Journal of Experimental Botany, Vol. 64, No. 13, pp. 3951–3963, 2013
doi:10.1093/jxb/ert044 Advance Access publication 22 March, 2013
Review paper
Measurement of the matric potential of soil water in the
rhizosphere
W.R. Whalley,1,* E.S. Ober1 and M. Jenkins2
1
Rothamsted Research, West Common, Harpenden, St Albans AL5 2JQ, UK
Delta-T Devices, 130 Low Road, Burwell, Cambridge CB25 OEJ, UK
2
*To whom correspondence should be addressed. E-mail: [email protected]
Received 1 November 2012; Revised 22 January 2013; Accepted 30 January 2013
Abstract
The availability of soil water, and the ability of plants to extract it, are important variables in plant research. The matric
potential has been a useful way to describe water status in a soil–plant system. In soil it is the potential that is derived
from the surface tension of water menisci between soil particles. The magnitude of matric potential depends on the
soil water content, the size of the soil pores, the surface properties of the soil particles, and the surface tension of
the soil water. Of all the measures of soil water, matric potential is perhaps the most useful for plant scientists. In this
review, the relationship between matric potential and soil water content is explored. It is shown that for any given soil
type, this relationship is not unique and therefore both soil water content and matric potential need to be measured
for the soil water status to be fully described. However, in comparison with water content, approaches for measuring
matric potential have received less attention until recently. In this review, a critique of current methods to measure
matric potential is presented, together with their limitations as well as underexploited opportunities. The relative merits of both direct and indirect methods to measure matric potential are discussed. The different approaches needed
in wet and dry soil are outlined. In the final part of the paper, the emerging technologies are discussed in so far as our
current imagination allows. The review draws upon current developments in the field of civil engineering where the
measurement of matric potential is also important. The approaches made by civil engineers have been more imaginative than those of plant and soil scientists.
Key words: Matric potential, measurement, porous matrix sensors, sensors, tensiometer, water release characteristic.
Introduction
A quantitative description of the water status of soils and
plant tissue is a necessary component of most experiments
in plant biology. However, perhaps because the importance
of the issue is not appreciated, or that methods are poorly
understood, it is not uncommon that such measurements—if
made at all—are inadequate, making it difficult to replicate
the experiments under similar conditions. Knowledge of the
water available to plants in the growth medium is often critical to understanding growth, development, physiology, and
gene expression patterns of plants in any system. This review
attempts to explain concepts of soil water and some ways in
which it can be measured, with particular emphasis on soil
matric potential sensors. Comprehensive treatment of methods for measuring plant and soil water status are found elsewhere (e.g. Boyer, 1995).
The water-filled tensiometer is synonymous with the measurement of matric potential. Tensiometers tend to be the
preferred sensor because, when working correctly, they give
a direct measurement of matric potential. The working principles of the water-filled tensiometer have been understood
for >100 years following the early description by Livingstone
(1908). A helpful summary of the history of the development
of the tensiometer as an instrument is given by Or (2001).
Despite the long history of the water-filled tensiometer, those
© The Author [2013]. Published by Oxford University Press on behalf of the Society for Experimental Biology. All rights reserved.
For permissions, please email: [email protected]
3952 | Whalley et al.
used by plant and soil scientists have not been particularly
improved in comparison with the early descriptions, except
for the use of improved pressure transducers and data logging systems. The perceived limitation of a narrow measurement range is widely reported in text books (e.g. Marshall
et al., 1999). It is because of this that there is a widely held
view that the water-filled tensiometer can only be used to
measure matric potentials greater than approximately –90
kPa, due to cavitation of water at lower pressures. We will
describe the basis of this belief and show how water-filled
tensiometers can actually be used to measure much lower
matric potentials. Civil engineers, by improved saturation
procedures, have in the last 20 years considerably extended
the range of matric potentials over which the water-filled tensiometer can be used, to matric potentials as low as –1500
kPa (Ridley and Burland, 1993). Tensiometers designed for
this purpose have become known as ‘high-capacity tensiometers’ (Take and Bolton, 2003; Marinho et al., 2008). Careful
saturation of commercially available tensiometers can allow
matric potentials as low as –200 kPa to be measured (Whalley
et al., 2009). In this review, we explore the possibility of using
the high-capacity tensiometer in plant sciences. An alternative to the high-capacity tensiometer is described by Bakker
et al, (2007), where the water in the ceramic cup is replaced by
an osmoticum. This has the effect of the hydrostatic pressure
in the tensiometer cup being zero when the soil is at a matric
potential equal to the osmotic potentials of the osmoticum.
This has the advantage of a positive pressure in the tensiometer cup even in dry soils; thus, cavitation is no longer an issue.
