the design of porous material sensors to measure the matric potential of water in soil

The design of porous material sensors to measure thematric potential of water in soil

W . R . W H A L L E Ya , C . W . W A T T S

a , M . A . H I L H O R S Tb , N . R . A . B I R D

a , J . B A L E N D O N C Kb &

D . J . L O N G S T A F Fa

aSilsoe Research Institute, Wrest Park, Silsoe, Bedford MK45 4HS, UK, and bIMAG, PO Box 43, 6700 AA Wageningen,

The Netherlands

Summary

In recent years the use of porous material sensors for matric potential, which were originally intended for

soil drier than ±100 kPa, has been extended to wet soils. In these wetter soils, unpredictable behaviour of

the sensors has been reported. We have studied the design of porous material sensors of matric potential

in soil and propose a hypothesis to explain this unpredictability, and suggest recommendations for a

design of sensor which will behave more reliably. The development of an experimental porous material

sensor of matric potential based on this design is described. It operates between 0 and ±60 kPa, and both

the drying and wetting moisture characteristics were measured. In this sensor the porous material was a

ceramic and its water content was measured with a dielectric water content sensor. We tested a simple

closed-form hysteresis model to convert the measured water content of the porous material into matric

potential under laboratory conditions. This was shown to give better results than using a calibration based

on the drying moisture characteristic curve, where the predicted matric potentials were too small. The use

of the experimental sensors in the ®eld environment is described. Both types of sensor were installed

using the same procedure. As far as we are aware the experimental sensor described in this paper is the

®rst porous material sensor of matric potential that can be installed in the same way as a conventional

tensiometer. Both conventional tensiometers and the experimental porous material sensors gave similar

estimates of matric potential.

Introduction

The most commonly used sensor for measuring the matric

potential of water in the soil is the water-®lled hydraulic

tensiometer, described by Richards (1949) and more recently

by Mullins et al. (1986). Tensiometers are widely available,

but fail at approximately ±85 kPa and need regular main-

tenance if the soil becomes drier than this limit. Recently,

Ridley & Burland (1999) described how a tensiometer could

be used at matric potentials as little as ±1 MPa. To achieve this

extended range a complex method for sensor preparation is

needed, which involves saturating the tensiometer under very

large positive pressures of the order of several MPa.

Bouyoucos & Mick (1940) described an alternative design

that consisted of a porous plaster of Paris block moulded

around two electrodes, now generally known as a resistance

block. The AC resistance between the electrodes, which is a

measure of water content of the porous material, was

calibrated against matric potential. Typically plaster of Paris

drains at matric potentials less than ±100 kPa, and a graph of

log matric potential against log resistance is generally linear.

The use of plaster of Paris ensured that the electrodes were

surrounded by calcium-saturated water, which buffered the

sensor's calibration against changes in the electrical con-

ductivity of the soil water. Hysteresis in the relation between

matric potential and water content complicates the use of

resistance blocks. Bourget et al. (1958) suggested that it could

be ignored provided a range of matric potentials is identi®ed

where the hysteresis is small. The use of different mixtures of

plaster of Paris allows these sensors to be adapted to different

ranges of matric potential (Perrier & Marsh, 1958). More

recently, Watermark (see Spaans & Baker, 1992) sensors have

been available. These are resistance block type sensors, and

they have been optimized for use between ±10 and ±100 kPa.

However, Spaans & Baker (1992) concluded that they were

inaccurate. A particularly serious problem was that the

calibration curve was not repeatable when the sensor was

used in different soils. This ®nding is supported by the data of

Yoder et al. (1998). Spaans & Baker (1992) observed that,

even for a given soil, the sensor output was not reproducible.

Possible explanations for this include complications intro-

duced by hysteresis and the problem of how the larger pores ofCorrespondence: W. R. Whalley. E-mail: [email protected]

Received 4 September 2000; revised version accepted 12 February 2001

European Journal of Soil Science, September 2001, 52, 511±519

# 2001 Blackwell Science Ltd 511

the sensor matrix drain (associated with matric potentials in

the range ±10 to ±100 kPa) when embedded in a saturated soil

matrix of ®ne pores with smaller air entry potentials.

