, J., Deml, M. and Penka, M., 1973: A new
method of sap flow rate determination in trees. Biol. Plant.,
15, 171-178.
2. Sakuratani, T., 1981: A heat balance method for measuring
water flux in the stem of intact plants. J. Agric. Meteorol.,
37, 9-17.
3. Sato, K. and Sakuratani, T., 1982: Water consumptions at
different levels of soybean canopies of different plant spacings
in the field estimated from the water fluxes in the stem. Jpn.
J. Crop Sci, 51, 75-81.
4. Sakuratani, T., 1984: Improvement of the probe for measuring
water flow rate in intact plants with the stem heat balance
method. J. Agric. Meteorol., 40, 273-277.
5. Sakuratani, T. and Abe, J., 1985: A heat balance method for
measuring water flow rate in stems of intact plants and its
application to sugarcane plants. JARQ, 19, 92-97.
6. Baker, J.M. and van Bavel, C.H.M., 1987: Measurement of mass
flow of water in the stems of herbaceous plants. Plant Cell
Environ., 10, 777-782.
7. Sakuratani, T., 1987: Studies on evapotranspiration from crops
(2) Separate estimation of transpiration and evaporation from a
soybean field without water shortage. J. Agric. Meteorol.,
42, 309-317.
8. Sakuratani, T., 1990: Measurement of the sap flow rate in stem
of rice plant. J. Agric.Meteorol., 45, 277-280.
9. Ham, J.M. and Heilman, J.L., 1990: Dynamics of a heat balance
stem flow gauge during high flow. Agron. J., 82,
147-152.
10. Steinberg, S.L., van Bavel, C.H.M. and McFarland, M.J., 1990:
Improved sap flow gauge for woody and herbaceous plants. Agron.
J., 82, 851-854.
11. Inoue, Y., Sakuratani, T., Shibayama, M. and Morinaga, S.,
1994: Remote and real-time sensing of canopy transpiration and
conductance. - Comparison of remote and stem flow gauge methods
in soybean canopies as affected by soil water status -. Jpn.
J. Crop Sci., 63, 664-670.
12. Sameshima, R., Sakuratani, T. and Takenouti, A., 1995:
Relationship between transpiration rate of Soybean plants (Glycine
max Merr. cv. Enrei) and soil water content estimated
by stem heat balance and heat probe method. J. Agric. Meteorol.
51, 153-157.
13. Higuchi, H. and Sakuratani, T., 1996: Water dynamics of mango
tree as measured by a modified heat balance sap flow sensor. Agronomy
Abstract, ASA, 10.
14. Sakuratani, T., Clothier, B.E. and Green, S.R., 1997:
Measurements of sap flow in the roots, trunk and shoots of an
apple tree using heat pulse and heat balance methods. J.
Agric. Meteorol., 53, 141-145.
15. Sakuratani, T., Higuchi, H., Yano, T. and Takagi, S., 1998:
Water dynamics in citrus tree. Annual Report 1997-98, Arid
Land Research Center, Tottori University, 44.
16. Sakuratani, T., Aoe, T. and Higuchi, H., 1999: Reverse flow
in roots of Sesbania rostrata measured using the constant
power heat balance method. Plant Cell Environ., 22,
1153-1160.
17. Van Bavel, M.G., 2002: Flow4 Installation and Operation
Manual, Dynamax, Inc., Houston, 139pp.
18. Hirota, T., Sakuratani, T., Sato, T., Higuchi, H. and Nawata, E. 2004:
A split-root apparatus for examining the effects of hydraulic lift
by trees on the water status of neighbouring crops. Agroforestry Systems,
60,181-187.
19. Higuchi, H. and Sakuratani, T., 2005: The sap flow in the peduncle
of the mango (Mangifera indica L.) inflorescence as measured by the stem heat balance method. J. Japan. Soc. Hort. Sci, 74, 109-114.
20. Higuchi, H. and Sakuratani, T., 2006: Water dynamics in mango (Mangifera indica L.) fruit during the young and mature fruit seasons as measured by the
stem heat balance method. J. Japan. Soc. Hort. Sci., 75, 11-19.
21. Harigane, I., Sakuratani, T., Higuchi, H., Nawata, E., Asano, S., Yamamoto,
S. and Maskow, I., 2009: Hydraulic lift in mango trees (Mangifera indica L.) and early growth of intercropped groundnut. Trop. Agr. Develop., 53, 90-94.