A significant effort has been made to develop sensors which
can reliably measure matric potentials which are much lower
than –90 kPa. The most common design is the porous matrix
sensor. Here a porous material is allowed to equilibrate with
the soil water, then the water content of the porous matrix is
measured and converted to a matric potential using a calibration curve. The original sensors of this type were made using
plaster of Paris and monitored by measuring electrical resistance (Bourget et al., 1958). The use of electrical resistance
measurements to measure soil water content was described
in 1887 by Professor Milton Whitney, who became one of the
first to develop approaches for the in situ determination of
soil water content based on the measurement of the electrical
conductivity of soil (see Freeland, 1989). The encasement of
the resistance sensor in plaster of Paris provided some stabilization of resistance measurement between soil types because
of its buffering capacity against variable electrical conductivity of the soil water. These sensors are best suited to dry
soils (matric potential less than −500 kPa), where they work
well, in part, because hysteresis in the sensor is small at these
matric potentials. However, with careful calibration, taking
into account the logger calibration and temperature, gypsum
blocks can be used at higher matric potentials (Johnston,
2000). Recently, they have been modified by increasing the
pore size of the porous matrix to obtain a sensor that will
work at matric potentials between 0 and −200 kPa. However,
in making this adaptation, the sensor became unreliable, as
the calibration varied when the same sensor was repeatedly
calibrated in the same soil (see Spaans and Baker, 1992).
Whalley et al. (2001) analysed this adapted design and concluded that it could never work well because (i) performance
in wet soils is likely to be a function of the soil rather than the
sensor; and (ii) even in drier soils, hysteresis is not taken into
account in the calibration. However, Whalley et al. (2001)
showed how hysteresis could be taken into account in the
calibration of a ceramic-based porous matrix sensor between
matric potentials of 0 and −60 kPa. Recently, Whalley et al.
(2007, 2009) have designed dielectric tensiometers that work
over a much wider range of matric potentials.
In the introductory part of this review, we have introduced
the more common approaches to measuring matric potential
and highlighted some of the issues to be considered. Before
considering these in more detail, the nature of the water
release curve is explored. The purpose is to emphasize the
point that both water content and matric potential need to
be measured if soil water status is to be fully described. It is
not the purpose of the review to catalogue a number of sensors; instead, we wish to outline the concepts and principles
that underpin the different methods of measuring matric
potential. To rationalize our discussion we first consider direct
measurements of matric potential, including the measurement
of relative humidity with psychrometers. Secondly, we explore
the use of indirect measurements of matric potential. Finally,
we attempt to identify some new approaches that are not yet
used, but which may fill gaps left by the current technology.
Matric potential and the water release
characteristic
What is matric potential?
Passioura (1980) provides an excellent account of matric
potential both in the soil and in the plant. He reminds us
that the matric potential was originally introduced by T.J.
Marshall in 1959 and that two instruments, the tensiometer
and pressure plate apparatus, measure or generate a matric
potential consistent with the operational definition: ‘matric
potential is the difference in water potential between a system and its equilibrium dialysate when both are at the same
height, temperature and are subjected to the same external
pressure’. The ‘equilibrium dialysate’ is a solution in equilibrium with the soil solution, separated by a semi-permeable
membrane or barrier, one which allows the movement of
water but not solutes or soil particles.
Both the tensiometer (see below) and the pressure plate
apparatus depend, respectively, on the measurement or creation of a pressure difference across a membrane which is permeable to soil water solution, but not the soil particles.
Passioura (1980) explains that the attractive forces between
liquids and solids consist of the short-range London–van
der Waal’s forces that act over a few molecular layers and the
longer range electrostatic forces present when the surfaces of
the soil particles are charged. In the case of an uncharged
hydrophilic soil, which is an approximation of sand, the
short-range forces and cohesive force between the water molecules interact to produce a concave meniscus at the air–water
interface. This is recorded by the tensiometer, in equilibrium
Matric potential of soil water | 3953
with the soil water, as a negative hydrostatic pressure, which is
called ‘matric potential’. The capillary pressure is frequently
written with the Young–Laplace equation as
ψ=−
2 γCos( θ)
r
(1)
where γ is the surface tension of water, θ is the angle of
contact between the water and soil at the air–soil–water interface, and r is the radius of the pore. Recently there has been
much interest in hydrophobic soils (Hallett et al., 2011), and
here the contact angle is given by the Young equation
Cos (θ) = ( γ SV − γ SL ) / γ LV
(2)
where the interfacial tensions are annotated in Fig. 1. In
hydrophilic soil, Cos(θ)=1 and it becomes smaller in more
hydrophobic soils. In agricultural soils, hydrophobic behaviour is often associated with higher clay content where
organic molecules are adsorbed to the charged clay surfaces
(Matthews et al., 2008) or with plant waxes adsorbed to siliceous sands (Roper, 2005). In clay-rich soils, the charges on
the particle surfaces need to be balanced by counter ions. As
Passioura (1980) explains, these counter ions are not free to
diffuse but are constrained, and this has the effect of creating
a localized osmotic pressure, analogous to that generated by
a semi-permeable membrane. In these soils, matric potential,
ψm, is a combination of the effects of hydrostatic pressure
and osmotic pressure, which cannot be dissected experimentally, and is defined by the equation
P=ψm–πD(3)
where P is the hydrostatic pressure and πD is the osmotic
pressure of the dialysate. In sands with a negligible surface
charge, P=ψm. In saturated clay pastes, a tensiometer can
record an apparent matric potential due to πD.