Since the early work on plaster of Paris sensors for matric

potential (e.g. Bouyoucos & Mick, 1940; Bourget et al., 1958;

Perrier & Marsh, 1958) signi®cant advances have been made

in techniques for measuring soil water content. These advances

have been exploited in the construction of a new set of porous

sensors for measuring matric potential. Hilhorst & de Jong

(1988) reported on the design of a dielectric tensiometer in

which the water content of glass beads in equilibrium with the

soil was monitored by dielectric measurements. This sensor

was calibrated to a matric potential of ±1 MPa. Recently,

Delta-T Devices Ltd (128 Low Road, Burwell, Cambridge,

UK) have marketed a sensor which in essence is similar to that

described by Hilhorst & de Jong (1988). It has granular matrix

material held around a dielectric probe that operates at

100 MHz. At this frequency the error introduced from the

electrical conductivity of the soil water is small. Or & Wraith

(1999) describe how time domain re¯ectance can be used to

measure the water content of several porous ceramic and

plastic materials with different pore sizes. Their design has the

advantage of a stable porous structure, which does not change

with time. This has been a problem for the sensors which use

plaster of Paris as a porous material (Bouyoucos, 1953).

However, stable porous materials such as ceramics tend to

have a narrow pore size distribution. Or & Wraith (1999)

describe how several porous ceramics and plastics with

different pore sizes can be integrated into a single sensor so

that the measurement range can be extended.

Several issues relevant to the design of sensors of matric

potential that use porous material require closer attention.

Porous materials that display hysteresis in their working range

are increasingly being used, contrary to the advice of Bourget

et al. (1958). The implications of this need examination. In this

paper we report on the development of an experimental sensor

of matric potential, which uses a porous ceramic substrate with

known wetting and drying moisture characteristics, monitored

by a dielectric probe. We consider matric potentials between

saturation and ±60 kPa because this allowed us to investigate

hysteresis without complex apparatus. Our aim is to examine

the design requirements of porous sensors of matric potential

without advocating their use in preference to the conventional

tensiometer over this range of matric potentials. The design of

the experimental sensor that we developed avoids the problems

that may occur when the air entry potential of the sensor's

porous matrix is greater than that of the surrounding soil. The

problems associated with inserting transmission lines or

capacitor elements in rigid ceramics are also discussed.

Materials and methods

Choice of porous ceramic

We obtained a range of ceramics with different pore sizes from

Fairey Industrial Ceramics (Industrial Products Division, Filly

Brooks, Stone, Staffordshire, UK). The mean pore size and

porosity of these ceramics and the calculated air entry

potentials are given in Table 1. The moisture characteristic

curve of each ceramic was measured using conventional

tension tables and pressure plate apparatus.

Effect of boundary conditions on the drainage of ceramics

To investigate the drainage of ceramics with high air entry

potentials in comparison with the soil matrix, we embedded

several P5 ceramic blocks, 30 mm diameter by 25 mm long, in

®nely ground silica powder on a tension plate. We used six

ceramic blocks that were covered by varied amounts of wet

silica powder. The air entry potential of the P5 ceramic was

approximately ±4 kPa in comparison with approximately

±100 kPa for the silica powder. The tension plate was set at

±4 kPa, and the equilibrium water contents of the ceramic

blocks were then measured by oven-drying.

Dielectric measurement of the saturation of the ceramic

The sensor was built around an application speci®c integrated

circuit (ASIC) (Hilhorst et al., 1993) developed for dielectric

water content measurement (Hilhorst, 1998). The ASIC

contains analogue and digital electronics needed to measure

the dielectric constant, �, of the ceramic. The measurement

frequency was 30 MHz. In principle any suitable dielectric

water content sensor can be used to measure �, either in the

frequency domain (FD) or in the time domain (TDR).

