3.
Measurement of soil water potential
3.1
Unit of potential
Soil water flows from areas of high potential to areas of low potential. When expressed
in units of mass, units of volume, and units of weight, each potential is respectively called
chemical potential μ [J/kg], soil water potential ψ [Pa], and soil water pressure head h[m].
Here, values shown in brackets [ ] are SI units. The conversions are μ = gh，ψ = ρwgh (ρw =
1000 kg/m3, g = 9.8 m/s2), so that if h = - 0.01m, μ = - 0.098 J/kg, ψ = - 0.098 kPa. In
reverse, ψ = -1 kPa can be converted to h = -10.2cm. The potential of soil water for the
potential energy of unit volume is suction [Pa] or tension [Pa]. Since suction refers to the
process of negative pressure on soil water, it is convenient for unsaturated soil. However,
points deeper than the level of groundwater are saturated and the pressure is positive, and
points shallower than the level of groundwater are unsaturated and the pressure is negative.
When making measurements under these conditions, it is easier to use the phrase soil water
pressure head [cm].
In soil physics, irrigation engineering, agricultural engineering, soil engineering, and
soil mechanics texts, a variety of expressions and units such as potential (cmH 2O), matric
potential (cm), pF value, suction head (cm), and suction (bar) are used and confusing. In
other words, soil water potential is not often considered as energy per unit mass, unit
volume, and unit weight. In general, salt is not contained in soil water, and osmotic
potential is ignored. It is alright to always use ρw = 1000 kg/m3 as the density of water.
When pressure head is negative, it is referred to as suction pressure head or suction head,
and pF is used as its common logarithm. This classical nomenclature continues to be used.
However, when considering agriculture in dry climates, it is not possible to assume that
there is no salt in soil. In that case, it is necessary to introduce the concept of potential. The
following terminologies are used: soil water potential (J/kg), soil water pressure (Pa), soil
water matric head (cm)，and soil water pressure head (cm).
3.2
Definition of total head
As explained previously, the soil water movement cannot be explained simply by the
distribution of water in soil. Therefore, it is necessary to measure the total potential (total
head) gradient, since water flows from areas of high total potential to areas of low total
potential. Total head ht is given as the sum of the following components:
ht = hg + hm + hp + ho + ha
(3.1)
Here, hg is gravitational head, hm is matric head related to the adsorptive forces of the soil
32
matrix, hp is the positive pressure head by hydro-static, ho is the osmotic head due to the
presence of dissolved salts in the bulk solution, and ha is the pneumatic head for air
pressure inside the soil pores.
Gravitational head hg is the vertical distance from the desired standard level to some other
point. If the z axis is defined as positive in the downward direction, hg = z. In unsaturated
conditions, matric head hm is a negative value, and it is equal to suction head hs, its
absolute value. The logarithm for matric suction, expressed in head cm, is pF. In an actual
field, positive pressure head hp is mostly applicable to saturated conditions in areas lower
than groundwater. In an unsaturated soil low in salt, hp = 0，ho = 0, and ha = 0 are applied,
and total head H is defined with the following expression:
H=h-z
(3.2)
Soil water pressure head h can be measured with a tensiometer.
3.3
Measurement of soil water pressure head
3.3.1
Tensiometer
A tensiometer is made up of a porous cup and a part for measuring the pressure inside
the porous cup. Livingston (1908) designed the current apparatus, and it is said that
Gardner’s (1922) description of its functions resulted in the first tensiometer. Now, nearly a
century have passed since then, but no practical instrument has been developed that can
replace the tensiometer for the measurement of pressure head in soil. Here, pressure head is
the pressure that indicates when the water is at equilibrium with soil water, and is a
negative pressure in relation to atmospheric pressure. In general, the SI units for pressure
are Pa (= N/m2). The relational expression １kPa = 10.2 cmH2O is often used to convert
this to a head display (cmH 2O), or in other words to convert it to pressure head. With a
tensiometer, since the ceramic porous cup is generally buried in the soil and connected to a
pressure gauge by a tube (PVC pipe is commonly used), the deaerated porous cup is filled
with water in advance. If the tensiometer is inserted into unsaturated soil, the water
pressure in the porous cup will be higher than the pressure of the soil water, and therefore
the water will pass from the tensiometer, through the saturated porous cup, until
equilibrium condition is achieved with the soil water. After rainfall or a moisturizing
process such as irrigation, the direction of flow will reverse. In general, the water in the
tensiometer is under negative pressure in unsaturated areas. This pressure (the difference
with atmospheric pressure) is measured with a pressure gauge, such as a U-tube filled with
water or mercury, a vacuum gauge (bourdon gauge), or a pressure (differential pressure)
33
converter.