The water release characteristic
The relationship between soil water content and matric potential is called the ‘water release characteristic’. In an idealized
form, the water release characteristic of a rigid soil (a soil that
does not shrink) can be divided into three regions (Fig. 2).
As the matric potential becomes more negative, initially no
water will drain and the soil is said to be ‘tension saturated’.
Eventually, as the matric potential becomes more negative,
air invades the soil matrix at the ‘air entry potential’ and
this region is called the ‘capillary fringe’. At very low matric
potentials, the water menisci become disconnected and the
soil is said to be at the ‘residual’ water content. These idealized phases can only be easily observed in sand (see Whalley
et al., 2012) where matric potential is usually plotted on a linear scale. In agricultural soils, the water release characteristic
is sigmoidal, highly non-linear, and commonly fitted to the
‘van Genuchten function’ (van Genuchten, 1980). This particular function is popular because fitted parameters can be
Fig. 1. Interfacial tensions of a partly saturated pore.
used to estimate the relative conductivity of unsaturated soil.
The van Genuchten function has also been modified to allow
the hysteretic nature of the water release curve to be described
(Kool and Parker, 1987). An additional complication is that
the temperature dependence of surface tension makes the
water release characteristic itself temperature dependent
(Haridasan and Jensen, 1972), which affects both the wetting
and drying limbs.
Fig. 2. Ideal water release curve.
3954 | Whalley et al.
The water release curves of six soils from Gregory et al.
(2010), which have been subjected to two compaction treatments and de-structuring by shear deformation, are shown
in Fig. 3. These data show that the water release characteristic is greatly affected by soil type and changes in soil structure induced by various types of soil damage. Thus, matric
potential cannot be easily estimated from measurements of
the volumetric soil water content of soil which is the output
of most soil moisture sensors. An additional complication is
that the non-linear nature of the relationship makes the estimation of low water potentials from measurements of soil
water content inaccurate. The difficulty in predicting matric
potential from soil water content makes the use of sensors to
estimate matric potential an important part of most experimental studies into soil–plant relationships, although water
content should still be measured.
Direct measurement of matric potential
The water-filled tensiometer
The most commonly used sensor for soil water matric potential is the water-filled hydraulic tensiometer, described in
its modern form by Richards (1949) and more recently by
Mullins et al. (1986). The concept of the water-filled tensiometer (Fig. 4) has been outlined above. There is a common
view that these tensiometers have a narrow measurement
range and will not record matric potentials smaller than –90
kPa. Figure 5 shows four sets of previously unpublished data
from the work described by Whalley et al. (2008). One of the
tensiometers records matric potentials smaller than –200 kPa,
while the others record matric potentials no smaller than –95
kPa. Marinho et al. (2008) explain that it is entirely possible
for water-filled tensiometers to record matric potentials much
smaller than –90 kPa, and they present a comprehensive thermodynamic analysis of the issue. Pure water has a very high
tensile strength of ~100 MPa (Marinho et al., 2008), so this is
not the limitation to the measurement range of a tensiometer
(Take and Bolton, 2003). Marinho et al. (2008) comment that
in measurements of tensile strength, water has never been successfully subjected to its theoretical limit. Instead, water cavitates at much smaller tensile loads due to imperfections in the
water or in the walls of the tensiometer. Cavitation within the
water is called ‘homogeneous nucleation’ and it arises because
the thermal vibration of molecules can cause microscopic
voids in the bulk liquid. Marinho et al. (2008) calculated the
Fig. 3. Soil water release characteristics of the six soils which had been lightly compressed with a 50 kPa axial pressure (L), moderately
compressed with a 200 kPa axial pressure (H), or shear deformed (S). The data are fitted to the van Genuchten function (lines). The error
bar gives the standard error of the difference [P < 0.001 except for Broadbalk (P)KMg (P=0.341); df=30] for the structural state×matric
potential interaction within a soil. Redrawn from Gregory et al. (2010). Used by permission of the Soil Science Society of America, Inc.
Matric potential of soil water | 3955
Fig. 4. Water-filled tensiometer.
pressure needed to expand such a void in pure water at 20 °C
to be –823 MPa, which has never been achieved experimentally. Impurities in the water probably lead to cavitation at a
smaller tension. However, it is the cavitation at the interface
between the water and the tensiometer cup that is most likely
to be the primary limitation to the measurement range of the
tensiometer. This is called ‘heterogeneous cavitation’.
The progression to heterogeneous cavitation is illustrated
in Fig. 6. In dry soil, as the water in the tensiometer cup
equilibrates with the soil water, the pressure becomes negative. Eventually, air/gas/vapour trapped in the ceramic in
microscopic bubbles expands. Air may also diffuse from the
water in the cup into the bubbles according to Henry’s law.