However, we have used a FD sensor because the electrodes

of such a sensor can be much shorter (< 1 cm) than those

needed for TDR. This makes it possible to use a small ceramic

block. The FD sensor can also be used to measure electrical

conductivity, which could be a useful measure of salinity. The

ASIC is 4 mm by 4.5 mm in size, and it is embedded in a hard

polyurethane moulded cylinder of about 2 cm diameter and

5 cm length. A temperature sensor was placed close to the

Table 1 Pore characteristics of ceramic substrates

Pore size /�m Porosity Air entry potential

Material Grade Mean Maximum /% /kPa

Pyrolitha P5 90 110 45 ±3.4

Pyrolitha P8 30 35 35 ±10

Pyrolitha P9 20 25 35 ±15

Coralithb C0 11 15 35 ±27

Cellotonc V3 3 ± 35±40 ±100

Cellotonc V1 1 ± 35±40 ±300

Composition: aalumino-silicate particles bonded by glass; balumina

particles bonded by glass; cporcelain mullite.

512 W. R. Whalley et al.

# 2001 Blackwell Science Ltd, European Journal of Soil Science, 52, 511±519

sensor's tip. The ¯exible polyurethane output cable contains

the RS232 signal wires and power supply wires. This cable can

be connected to either a Psion-Workabout or PC that runs the

software for further signal processing. A schematic diagram of

our experimental matric potential sensor is shown in Figure 1.

The three holes for the capacitor's sensing elements were

drilled into the ceramic, and then the dielectric sensor was

slotted in place. Various aspects of the design of this sensor are

discussed later. The degree of saturation, S, of the ceramic was

calculated from

S ��p ÿ ��

�dp��

�sp ÿ ��

�dp ; �1�

where �d and �s are the dielectric constants for the air-dry and

the water-saturated ceramic, and � is the dielectric constant of

the moist ceramic in equilibrium with the soil or a tension table

in the laboratory. For brevity and by comparison with the

resistance block we refer to the sensor illustrated in Figure 1 as

a dielectric block.

The use of a hysteresis model to interpret the moisture

characteristic curve

Jaynes (1984) and more recently Otten et al. (1999) have

reviewed advances in models for hysteresis in the moisture

relation for porous media. Our requirement, for a soil matric

potential sensor, is for a closed-form expression that can be

used to calculate matric potentials from the water content or

saturation of the porous ceramic substrate, provided the

wetting history is known. To this end we used the model of

Kool & Parker (1987) which combines the empirical model of

van Genuchten (1980) for the moisture characteristic curve and

the hysteresis model of Scott et al. (1983). The model requires

that the main drying and wetting curves be known and

expressed in terms of the van Genuchten (1980) equation:

S � �Sm ÿ Sr��1� ��h�n�ÿm � Sr; �2�

where S is the degree of saturation, Sm and Sr are the maximum

and residual values of S, respectively, h is the matric potential,

and �, m and n are shape parameters of the curve. We note that

this equation is expressed in terms of degree of saturation

derived from the dielectric sensor, i.e. Figure 1 and Equation

(1), as opposed to the more usual water content. The scanning

curves were derived by scaling these components from the

main hysteresis loop. Drying scanning curves were obtained by

scaling the main drying curve so that it passed through the

reversal point where there was a switch from wetting to drying.

This was achieved using Equation (2) with the parameters Sr,

�, m and n of the main drying curve and a new value of Sm

given by

S�m �S� ÿ Srf1ÿ �1� ��h��n�ÿmg

�1� ��h��n�ÿm ; �3�

where S� and h� are the degree of saturation and matric

potential, respectively, at the reversal point from wetting to

drying, and the parameters Sr, �, m and n in Equation (3) are

those ®tted to the main drying curve. Similarly, wetting

scanning curves were obtained by scaling the main wetting

curve so that it passed through the reversal point where there

was a switch from drying to wetting. This was achieved using

Equation (2) with the parameters Sr, �, m and n of the main

wetting curve and a new value of Sr given by

S�r �S� ÿ Sm�1� ��h��n�ÿm

1ÿ �1� ��h��n�ÿm ; �4�

where S� and h� are the degree of saturation and matric

potential at the reversal point from drying to wetting, and the

parameters Sm, �, m and n in Equation (4) are those ®tted to

the main wetting curve.