1)
Tensiometer with mercury manometer
When using a U-tube filled with water or mercury, there is a large measurement time
lag, and its degree is dependent on the permeability of the ceramic porous cup. Due to
recent environmental issues, mercury manometers are no longer commonly used, but the
measurement principles are easy to understand.(See Fig. 3.1)
Calculating soil water pressure head
h = -12.55 a + (b + z )
(3.3)
where, a : reading of mercury manometer,
b : distance of mercury surface to soil surface,
z : depth of tensiometer cup.
If the soil becomes dry, the hydraulic flow
between the water in the porous cup and the soil
water will be lost, and measurement will not be
possible. The range of measurement for a
tensiometer depends on the characteristics of the
ceramic porous cup. For example, depending on
the air penetration value, 0.5bar, 1.0bar, and other
tensiometers are available. With the former,
measurements within a pressure head range of up
to approximately -500cmH2O are possible, with
Fig.3.1 Tensiometer set with mercury
manometer
good permeability and little time lag.
For laboratory experiments, small-size tensiometers with pressure converters are
commercially available. High-flow type porous cups are suitable for laboratory
experiments, since the permeability and air penetration value of the porous cup are uniform
and there is little individual difference. If a porous cup with insufficient dearation or poor
permeability is used, air will penetrate during the experiment, and a time lag will occur in
the measurement value. When measuring the changes in pressure head over time to
determine the physical properties of soil using inverse analysis, it is important to rapidly
change the water pressure and examine the response characteristics of each porous cup
before performing an experiment.
2)
Tensiometer with negative pressure gauge
The most inexpensive and commonly used tensiometers are shown in Fig. 3.2: (a)
34
tensiometer with vacuum gauge, (b) tensiometer with pressure transducer and needle
inserted in to septum stopper, and (c) tensiometer with fixable negative pressure gauge.
Fig.3.2
Various types of tensiometer .
The tensiometer with vacuum gauge shown in Fig. 3.2(a) is used commonly for the
cultivation of crops, to determine when to start irrigation. Since the tensiometer shown in
Fig. 3.2(b) measures the air pressure at the top, it corrects the value shown on the gauge’s
LCD (kPa display) to the height of the water column Lb, to measure the pressure head of
the soil. A septum stopper is placed at the top of the tensiometer, and the tensiometer’s
needle is inserted through the stopper to measure the internal air pressure. With this system,
measurements can be made about once/day. In the same way, if measurements are made
several times/day with the tensiometer with fixable negative pressure gauge shown in Fig.
3.2(c), the negative pressure will gradually drop when the digital negative pressure gauge is
removed/mounted, until it nears atmospheric pressure. More precise measurements can be
achieved by installing this apparatus on site with the digital pressure gauge always installed.
For Fig. 3.2(a) and (c), the gauge pressure value (converted to head) and the vertical
distance La, Lc from the gauge’s installation position to the center of the porous cup are
measured, and converted to pressure head. For Fig. 3.2(b), the position of the water su rface
is measured, corrected with the vertical distance L b from the water surface to the center of
the porous cup, and converted to pressure head. In each case, if the tensiometer is installed
perpendicularly, it is necessary to correct the measurement value p (relative pressure of
converted head) for the digital negative pressure gauge with the value for L in order to
determine the value h of the pressure head.