This situation proceeds until the bubble escapes from the wall
of the ceramic and enters the tensiometer cup. Since absolute vapour pressure cannot be negative, the bubble expands
rapidly until a pressure is reached that is determined by the
phase relationships, usually approximately –100 kPa (relative
to atmospheric pressure). In the tensiometer that recorded a
matric potential of –200 kPa in Fig. 5, the point of cavitation is marked. Following cavitation the matric potentials
recorded by all the tensiometers were similar (between –80
kPa and –95 kPa) until eventually they reported a matric
potential of approximately zero kPa. However, following
cavitation, measurements of soil water content showed that
the soil continued to dry. The point at which the tensiometers
returned to zero kPa corresponds to the point at which air
permeates throughout the ceramic (see Fig. 6) and the tensiometers have collapsed completely. Between cavitation and
complete collapse (see Fig. 5), up to a week elapsed when tensiometers falsely reported that the soil was at a matric potential between –80 kPa and –90 kPa. Such data should always
be viewed with suspicion, since in the field a matric potential
that does not change with time is unlikely.
A key target for civil engineers has been to minimize or prevent cavitation events, which has been achieved by improved
saturation methods. The primary goal of civil engineers
has been to extend the range of matric potentials that can
be measured, and the high capacity tensiometer allows the
direct measurement of matric potentials as low as –1500 kPa.
Take and Bolton (2003) describe the design of a device for
saturating tensiometers by the application of a vacuum (0.05
kPa) to the ceramic, which can then be immersed in water
and degassed under the same vacuum. This is followed by the
application of a high positive pressure to force water into any
of the remaining crevices or unsaturated pores. This approach
was developed by Ridley and Burland (1993). A theoretical
justification of the two-stage saturation process is given by
the equation
Fig. 5. Matric potential data measured with four water-filled
tensiometers used by Whalley et al. (2008). Note that one of the
tensiometers recorded matric potentials as low as –200 kPa (set
3) and it cavitates at its most negative matric potential.
∆P = Pi
(S − Si )(1 − H )
(4)
1- S (1- H )
where ΔP is the increase the pressure needed to achieve a
final saturation, S (here S=1); Pi is the initial pressure; Si is
the initial saturation, and H is Henry’s constant. According
to Equation 4, ΔP can be minimized by a low value of Pi
and a high value of Si, which is what is achieved in vacuum
saturation.
Suction tests on a fully saturated high capacity tensiometer
are shown in Fig. 7a–e. When fully saturated (Fig, 7a), the
3956 | Whalley et al.
Fig. 6. Failure stages of the water-filled tensiometer.
tensiometer accurately follows the applied negative pressure.
When the saturated tensiometer was exposed to low water
potentials by allowing water to evaporate from the surface
of the ceramic, it cavitated (point E, Fig. 7b) and reported
a pressure of about –90 kPa until it was returned to water.
The cavitated tensiometer was not able to track the applied
pressure accurately (compare Fig. 7a and c). At point N in
Fig. 7d, the tensiometer failed completely and the recorded
pressure returned to zero kPa as air permeated the ceramic
cup. Interestingly, when the completely failed tensiometer
(from Fig. 7d) was tested (Fig. 7e) it gave an appearance of a
‘sensible’ result, although here it was known to be erroneous.
There are similarities between these laboratory data and our
field data (Fig. 5) that allow us to identify the failure of the
fully saturated tensiometer (compare Fig. 7b with trace 3),
and that three of the tensiometers had cavitated, by comparison with (Fig. 7c). In contrast to the ephemeral measurement
of low matric potential (approximately –200 kPa; Fig. 5),
Cunningham et al. (2003) report a measurement of –850 kPa
for 8 d.
It appears that the primarily limitation of the tensiometer is not the restricted measurement range, but uncertainty over the saturation state and hence the accuracy of
the recorded pressures. To put it in another way, it may not
be obvious if your tensiometer is working reliably. While we
have shown that commercial tensiometers can record low
matric potentials, this is not the norm. However, we note
that one commercial tensiometer has a lower measurement
limit of –200 kPa (UMS, Munich, Germany): this will be
shown in a following section when the comparisons between
water-filled and porous matrix sensors are explored. From
the preceding discussion, it seems likely that the UMS tensiometer has achieved the extended measurement range by
using a tensiometer design that minimizes heterogeneous
cavitation. As far we know, the designs of tensiometers
used by soil and plant scientists cannot be exposed to the
Matric potential of soil water | 3957
very high pressures that have been reported in the civil engineering community (e.g. 1000 kPa) that are used to saturate
their tensiometers.
Even the civil engineers have challenges to overcome, summarized by Marinho et al. (2008). Those most relevant to soil
and plant science are equilibrium time, air diffusion, longterm measurement, and tensiometer saturation.
The osmotic tensiometer
An alternative to decreasing the pressure at which tensiometers cavitate is to add osmoticum to the water in the tensiometer cup in order to increase the hydrostatic pressure
when the matric potential is zero. Thus, on soil drying, the
pressure in the tensiometer cup remains positive (Peck and
Rabbidge, 1966, 1969). The idea of Peck and Rabbidge is
a good example of lateral thinking; however, their sensor
was prone to measurement errors primarily due to temperature fluctuations and a drift in the pressure corresponding to a zero matric potential. The response of an osmotic
tensiometer to changing temperature and water potentials
has been modelled (Biesheuvel et al., 1999, 2000), and the
tensiometer designs that arose from this work have been
tested more recently by Bakker et al. (2007). They showed
that it was possible to use the osmotic tensiometer reliably
for an extended period of time (Fig. 8). In our view this
recent work on osmotic tensiometers in The Netherlands is
an encouraging technological advance (van der Ploeg et al.,
2010).