Values for the matric potential as a function of degree of

saturation are given by inverting Equation (2) to yield

h � 1

�

Sÿ Sr

Sm ÿ Sr

� �ÿ1m

ÿ1

" #1n

; �5�

with substitution of the van Genuchten parameters, Sr, Sm, �, m

and n, in accordance with the status of the curve.

Figure 1 Schematic diagram of the prototype sensor. The ceramic

was 25 mm long and 19 mm in diameter and its water content is

measured with a frequency domain dielectric sensor.

Porous sensors of water potential 513


Our code based on this algorithm takes as input a sequence

of degree of saturation representing the drying and wetting

history of the ceramic, together with the eight van Genuchten

parameters characterizing the main drying and wetting curves

(Sr and Sm were set to be the same for both curves). Starting on

the main drying curve we examined the sequence of degree of

saturation until a reversal point was identi®ed. Matric

potentials were computed for each degree of saturation up to

this reversal point using the inverse of the van Genuchten

equation, Equation (5), with parameters for the main drying

curve. Examination of the sequence was then resumed to ®nd

the second reversal point. This resulted in the identi®cation of

a set of degrees of saturation belonging to the ®rst wetting

scanning curve. The associated matric potentials were

computed using the inverse of the van Genuchten equation

with parameters obtained from the Kool & Parker (1987)

algorithm for the ®rst wetting scanning curve. Examination of

the degrees of saturation was then resumed along the ®rst

drying scanning curve until a further reversal point was met,

and matric potentials were computed in a similar manner using

the van Genuchten parameters for the ®rst drying scanning

curve. This process was repeated until the saturation sequence

was exhausted.

To test the hysteresis model we exposed our experimental

sensor to a series of random changes in matric potential in the

range 0 to ±60 kPa on a tension table. Our sensors were

immersed in wet silica paste together with conventional

tensiometers, which were used to monitor the matric potential

of the silica paste.

Use of the dielectric block in the ®eld environment

We compared the dielectric block and conventional tensi-

ometers in the ®eld. For both types of sensor a hole slightly

larger than the sensor was augered. When the sensors were

then inserted into the soil, the gap between the sensor and the

soil was ®lled with slurry made from ®ne silica ¯our. We used

four dielectric blocks and four conventional tensiometers.

Figure 2 Drying cycle moisture characteristic curves of various ceramics measured using (a) a tension plate and (b) a pressure plate.



Results

Choice of porous ceramic

Figure 2(a,b) shows the results of degree of saturation against

matric potential for the ceramics listed in Table 1. The range

of matric potentials over which these ceramics drain is

consistent with the ranges of matric potentials that need to

be measured in routine investigations of the soil water. They

are also similar to the range of porous materials that were

identi®ed by Or & Wraith (1999). We used ceramic C0 as the

porous material in our experimental sensor. This ceramic

drains between saturation and ±60 kPa, which makes it

possible to investigate hysteresis phenomena using a conven-

tional tension plate apparatus. However, the results that we

obtained are also relevant to ceramics that drain at much

smaller matric potentials.

In our initial trials the dielectric block indicated that the

ceramic experienced a large amount of drainage at matric

potentials much larger than the air entry potential. Saturation

was reduced to 50% when the matric potential of the tension

plate was diminished from zero to ±0.01 kPa (Figure 3a). For a

ceramic with an air entry potential of ±25 kPa, this was clearly

an artefact and consistent with the gap problem in time domain

re¯ectance that occurs when there is poor contact between the

soil and the transmission line (Knight, 1992; Whalley, 1993).