35
h=p+L
(3.4)
For example, if the value of L shown in Fig. 3.2 is 100cm and the value (head
conversion) read on the digital negative pressure gauge is -234cmH2O, the value for
pressure head would be -134cmH2O, or pF = log (-h) = 2.13 when converted to pF value. If
the measurement point becomes deep, the value for L gets larger, and even if pressure head
is measured near saturated soil, the negative pressure level near the top of the tensiometer
becomes larger. For example, when L = 1000cm, even if the value for pressure head is
-10cm, the measured value (water head conversion) for the digital negative pressure gauge
becomes -1010cm from Eq. (3.4), resulting in the measurement of condition that is close to
a vacuum. Therefore, we can see that the limit for this measurement system is a depth of
about 10m.
When soil is dried and the absolute value for pressure head becomes large, or when
measuring a deep location, the negative pressure at the top of the tensiometer will increase,
and therefore air is produced inside the tensiometer. It is necessary for the top of the
tensiometer to have a transparent tube that allows the internal air to be seen, and a septum
stopper or cock that allows the additional supply of degassed water is required.
When supplying degassed water, the pressure in the tensiometer would be released. To
prevent this, the top is designed as a double tube with two cocks, and the bottom cock is
used to supply water. When the system is sealed the upper cock is opened to refill the tube
with degassed water.
<Example 3.1>
Calculating soil water pressure head
Given:
Two tensiometers are installed at the depth of 80 and 100 cm.
p1 = -110.65cm, b1 = 7.4cm, z1 = 80 cm
p2 = -215.38cm, b2 = 7.7cm, z2 = 100 cm
h = p + L= p + (b + z)
p : reading of pressure gauge
b : distance of water surface to soil surface
z : depth of tensiometer cup from soil surface
Find:
1)
Soil water pressure head h
2)
Hydraulic head H
3)
Hydraulic gradient dH/dz
4)
Direction of flux
36
Since tensiometers use water, there is the danger of freezing. To prevent this,
Nakashima et al. (1995) reported that the use of propylene glycol solution is effective
within a certain measurement range in an experiment under cold conditions.
3)
Tensiometer with pressure transducer
There is a tensiometer with a digital negative pressure gauge that is always installed,
with the same design as the removable digital negative pressure gauge shown in Fig. 3.2(c).
This model includes a digital negative pressure gauge, which makes it expensive, but
measurement precision is improved since the changes in pressure caused by the
removal/attachment of the digital negative pressure gauge are prevented.
Automated recording is required when measuring pressure head in situ for long periods
of time or through both day and night. The tensiometer shown in Fig. 3.2(c) is a commonly
used model. For automatic recording, a measurement system that records an output voltage
or output current from a pressure converter to a data logger is required. In general, a
specific direct current voltage is applied to the voltage sensor, voltage is output according
to the measured voltage, and this voltage is amplified and recorded as necessary. There are
voltage sensors for -100kPa, -50kPa, and other measurement ranges, as well as those for
positive pressure, negative pressure, and both positive and negative pressure. It is necessary
to correct the relationship between pressure head (h) and output voltage (v) in advance.
The following linear expression is used for calibration in many cases:
h=aV+b
(3.5)
The correlation coefficient is high at 0.9999.
Here, a and b are fitting parameters. When using
this equipment, although there are some sensors
that can be used simply by using the zero
adjustment and trimmer adjustment, it is
necessary to calibrate each sensor individually,
and then perform a correction again for the
value for the constant b in the expression for the
known pressure head of the constructed system
Fig.3.3 Calibration curve of UNSUC sensor
in actual measurement conditions, to develop a
high-precision measurement system.
