Instrumentation & Measurement Magazine 23-2 - 42

flux density because wood thermal properties change with
the water content. As zero-flow increases when water-content decreases, ΔTmax measured at night-time introduces error
in sap flux density estimated during the day with the TDP
method.
Heat field deformation method (HFD) attempts to address
issues of Granier TDP method related to zero-flow conditions. HFD enables wider (full) measurement range of sap
flux densities and measurement of reverse flows. It features
a four-needle configuration. Continuous heating is applied
to the central needle, and the temperature difference with respect to the heater is measured at the remaining three needles:
two axial (one downstream, one upstream) and the third, lateral. Each needle may feature multiple thermocouples to map
temperature at different depths from the surface [8]. This
method is semi-empirical and requires corrections due to
tissue wounding. Commercial HFD sensors (Fig. 4a) are available on the market [18].

Heat Balance Methods (HB)
In contrast to heat deformation methods where applied heating power is continuous, but non-regulated, in heat balance
(HB, Fig. 4b) methods the heating power is regulated in a feedback loop, such that the temperature difference between the
heated xylem tissue-volume and unheated referent tissue is
kept constant. Increase in flow causes the increase in required
heating power, in order to maintain some preset (regulated)
temperature difference. Thus, mass flow is proportional to
the required heating power [19]. The merit of this method is
that it does not require field-calibration. Commercial devices
are available on the market, typically featuring heating power
spans within 0.3-1.0 W at 1 kHz (ac, floating) for a regulated
temperature difference of 2-8 °C.

Pulsed-heating Methods
Such high-power requirements may be lowered by pulsed
heating. Heat ratio method (HRM, Fig. 4c) features three
needles: one central heater needle and two temperature
measurement needles inserted equidistantly upstream and
downstream of the heater. Each temperature sensing needle
features two thermocouples at different depths. The method
estimates the magnitude and direction of water flux, by measuring the ratio of the temperature increase sensed by each
thermocouple upon reception of the heat-pulse.
A drawback of this method is that the measurement range
covers only the lower-half of the sap flow fluxes (max. 45
cm3cm−2 h−1 [8]). Also, relying on empirical conversion from
heat velocity to the sap flux density, HRM requires periodic destructive calibration-measurements on the wood's core.
Overcoming these drawbacks is the four-needle "Sapflow+" heat-pulse method [20]. It takes the same asymmetrical
heater/measurement-probes configuration as the continuousheating HFD method and adapts it for pulsed-heating. It uses
an analytical heat conduction-convection model to convert
measured temperatures into heat velocity, and finally to sap
flux density. Reported accuracy is within 5% relative error [20].
42

Minimally-invasive Sap-flow Methods
One of the most common problems with thermal heat pulse
methods is tissue wounding/scarring occurring around needles and affecting the flow. A novel, non-invasive, non-contact
heat pulse method [22] addresses the problem of scarring. A
near infra-red laser beam is proposed to optically concentrate
a heat pulse onto the stem surface painted black to absorb laser's heat. Temperature is then measured on the stem surface
at two points-one upstream, and the other downstream-using either thermocouples on the bark-surface or non-contact
infra-red sensors.
Also, an another especially interesting direction of research
is a cost-effective single-needle sensor, simultaneously acting
as an intermittently operated heater and temperature sensor
[23]. Clearly, this method sacrifices the information on the direction of the flow.
Recent sap-flow research in plant-physiology is aimed
towards up-scaling (generalizing) individual sap-flow measurements and correlating the measured flow with other
plant-hydraulic quantities, mostly extrapolating the sapflow readings to the whole-tree transpiration rate [19].
However, this research area is still inconclusive, leaving many
opportunities.

Electromagnetic Sensing of Stem Water
Content
Complex dielectric permittivity is an intrinsic property of a
material that relates to its ability to store and conduct electrical
charge. Because the dielectric permittivity of water is far higher
than that of air or the woody matrix in plant stems (i.e., relative dielectric constant, εr, air =1, εr, solids < 10, εr, water = 80), change in
the dielectric of the tissue reflects a change in its water content.
Thus, a stem's volumetric water content is typically estimated
with electromagnetic sensors measuring complex permittivity
of the xylem (i.e., its relative dielectric constant εr).
Design of direct, in-situ, point-sensors for microwavefrequency range dielectric constant (εr) measurements was
motivated by the idea of extrapolating these measurements
to an averaged tree/canopy dielectric constant, which could
then be measured remotely over large geographic areas using
airborne microwave radar backscatter (remote sensing). This
approach was pursued, hoping that εr could be correlated to
water potential measurements.

Time-domain Reflectometry (TDR)
Time-domain reflectometry is an impulse method of volumetric water content measurements. The measurement
probe consists of a transmission line, whose two end-terminals are nailed-in into the stem (i.e., line terminated by
the xylem tissue). As the water content declines with water
stress, the overall dielectric constant of the material also declines which is detected as a decrease in transit time of the
impulse signal.
Comparison of TDR VWC measurements to gravimetric
water content showed linear fit within the range of 10-60%
VWC [24]. A shortcoming of the method is non-linear and

IEEE Instrumentation & Measurement Magazine

April 2020

Instrumentation & Measurement Magazine 23-2

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