To overcome this problem we installed the dielectric probe

into the ceramic using electrically conducting, silver-loaded

epoxy glue to ®ll any gap that might exist between the

capacitor elements and the ceramic. Figure 3(a,b) shows both

drying and wetting moisture characteristic curves for the same

sensor with unglued and glued capacitor elements. These data

con®rmed our hypothesis that the gap between the sensing

elements of a dielectric sensor and the porous material was

responsible for the underestimate of the degree of saturation of

the ceramic. Or & Wraith (1999) allude to this problem and

they suggest that a different construction might minimize or

eliminate it. We have shown that electrically conducting glue

can be used to compensate for the dif®culty of making the

holes in the porous material that exactly match the size of the

sensor elements. We do not know, however, whether the glue

will provide a long-term solution.

Figure 4 shows drying and wetting moisture characteristic

curves for 13 prototype sensors. The variation in the data of the

wetting part of the cycle is greater than that in those of the

drying part. The silica paste in which the ceramics were

embedded shrunk slightly during the drying cycle, and so

contact between the ceramic and the silica paste would have

been poorer during the wetting than during the drying. This

may be the explanation for the greater variation in the data

obtained from the wetting part of the cycle.

Effect of boundary conditions on the drainage of ceramics

Our results for the drainage of ceramics that were surrounded

by varied amounts of silica paste with saturated ®ne pores are

Figure 3 Drying (d) and wetting cycle (s) moisture characteristic

curves measured with the prototype sensor shown in Figure 1 based

on the use of ceramic C0. Panel (a) shows data from the sensor

obtained when the sensing elements were simply inserted into holes

drilled in the ceramic. Panel (b) shows data obtained from the same

sensor when the sensing elements were glued in place with

electrically conducting epoxy glue.

Figure 4 Summary of data obtained from calibrating 13 prototype

dielectric blocks over both the drying (d) and wetting cycles (s)

of the moisture characteristic curves. The standard error of the

mean degree of saturation is indicated.



shown in Figure 5. The drainage of water from the ceramic

depends on the boundary conditions. In particular, for a

ceramic of a ®xed size and geometry, the water release

characteristic depends on the area of surface exposed to air at

atmospheric pressure relative to the area in contact with soil

when the air entry potential of the soil is less than that of the

ceramic. These data suggest that it is better to standardize the

ceramic±soil and ceramic±air contact in porous material

sensors of matric potential during both their calibration and

use. To this end we have included access to air at atmospheric

pressure for the draining ceramic (see Figure 1). This will

allow us to install the sensor in exactly the same way as a

conventional tensiometer.

A hysteresis model to interpret the moisture characteristic

curve

For some of our sensors the ®t to both wetting and drying

curves was poor when the ®tting procedure was constrained by

forcing m and n to be the same for both the wetting and the

drying. Kool & Parker (1987) made a similar observation

when they ®tted the model to data from soil. To improve the ®t

we used the best ®t values of m and n for both the main wetting

and drying moisture characteristic curves. We found that this

could lead to the main wetting and drying curves crossing

small saturations. We also found that the scanning curves

could stray across the main wetting curve. When this occurred

we adopted the main wetting curve as the appropriate

calibration curve after the point of cross-over. Figure 6 shows

both main drying and wetting curves and some calculated

scanning curves for one of the dielectric blocks. The curves

plotted in Figure 6 are for best ®t wetting and drying curves

which cross each other.

The results of the laboratory tests of the hysteresis model are

shown in Figure 7, and the results of a different experiment are

plotted in Figure 8 against time. The data in both Figures 7 and

8 showed that the use of a hysteresis model to convert the

degree of saturation of the ceramic into matric potential gave

better results than the drying moisture characteristic curve

alone.

The dielectric block in the ®eld environment

The output for both a conventional tensiometer and a dielectric

block is shown in Figure 9. For clarity the output from one of

each type of sensor is shown. Variation between sensor output

was evident for both types of sensor. It is likely that this results

from the natural spatial variation. The dielectric blocks

indicated a smaller matric potential than the tensiometers.