As a measurement example, a porous cup was buried to a depth of 20cm, a data logger
was connected to a fixable digital negative pressure gauge, and the pressure head was
measured for 3 days, both day and night in clear weather. The trends in air temperature and
37
results are shown in Fig. 3.4. This shows that the pressure head fluctuates 30cm or more
with a change of 10°C between day and night. Tiny air bubbles formed at the top of the
tensiometer, and it was affected by the differences in temperature between day and night.
To prevent this, it was necessary to record the value of the tensiometer once every day at
either 9am or 10am, for example, and reduce the effects due to temperature such as by
shielding the top of the tensiometer from light and heat, and measuring the soil water
pressure head, as shown by the arrows in the figure for example.
Fig. 3.4
Fluctuation of soil water pressure head reading due to hourly temperature variation.
The 38mm external diameter buried type tensiometer with pressure transducer
(buried-type underground suction gauge, UNSUC) shown in Fig. 3.5(b) was developed as a
method for reducing the effects of temperature. Since this sensor includes temperature
compensation circuitry, pressure head can be measured in a range up to -850cm at a
precision of ±2cm for a change of 15°C. In addition, the pressure transducer is built into the
porous cup, a design that makes it difficult to be affected by air temperature. The change in
pressure head over time measured by the buried-type underground section gauge is shown
in Fig. 3.4. It can be seen that effects due to temperature are reduced by a fluctuation of
about 5cm in pressure head for a 10°C change in air temperature. This buried -type
underground section gauge is applied to control water content in soil, in order to improve
the yield and quality of vegetables (Nishihara et al., 2001). Since irrigation is frequently
used in the cultivation of vegetables and drying is only allowed to about pF2, these sensors
38
can be used all year without air penetrating the porous cup. However, if a significant
amount of drying occurs, such as with the moisture control of trees, a negative pressure of
-850cmH2O or less will occur, air will penetrate the porous cup, and measurement will not
be possible. If this happens, a sensor that can refill degassed water into the porous cup is
required. This type of tensiometer is also available. There are also dual buried type
tensiometers with pressure transducers available that can refill the tube with degassed water,
to accurately measure the total head gradient between two points in the ground.
Fig.3.5
Buried-type tensiometer with pressure transducer.
And, there are waterproof micro tensiometers (with porous cups of 6.3mm external
radius and 10mm length) shown in Fig. 3.5(c), for use in small areas on site to measure
pressure head in the soil. To remove even slight noise for precise measurements, a
measurement system that can supply a stable voltage is required, and it is important to take
measures against noise, such as providing an earth for the data logger. Recently, pressure
sensors with temperature conversion circuitry have been used to precisely measure the
pressure head in soil water with a resolution of 0.1cm and an error of 0.5cm, but such
systems are not cheap. For self-recording tensiometers with pressure transducer shown in
Fig. 3.2(c), it would be difficult to make measurements if the value for L in the figure
approaches 10m, as mentioned before. However, for the buried type tensiometer with
pressure transducer shown in Fig. 3.5(b), there is no restriction for burying depth, as long
as the cord length is sufficient.
Pressure measurement systems for deep layer soil are also being tested overseas. A
waterproof tensiometer with an external diameter of 25mm that can measure pressure
39
within a range of 10kPa to -85kPa (Hobbell 1996) has been developed (See Fig. 3.5(a)). In
addition, the micro tensiometer shown in Fig. 3.5(d) is also available. This is a model for
burying in the soil, and makes it easy to automatically record the pressure head of soil
water (Young 2002).
4)
Buried-type underground suction gauge
As
shown
in
Fig.
3.6,
buried-type
underground suction gauges (UNSUC) have
expensive pressure receivers and electrical
circuitry for converting pressure to voltage
(pressure transducers) in their sensors, and a
porous cylinder that can withstand a negative
pressure of 1 bar. Special cords include a tube
for atmospheric pressure, two wires (+ and -) for
applied voltage (DC10V), and two wires (+ and
-) for measuring output voltage. It is a simple
measurement
that
applies
a
direct-current
voltage (10V) to the sensors and reads the
output
voltage
(from
0mV
to
50mV).