Measurement of relative humidity
The water potential (ψw) of soils is determined by the
osmotic and matric forces on water attached to the soil particles (see earlier discussion). The water potential of soil
water—or Gibbs energy of a system in thermodynamic
terms—determines how much work plant roots must expend
Fig. 7. Laboratory studies of tensiometer failure using a high
capacity tensiometer (taken from Whalley et al., 2009; used
by permission of the Soil Science Society of America, Inc.)
The tensiometer had a ceramic with an air entry pressure
of 300 kPa. In these panels, the applied pressure is always
shown by the dashed line and the output recorded by the
tensiometer is shown by the solid line. In (A), a fully saturated
tensiometer is able to follow the allied pressure and the
dashed and solid lines are coincident. In (B), the tensiometer
is allowed to cavitate (point E) by letting water evaporate from
the surface of the ceramic in air. The tensiometer is returned
to water at point G in (B). In (C), the cavitated tensiometer is
tested and it can no longer follow the applied pressure. In (D),
the tensiometer is allowed to collapse completely at point N
by allowing water to evaporate from the ceramic. Finally in (E),
the results of a test on the ‘completely collapsed’ tensiometer
are shown.
Fig. 8. A comparison of soil drying measured with a conventional
water-filled tensiometer and an osmotic tensiometer. The matric
potential was also deduced from measurements of soil water
content. Also shown are the limit to water extraction by plant
roots (approximately –1.5 MPa) and the usual limit of water-filled
tensiometers (approximately –90 kPa). This is redrawn from
Bakker et al. (2007). Used by permission of the Soil Science
Society of America, Inc.
3958 | Whalley et al.
in order to extract this water. The Kelvin equation describes
the principle:
ψw =
RT
Vw
e 
ln  w  (5)
 e0 
where R is the gas constant; T, the temperature in Kelvin;
Vw , the partial molal volume of water; ew, the partial vapour
pressure of the water in the system; and e0, the saturated
vapour pressure. Because ψw is energy per unit volume of
water, which is force per area, or pressure, the units to express
ψw are kPa, or MPa. Using ψw to describe the water within a
system can indicate the ability of water to do work (relative to
pure, unrestrained water) and which direction water will flow:
usually in the direction of more negative potentials within an
isothermal system.
Psychrometry is one method of measuring soil ψw, and
there are several variants, depending on the kind of instrument
that is used. These methods have been reviewed and described
in detail (Boyer, 1995; Campbell, 1990; Oosterhuis, 2007a).
Details of the theory and construction of psychrometers have
been published for some time (Boyer, 1966; Campbell, 1979);
however, their use can be problematic if researchers are not
aware of the basic principles, and particularly the issues that
can introduce errors into measurements.
The three types of instruments that are commonly used are
the dewpoint hygrometer, Peltier (wet-bulb) psychrometer,
and isopiestic thermocouple psychrometer. As water in the
sample itself is difficult to measure without disturbing the
original state of the water, all methods depend on the establishment of water vapour pressure equilibrium between the
water in the sample and the air above the sample under isothermal conditions. The relative humidity of the air is then
sensed in various ways.
One instrument that uses the dewpoint method cools a mirror until water begins to condense onto the mirror surface
when the dewpoint is reached (Decagon WP4, Pullman, WA,
USA). Accurate measurement of the sample temperature
and the mirror temperature allows calculation of the relative
humidity, which is then related to sample ψw using the above
relationship. The dewpoint temperature changes by –0.12 °C
per MPa. The electronics of the instrument allow the mirror temperature to be cycled above and back to the dewpoint
many times to improve the accuracy. The precision of the
method is ±0.1 MPa.
Thermocouple psychrometers make use of the Peltier
effect, which describes the phenomenon when two dissimilar metals are joined within a circuit: a voltage difference is
produced that is proportional to the temperature difference
between the two junctions. One junction can be cooled relative to the other junction by passing a current in one direction,
or warmed by reversing the direction of current flow. Based
on this principle, the Peltier (wet-bulb) type psychrometer
comprises a thermocouple junction held within the air space
of a sealed chamber containing the soil sample [e.g. Wescor
C-52/HR-33T, Logan, UT, USA, which can operate in either
hygrometric (dew point) or psychrometric (wet-bulb) mode].
Alternatively, pre-calibrated in situ thermocouples can be
buried directly in the soil. The thermocouple is protected by a
porous ceramic cup or stainless steel screen that allows water
vapour equilibrium with the surrounding bulk soil (Fig. 9).