This may be in part due to a genuine difference, but it is likely

that it is also due to the poorer performance of the dielectric

blocks when operating on the start of the drying curve where

the slope of the moisture characteristic is steep. Later, as the

Figure 5 Effect of boundary conditions on the drainage of P5

ceramic. The air entry potential of the ceramic is approximately

±4 kPa and the air entry potential of the silica paste is in the order

of ±100 kPa. Initially the ceramics were saturated under vacuum and

then covered with different amounts of saturated silica paste as

indicated in the diagram. The matric potential of the tension plate

was set at ±4 kPa and the saturation of the ceramic is given in the

diagram. All the ceramics were placed on the same tension table,

and the saturation for the top case is consistent with the previously

measured data in Figure 2.

Figure 6 Hysteresis model of Kool & Parker (1987). The data

plotted were obtained using the model parameters for one of the

dielectric blocks developed in this work. Both main drying and

wetting curves are shown, which were obtained from ®ts to

measured data. The wetting and drying scanning curves shown are

predicted from the hysteresis model and calculated from simulated

data.



soil dried, the matric potentials derived from the dielectric

blocks had a smaller range than those indicated by the

hydraulic tensiometer. This ®eld comparison of the dielectric

blocks and conventional tensiometers demonstrated that the

porous material sensor of matric potential can be installed in

the ®eld in exactly the same way as a tensiometer.

In this ®eld experiment the degree of saturation of the

ceramic was recorded with time, and the data were post-

processed to determine how matric potential changed with

time. Power failures at various times in some of our

experiments resulted in our losing the saturation history, and

this in turn meant that we could not compute the matric

potential with the hysteresis model. We would advise real-time

processing of the ceramic saturation data and advise against

storing these data for post-processing.

Discussion

The development of our experimental sensor has raised

important issues that are generally relevant to the class of

sensors for matric potential based on the use of porous

materials, in particular the importance of air access to the

porous material to allow the porous material to drain

predictably. In calibration of the Watermark sensor by

Spaans & Baker (1992), variable and uncontrolled contact

between air and the porous material may well be the

explanation for the apparently poor performance of the

sensors. The original plaster of Paris sensors, described by

Bouyoucos & Mick (1940), were intended for use in soil drier

than ±100 kPa. Under these conditions it is probable that most

of the outside surface of the plaster of Paris is close to an air±

water interface. In wetter conditions (> ±100 kPa), as intended

for the Watermark sensor, the amount of contact between the

surface of the porous material and the air is likely to be less

predictable, because the air entry potentials of many soils will

Figure 7 Comparison between known matric potentials and those

calculated from the prototype dielectric block using either (a) the

drying cycle moisture characteristic curve or (b) the Kool & Parker

hysteresis model. These data were obtained from an experiment in

which the dielectric blocks were placed on a tension table and then

the matric potential was adjusted at random between 0 and ±60 kPa.

The sequence of matric potentials was 0, ±39.1, ±32.6, ±18.3, ±5.1,

±48.1, ±11.5, ±46.1, ±14.4, ±37.9, ±17.3, ±20.8, ±45.6, ±28.3, ±42.8,

and ±23.5 kPa.

Figure 8 Comparison between the output of a conventional

tensiometer (curve a) and a dielectric block with time when placed

on a tension table where the matric potential was adjusted in

random movements. For the dielectric block both output calculated

from the model of Kool & Parker (1987) (curve b) and that

calculated using the drying cycle of the moisture characteristic

curve (curve c) is given.

Figure 9 Comparison of the output of a conventional tensiometer

(dotted line) and a dielectric block (solid line) from a ®eld

experiment in which the sensors were installed in the surface of a

bare seed-bed.