Fig. 3.6
Inner structure of UNSUC sensor
Measurements can be made easily, with just a
battery and a tester.
Buried-type underground suction gauges consume 3mA/second each. In a farm,
although it is preferred to observe with a battery, since 7000mA/s/(6 × 3mA/s) =
388.9>384h = 16day with a 7Ah battery, it can be seen that a battery cannot be used
continuously for 10 days (16 days × 60％ efficiency). Therefore, it is necessary to
continually rec harge the battery while using it, to include a preheat function so that the
battery is consumed only while performing measurements, or to use a separate power
supply such as a solar battery.
As shown in Fig. 3.7, a calibration box, water level adjustment tank, and a scale for
measuring the level are provided to make calibrations. (1) Turn the sensor upside down,
place it in the calibration box, use a screwdriver to remove the screws, and fill the
calibration box with degassed water. (2) Use the bolts to fix the cover on the calibration
box, seal the calibration box, and degas for 12 hours with a vacuum pump with a negative
pressure of approximately 900cm. When air no longer comes out of the screw holes, the
porous cylinder is saturated. At that time, if air penetrates through the O-ring on the
40
calibration box, check for damage to the sensor and packing. (3) As shown in Fig. 3.7, use
the pisco tube to connect the calibration box and water level adjustment tank. This
completes the preparation for calibration. (4) When the water level in the water level
adjustment tank is even with the center of the sensor (center of the porous cylinder), the
pressure head is zero. To confirm this, check the water filled tube for levelness. (5) To
perform an experiment to create a calibration curve, move the water level adjustment tank
down and fix it in place for every 5cm or 20cm of pressure. (6) The difference between the
water level in the water level adjustment tank and the center of the porous cylinder is
pressure head h. Measure the output voltage V of the sensor. (7) Use spreadsheet software
to find the linear regression shown in Eq. (3.5) for the relationship between the pressure
head h and the output voltage V. At this time, when checking the correlation coefficient,
determine whether the linearity is high.
Fig.3.7
Calibration test of UNSUC (buried-type Underground Suction gauge)
<Example 3.1>
Calculating soil water pressure head
Solution:
h, H and dH/dz are calculated using Eq.(3.3) as follows
h1 =p1 + (b1 + z1) = -110.65 + (7.4 + 80) = -23.25
H1 = h1 -z１ = -23.25 -
80 = - 103.25
h2 = p2 + (b2 + z2) = -215.38 + (7.7 + 100) = -22.08
H2 = h2 - z2 = -22.08 - 100 = - 122.08
dH/dz = (H1 -
H2)/(z1 -
z2) = [-103.25 - (- 122.08)]/(80 -
100) = - 0.942
The direction of flux is downward flow, since the value of dH/dz
is negative. If the value of dH/dz is positive, the direction of flux
is upward flow.
41
<Exercise 1>
To understand dynamic flow in an actual field using soil core
sampling method and tensiometer data.
Water balance equation
Input = Output + Change
Rainfall + Irrigation = Evaporation +
Transpiration + Drainage +
Soil water storage(t=t 1) - Soil
water storage (t=t2)
Given:
Following data were obtained on 6 June,
1990
z
Core
layer
Wa
Wb
(cm) Number (mm)
(g)
(g)
5
M1
100 251.27 244.82
15
M2
100 254.62 248.1
25
M3
100 264.52 254.99
35
M4
100 267.39 254.38
50
M5
200 261.94 248.5
Wc
(g)
102.74
100.88
102.78
100.2
96.3
Fig. 3.8
Water balance concept
in an actual field.
Following data were obtained on 6 Oct.