Current is passed through the circuit, causing the junction to
cool to a temperature lower than the dewpoint, which causes
water to condense on the thermocouple junction surface. The
current flow is then stopped and the condensed water begins
to evaporate back into the sample chamber air. The change
in temperature caused by the rate of evaporation, which is
a function of the humidity of the sample chamber air, is
measured as a voltage produced between the measurement
and reference junctions. Because humidity in the chamber is
always high (even soils as dry as –4 MPa equilibrate with a
relative humidity of 97% at 25 °C), the measured temperature changes are small, as are the voltages produced, so it is
vital that the system is thermally and electrically insulated.
The output of thermocouples is typically 5 μV per MPa, so
circuitry designed with minimal contact potentials and a sensitive and stable microvoltmeter is required. Each thermocouple has unique electrical output characteristics that require
individual calibration with solutions of known ψw. The accuracy can range between ±0.1 MPa and ±0.01 MPa, depending
on thermal stability and other factors, detailed below.
A system can be measured most accurately when the system itself is minimally disturbed. This can be achieved by
maintaining a state of equilibrium: for instance, pressure
can be quantified by applying a measured counterbalancing pressure so that no flow takes place, no work is done by
the elements that are desired to be measured, and the system remains relatively unchanged. The isopiestic (‘equal
pressure’) psychrometer uses such an equilibrium method.
Instead of a droplet of pure water on the thermocouple junction, a droplet of solution nearly matching the ψw of the sample is applied to the junction, minimizing water vapour flux
from the sample (Boyer, 1966; Fig. 9). If the solution applied
to the junction has a ψw slightly more positive than the sample, the junction cools slightly as water evaporates; a more
negative solution ψw results in condensation and the junction
Fig. 9. An isopiestic thermocouple psychrometer (left) and an in
situ soil psychrometer (right; from Wescor, USA). On the isopiestic
thermocouple psychrometer, note the thermocouple junction
centred in the loop, which holds a droplet of solution of known
water potential. The sample chamber may contain plant tissue,
soil, or a solution such as plant sap.
Matric potential of soil water | 3959
warms. The isopiestic value (equivalent to the sample ψw) is
determined by extrapolating to the zero value (no condensation or evaporation) between the two solutions. The accuracy
of this technique is ±0.01 MPa over the entire range of soil
water contents.
Psychrometric methods rely on using solutions of known
ψw, either for measurement (the isopiestic method) or for
calibration of thermocouple output. Solutions of KCl can
be prepared, although sucrose solutions are potentially less
corrosive. Although the van’t Hoff equation describes the
relationship between solute concentration and ψw, this is
derived from gas laws and applies only to ideal (i.e. weak)
solutions. The solutions needed to achieve low ψw are concentrated to the extent that the dissolved solute molecules no
longer behave like gases, but interact in a complex way. Thus,
empirical relationships are needed to correct for this, and
each solute has a unique osmotic coefficient. For example,
tables are available that give the ψw for sucrose solutions of
known molality and temperature (Michel, 1972).
To make accurate measurements of soil ψw using psychrometric methods, it is important to understand major sources
of error so as to minimize their effect (Brown and Shouse,
1992; Boyer, 1995; Oosterhuis, 2007b). Water vapour equilibrium between the sample chamber air and water within
the sample depends on resistances in the diffusion path.
The further the solution on the thermocouple is from the
isopiestic point, the greater the influence of the resistance
to water vapour flux from the sample to the air; errors can
vary 8–16% (Boyer, 1995). Isothermal conditions are critical and perhaps most difficult to verify. Small temperature
differences (>0.1 °C) between the sample and the measurement junction that are not accounted for will result in error,
and differences <0.001 °C are required for an accuracy of
0.01 MPa. Maintaining the instrument in a thermally stable
environment helps, but usually a housing with large thermal
mass (e.g. an aluminium block or water bath) is required
to dampen changes during measurements. The path of
water vapour flux between sample and thermocouple junction can be complicated if other surfaces (e.g. sample cup
walls) allow water adsorption. Clean surfaces made of, or
coated with, minimally sorptive material reduces this error
and speeds attainment of vapour equilibrium. In preparing
soil samples, loss of moisture to dry air, or absorption of
moisture from the air into very dry samples can be minimized by working quickly and taking appropriate caution,
for instance by using a humid box to handle and transfer
samples.
In summary, isopiestic thermocouple psychrometry is the
most precise and accurate method to measure soil ψw, but
cost, process time per sample, and availability of instrumentation may be other factors to consider.
Indirect measurement
The filter paper method
When a relatively large number of soil samples need to
be measured, and urgency is not an issue, a simple and
cost-effective method of estimating soil ψw is the filter paper
technique (Deka et al., 1995). A filter paper disk is placed in
contact with the soil sample in a sealed container until the
paper is in equilibrium with the soil (7 d may be required).
The gravimetric water content of the paper is determined by
careful weighing, and related to ψw via a calibration curve
determined for the particular type and batch of filter paper.
Soil ψw ranging from –10 kPa to –10 MPa could be measured,
although an accuracy of ±7% (compared with psychrometric
and tension table-derived values) was greatest between –250
kPa and –2.5 MPa, and coefficients of variation were 1–3%
(Deka et al., 1995). Johnston (2000) shows that good comparisons can be obtained between matric potential estimated
with the filter paper method and carefully calibrated gypsum
blocks.