fall within the intended range of operating potential of the

sensor. Yoder et al. (1998) found that when Watermark sensors

were calibrated in a drying cycle there was initially little

change in the sensor output. This accords with inhibited

drainage of the sensor matrix because it is surrounded by wet

soil with a smaller air entry potential. White et al. (1972) have

shown that boundary effects can affect the moisture char-

acteristic of porous materials. In particular they found that the

ratio of exposed surface area to the volume signi®cantly

affected the moisture characteristics at matric potentials

greater than the air entry potential. Such phenomena are

clearly demonstrated in our data in Figure 5. This suggests that

it would be better to standardize the geometry of the air±

ceramic interface, so that the shape of the moisture

characteristic at matric potentials greater than their air entry

potential is predictable. Perhaps a more serious point is that

without provision for air invasion, sensors made of porous

material will not register matric potentials greater than the air

entry potential of the soil if the air entry potential of the soil is

less than that of the sensor's matrix. Our experimental sensor

embedded in silica paste with much smaller air entry potential

followed the output of a tensiometer successfully, and it

demonstrates that air must be able to invade the draining

porous material. An advantage of designing the ceramic so that

air can invade is that it is then possible to install the sensors in

the ®eld in exactly the same way as a tensiometer. Surrounding

the sensor with a paste with a very small air entry potential

also has the advantage of providing good connection between

the soil and the sensor. This may help minimize the hydraulic

decoupling that Or & Wraith (1999) observed in their sensor in

dry soil.

We have shown that a model of hysteresis can be used in

both laboratory and ®eld conditions to track changes in matric

potential in a porous material in equilibrium with the soil.

Comparison of data from the dielectric block and the

conventional tensiometer (Figure 8) suggests that time

responses of these two types of sensor are similar. It is

reasonable to expect the response of sensors based on the use

of a porous material to become slower as the size of the porous

material increases. Modern dielectric sensors provide the

possibility of measuring the water content in volumes of the

order of a few cubic millimetres. In this paper we were

concerned with sensors that operated in the fairly wet soils

(wetter than ±60 kPa). Slow time responses are likely to be a

greater problem at much smaller matric potentials (less than

±100 kPa) where the hydraulic conductivity of the soil will be

very small. In this situation a small volume of porous material

in the dielectric block may well be an important design

consideration. This aspect needs further study.

The hysteresis model that we have used does not close the

scanning loops, as would be expected (Marshall et al., 1996).

Thus, the calibration may drift after several wetting and drying

cycles because the model that we used does not accurately

describe hysteresis. However, we found no clear evidence of

calibration drift in our laboratory experiments when we

compared tensiometer readings with those from the dielectric

blocks. In practice, the matric potential returns to zero when

the sensor matrix saturates and the program that follows the

hysteresis can be restarted. This would help to minimize any

drift. In the absence of periodic saturation of the soil and

sensor matrix, it may be necessary to consider more

sophisticated models for hysteresis in the moisture character-

istic (e.g. Otten, 1994), which have closed scanning loops.

However, even for these models the issue of calibration drift

would need to be investigated.

The simplicity of the suggestion of Or & Wraith (1999) for

the use of several different porous materials in a single sensor

to cover a wide range of matric potentials is attractive. In this

design, Or & Wraith (1999) showed that it might not be

necessary to use a model for hysteresis. The ceramics that we

have identi®ed could be used in the same way as described by

Or & Wraith.

Conclusions

We have demonstrated serious limitations of porous sensors

for measuring matric potential, and we describe the steps that

need to be taken to minimize their impact. We have shown that

it is possible to use simple models of moisture characteristic

hysteresis to track changes in matric potential from measure-

ments of water content. We have also demonstrated that for

porous sensors of matric potential the geometry of the contact

between soil and sensor can affect the response of the sensor

when the air entry pressure of the soil is much less than the air

entry pressure of the porous material used in the construction

of the sensor.

Acknowledgements

This work was funded by EU grant FAIR1 PL95 0681 and by a

competitive strategic grant to Silsoe Research Institute

awarded by the Biotechnology and Biological Sciences

Research Council. We thank an anonymous referee for

constructive comments on our script and Dr W.E. Finch-

Savage for the use of his ®eld site to test the sensors.

References

Bourget, S.J., Elrick, D.E. & Tanner, C.B. 1958. Electrical resistance

units for moisture measurements: their moisture hysteresis,

uniformity and sensitivity. Soil Science, 86, 298±304.

Bouyoucos, G.J. 1953. More durable plaster of Paris blocks. Soil

Science, 76, 447±451.