1990.
z
Core
layer Wa
Wb
Wc
(cm)
Number (mm) (g)
(g)
(g)
5
T1
100
250.22 243.77 100.66
15
T2
100
255.8 249.25 103.11
25
T3
100
262.55 254.64 103.43
35
T4
100
261.73 251.77 98.61
50
T5
200
256.68 247.18 94.95
Where, z is soil depth, distance from soil surface to the center of
sampler (cm), Wa is total mass of soil sample plus the cylinder
with saucer (g), Wb is total mass of dry soil sample plus the
cylinder with saucer (g), Wc is mass of the cylinder with saucer (g)
Find:
1)
Calculate water content mass ratio wz, volumetric water content θz, soil water storage Wz on 6
June, 1990.
z
(cm)
Ms
(g)
Mw
(g)
5
15
25
35
50
42
w
(g/g)
d 
3
(g/cm )

3
Wz
3
(cm /cm )
(mm)
Calculate water content mass ratio wz, volumetric water content θz, soil water storage Wz on 6
2)
Oct., 1990.
z
Ms
(cm)
(g)
Mw
(g)
w
(g/g)
d 
3
(g/cm )

3
Wz
3
(cm /cm )
(mm)
5
15
25
35
50
Where, Ms is total mass of dry soil sample (g), Mw is mass of soil water in the soil
sample (g), wz is water content mass ratio (g/g), ρｂ is dry bulk density (g/cm3),
and Wz is soil water storage (mm).
Soil water storage, W (L) per unit area from the soil surface to depth L is given
L
W (t ) z  L    dz
0
For instance, soil water storage at 40 cm depth, W40, is approximated as
corresponding to the area from the soil surface to 40 cm depth in soil water
content profile.
40
W40    dz  10 ( 5  15   25   35 )
0
θ5, θ15, θ25, θ35 represent the mean water content of soil measured in the depth ranges
of
0-10, 10-20, 20-30, and 30-40 cm respectively.
3)
Calculate soil water storage W from z = 0 to L = 60 cm
-----------------------------------------------
Two tensiometer set are installed at the depth of 5, 15, 25, 35, and 50cm.
Given:
Following table data obtained on 6th June, 1990
and 6 th Oct. 1990
Find:
4)
Soil water pressure head h
h = p + L= p + (b + z)
p : reading of pressure gauge (cm)
b : distance of water surface to soil surface (cm)
z : depth of tensiometer cup from soil surface (cm)
5)
6)
7)
Hydraulic head H
Hydraulic gradient dH/dz
Direction of flux
Fig. 3.9
43
Photograph of pressure transducer
placed on tensiometer and digital
read-out.
Calculate h, H and dH/dz
and fill the blanks in following table.
6 June,1990
Z
p
b
h
Average_h
H
dH/dz
(cm)
(cm)
(cm)
(cm)
(cm)
(cm)
(-)
5
-154.625
7.3
5
-150.105
7.8
15
-88.51
7.7
15
-86.955
7.4
25
-71.695
7.2
25
-73.65
7.9
35
-77.115
7.6
35
-78.57
7.8
50
-94.485
7.4
50
-90.62
7.3
6
Oct,1990
Z
p
b
h
Average_h
H
dH/dz
(cm)
(cm)
(cm)
(cm)
(cm)
(cm)
(-)
5
-135.8
7.3
5
-139.865
7.6
15
-82.89
7.1
15
-81.935
7.4
25
-66.975
7.5
25
-68.43
7.7
35
-72.395
7.9
35
-73.55
7.8
50
-88.01
7.2
50
-85.6
7.3
44
8)
Draw the soil water content and hydraulic head profiles on 6 June and 6 Oct., 1990
Fig. 3.10
9)
Soil water content and hydraulic head profiles
Considering the change of soil water storage, determine the direction of water flow at
each depth.
Hint:
The hatched area shown in Fig. 3.10 indicates the change in the soil water
storage, found from the vertical distribution of the soil water content sampled with
the soil core sampling method. However, these changes in soil water storage are
due to either evaporation moving upward to the soil surface, or wastewater
moving downward due to force of gravity, and cannot be explained simply from
the measurement of soil water content. Measurement of changes in soil potential
and total head gradient is required.
45