Porous matrix sensors
The concept of the porous matrix sensor has been introduced.
Developments in porous matrix sensors have focused on the
identification of more appropriate porous materials and the
use of improved methods to measure their water content
(e.g. Whalley et al., 2001, 2007, 2009; Malazian et al., 2011),
but this has produced mixed results. Wraith and Or (2001)
described the use of calibrated soil as a reference material for
use with TDR (time domain reflectrometry) probes to infer
the matric potential of soil from its water content.
The most well-known attempt to alter the measurement
range of the gypsum block sensors is probably the ‘Water
Mark®’ sensor which is currently widely used in irrigation
control. This was achieved by increasing the pore size of
the porous matrix and had the desired effect of making the
sensor sensitive to higher matric potentials (i.e. it could be
used in wetter soils), which are helpful in root growth studies.
However, the accuracy of these sensors is not sufficient for
most scientific purposes without calibration. Unfortunately,
the repeatability of calibrations is poor even when the same
sensor is repeatedly recalibrated in the same soil (Spaans and
Baker, 1992). Whalley et al. (2001), based on some idealized
experiments (Fig. 10), showed that a porous matrix could
remain saturated at matric potentials much lower than its
air entry potential if the surrounding soil had pores small
enough to remain tension saturated. It was proposed that
an ‘air entry pipe’ should be used with porous matrix sensors to improve their reliability (e.g. Whalley et al., 2009).
The non-linear nature of electrical resistance measurement
used in ‘Water Mark’® sensors to measure the water content
of the porous matrix is an additional source of variability.
Recently, Decagon Inc. have developed a new commercial
porous matrix sensor which uses dielectric measurement to
monitor the water content of a ceramic material. This is a
relatively low cost sensor but its accuracy is poor (Malazian
et al., 2011). With individually constructed porous matrix
and calibrated sensors, it is possible to achieve good agreement with the water-filled tensiometers (see the following section and Fig. 11; Whalley et al., 2009; Malazian et al., 2011).
Although much effort has been made to increase the matric
potentials at which gypsum blocks can be used, they are in
3960 | Whalley et al.
into account (Whalley et al., 2009), although this may add a
layer of unwanted complexity for some applications of the
sensors.
Lessons from the conjunctive use of direct and indirect
measurements
In Fig. 11, two lessons on the use of water-filled tensiometers
are clearly illustrated. First, as we have discussed in Fig. 5, a
steady output from a water-filled tensiometer must be viewed
Fig. 10. This shows the drainage of a ceramic with an air entry
potential of –4 kPa which is surrounded by silica paste with an
air-entry pressure of –100 kPa. The ceramics were put on a tension
plate set at a matric potential of –4 kPa surrounded by different
amounts of silica paste, and the degree of saturation following a
period of equilibrium is indicated. A saturation of 44% corresponds
to the expected water release characteristic, measured with the
same silica paste boundary. When the coverage of silica paste
increases, the drainage of the ceramic decreases, until eventually
the porous ceramic does not drain at all. Taken from Whalley
et al. (2001) Reprinted from European Journal of Soil Science,
52, Whalley WR, Watts CW, Hilhorst MA, Bird NRA, Balendonck
J, Longstaff DJ. 2001. The design of porous material sensors to
measure matric potential of water in soil. pp. 511–519, Copyright©
2001, with permission from John Wiley and Sons.
fact very useful for measuring low matric potentials. Typically
plaster of Paris drains at matric potentials below –100 kPa
and a plot of log matric potential against log resistance is
generally linear. The use of different mixtures of plaster of
Paris allows these sensors to be adapted to different ranges of
matric potential (Perrier and Marsh, 1958).
The use of plaster of Paris ensures that the electrodes are
surrounded by calcium-saturated water, which buffers the
sensor’s calibration against changes in the electrical conductivity of the soil water. Hysteresis in the relationship
between matric potential and water content within the sensor presents a complication in the use of resistance blocks.
However, Bouget et al. (1958) suggested that it could be
ignored, provided that a range of matric potentials is identified where the hysteresis is low. Modern computers and
microprocessors allow the effects of hysteresis to be taken
Fig. 11. A comparison between water-filled tensiometers and
porous matrix sensors in the laboratory (A) and in the field (B). In
the laboratory comparison, T5× tensiometers were used and in
two cases they recorded matric potentials more negative than –90
kPa (sensors 1 and 3). In one case, the water-filled tensiometer
and porous matrix sensor were in good agreement until
approximately –200 kPa (sensor 3). While the porous matrix senor
continued to show the soil drying, the water-filled tensiometers
failed to track the decreasing matric potential. One of the waterfilled tensiometers indicated that the soil dried to a matric potential
of only –90 kPa and then failed (sensor 2). In the field data (B),
comparison of the water-filled tensiometer with sensor 2 (A)
indicated that it had cavitated. For both laboratory and field data,
complete tensiometer collapse occurred when the porous matric
sensor indicated a matric potential of approximately –350 kPa.