Bouyoucos, G.J. & Mick, A.H. 1940. Electrical Resistance Method

for the Continuous Measurement of Soil Moisture under Field

Conditions. Technical Bulletin 172, Michigan Agricultural

Experimental Station, East Lansing, MI.



Hilhorst, M.A. 1998. Dielectric characterisation of soil. Doctoral

thesis, Wageningen Agricultural University, Wageningen.

Hilhorst, M.A. & de Jong, J.J. 1988. A dielectric tensiometer.

Agricultural Water Management, 13, 411±415.

Hilhorst, M.A., Balendonck, J. & Kampers, F.W.H. 1993. A broad-

band width mixed analogue/digital integrated circuit for the

measurement of complex impedances. IEEE Journal of Solid

State Circuits, 28, 764±769.

Jaynes, D.B. 1984. Comparison of soil-water hysteresis models.

Journal of Hydrology, 75, 287±299.

Knight, J.H. 1992. Sensitivity of time-domain-re¯ectometry measure-

ments to lateral variations in soil water content. Water Resources

Research, 28, 2345±2352.

Kool, J.B. & Parker, J.C. 1987. Development and evaluation of closed

form expressions for hysteretic soil hydraulic properties. Water

Resources Research, 23, 105±114.

Marshall, T.J., Holmes, J.W. & Rose, C.W. 1996. Soil Physics.

Cambridge University Press, Cambridge.

Mullins, C.E., Mandiringana, O.T., Nisbet, T.R. & Aitken, M.N. 1986.

The design, limitations, and use of a portable tensiometer. Journal

of Soil Science, 37, 691±700.

Or, D. & Wraith, J.M. 1999. A new soil matric-potential sensor based

on time-domain-re¯ectometry. Water Resources Research, 35,

3399±3407.

Otten, W. 1994. Dynamics of water and nutrients for potted plants

induced by ¯ooded bench fertigation: experiments and simulation.

Doctoral thesis, Wageningen Agricultural University, Wageningen.

Otten, W., Raats, P.A.C. & Kabat, P. 1999. Hydraulic properties of

root-zone substrates used in greenhouse horticulture. In:

Characterization and Measurement of the Hydraulic Properties

of Unsaturated Media; Proceedings of an International Workshop,

22±27 October 1997 (eds M.T. van Genuchten, J. Ley & L. Wu),

pp. 477±489. University of California, Riverside, CA.

Perrier, E.R. & Marsh, A.W. 1958. Performance characteristic of

various electrical resistance units with gypsum materials. Soil

Science, 86, 140±147.

Richards, L.A. 1949. Methods for measuring soil moisture tension.

Soil Science, 68, 95±112.

Ridley, A.M. & Burland, J.B. 1999. Use of the tensile strength of

water for the direct measurement of high soil suction: discussion.

Canadian Geotechnical Journal, 36, 178±180.

Scott, P.S., Farquhar, G.J. & Kouwen, N. 1983. Hysteretic effects on

net in®ltration. In: Advances in In®ltration: Publication 11-83, pp.

163±170. American Society of Agricultural Engineering, St Joseph,

MI.

Spaans, E.J.A. & Baker, J.M. 1992. Calibration of Watermark soil

moisture sensors for soil matric potential and temperature. Plant

and Soil, 143, 213±217.

Van Genuchten, M.T. 1980. A closed-form equation for predicting the

hydraulic conductivity of unsaturated soils. Soil Science Society of

America Journal, 44, 892±898.

Whalley, W.R. 1993. Considerations on the use of time-domain-

re¯ectometry (TDR) for measuring soil water content. Journal of

Soil Science, 44, 1±9.

White, N.F., Sunada, D.K., Duke, H.R. & Corey, A.T. 1972.

Boundary effects in desaturation of porous media. Soil Science,

113, 7±12.

Yoder, R.E., Johnson, D.L., Wilkerson, J.B. & Yoder, D.C. 1998. Soil

water sensor performance. Applied Engineering in Agriculture, 14,

121±133.



the design of porous material sensors to measure the matric potential of water in soil

Documents