Note that the porous matric sensor used in both laboratory and
field experiments had been previously calibrated.
Matric potential of soil water | 3961
with caution. In Fig. 11a, the calibrated porous matrix sensor
clearly shows that the soil continues to dry, which accurately
reflects the experiment. Similar conclusions can be arrived
at from comparisons between the output from tensiometers
in the field and adjacent porous matrix sensors (see data for
the end of June in Fig. 11b). Secondly, the point of complete
tensiometer collapse corresponds to a matric potential determined by the porous matrix sensor, which is very close to the
expected air entry point of the ceramic of the water-filled
tensiometer. Thus, if cavitated tensiometers are allowed to
continue in drying soil, they will provide information at the
point of complete collapse. We do not recommend the common practice of ‘topping-up’ tensiometers with water. If they
need topping up they have cavitated.
Discussion
In this review we have presented the various options for
measuring matric potential. The most common sensor is the
water-filled tensiometer. We wish to emphasize that even this
instrument is commonly used incorrectly. The experimenter
will often ask, ‘When should I refill?’ We hope to have shown
that if you need to ask this question then your data may not
be reliable. Resisting the temptation to refill, in a drying soil,
will allow the identification of a point in time when the soil
has dried to the air entry potential of the ceramic used to
make the tensiometer bulb (typically –350 kPa). The civil
engineering community has made significant advances in the
use of water-filled tensiometers at very low matric potentials.
It is important that plant scientists are aware of this work
because it will allow them to use currently available tensiometers in a more reliable way, specifically by paying more
attention to saturating the tensiometer, and by identifying
and making use of data traces that appear to come from a
cavitated tensiometer.
An alternative to the water-filled tensiometer is the porous
matric sensor, but presently its accuracy depends on calibrating individual sensors before use. A significant advantage of
some porous matrix sensors is that they are relatively inexpensive. For many applications such as irrigation scheduling,
this is important. Irrigation rates can be adjusted according
to the response of the crop, and highly accurate matric potential data may not be needed. For more accurate estimation
of matric potential with inexpensive sensors, calibration is
recommended. However, the experience of Spaans and Baker
(1992) suggests that this is not without difficulties. Laboratory
data suggest that the use of a simple pipe to allow air to enter
the porous matrix may improve the reliability of porous
matrix sensors, but this remains to be tested in the field.
The psychrometer can be used to measure water potential across a range of soil water contents, and the isopiestic
method is highly precise, but in practice it is not often used
because the measurement is more technically demanding to
make. However, for some applications, such as monitoring
soil during seed germination, it is the only sensible approach.
There is a need for simple measurement methods that can
cover a wide range of matric potentials. One emerging method
is measurement of shear wave velocity. In drying soils, the
decreasing matric potential increases the rigidity of the soil
fabric which results in a higher shear wave velocity. Yang
et al. (2008) have shown that this method compares favourably with the filter paper method; however, we believe that the
shear wave method needs further development. Specifically,
the effect of soil type and condition on the calibration needs
to be understood. Nevertheless, Whalley et al. (2012) have
shown that the shear wave velocity does provide a useful calibration with a wide range of matric potentials (see Fig. 12).
An important issue to consider is whether the measurements are made at the appropriate scale. In this respect, we
are constrained by the dimensions of the sensor, which is typically a few centimetres in size. However, a significant advantage of matric potential, compared with soil water content
measurements, is that interpolation between point measurements can produce a contour map showing lines of equipotential, which has a physical significance. This is not true for
water content measurements, where a similar plot would be
empirical. Recently, neutron radiographs have allowed steep
gradients in water content in adjacent roots to be visualized
(Carminati et al., 2010). Presently, as far as we know, it is
not possible to measure matric potential at the millimetre
scale, which would be required for direct measurement. This
remains a challenge (Chapman et al., 2012).
In order to understand plant behaviour, whether at a molecular or field level, it is necessary to quantify the availability of
water in the soil–plant system. In reporting experiments, it is
helpful to describe the plant growth medium or the soil texture class and to measure its water content, but because the
water release characteristic can change depending on how soil
is handled, these measurements are not sufficient. Current
advances in sensor technology and understanding of sensor
behaviour should make quantification of soil matric potential
standard practice.
Fig. 12. Matric potential plotted as a function of the velocity
of shear waves using data redrawn from Whalley et al. (2012).
Reprinted from Soil and Tillage Research, 125, Whalley WR,
Jenkins M, Attenborough K, The velocity of shear waves in
unsaturated soil. pp. 30–37, Copyright© 2012, with permission
from Elsevier.
3962 | Whalley et al.
Acknowledgements
Rothamsted Research is grant-aided by the Biotechnology
and Biological Sciences Research Council (BBSRC) of the
UK. ESO and WRW. are funded by the 20:20 Wheat® project at Rothamsted Research This work was partly funded
by EPSRC grant EP/H040617/1. We are also grateful for
the support of the Delivering Sustainable Systems project at
Rothamsted Research.
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