*2.2.1. Measuring soil water potential components*

**Name Symbol Definition Dimensions SI units**

Soil water potential *ψ<sup>t</sup>* Energy per volume ML-1T-2 N m-2 Soil water potential head *H* Energy per weight L m

Total soil water potential is defined as the amount of work per unit quantity of pure water that must be completed by external forces to transfer reversibly and isothermally an infinitesimal amount of water from the standard state to the soil at the point under consideration [3]. The transformation of water from the reference states can be divided into the components caused by each force field acting on soil water. These components are forces caused by gravity,

Following are presented the definitions of the most important components of total soil water

*Gravitational potential* (*ψz*) is defined as the difference in energy per unit volume or weight between standard water and soil water due to gravity. This component quantifies the effect of

*Hydrostatic pressure potential* (*ψp*) is defined as the difference in energy per unit volume or weight between standard water and soil water due to the pressure exerted by overlying free water. This component quantifies the pressure effect from overlying water on the energy of

*Osmotic (solute) potential* (*ψs*) is defined as the difference in energy per unit of volume or weight between standard water and soil water due to the presence of solutes. This component

*Matric potential* (*ψm*) is defined as the difference in energy per unit volume or weight between standard water and soil water due to capillarity and adsorption. This component quantifies

*Air potential* (*ψa*) is defined as the difference in energy per unit volume or weight between standard water and soil water due to effect of soil air pressure. This component quantifies the

Some of the components of water potential can be neglected like osmotic pressure and also the effect of air pressure in most of the cases due to its low effect (and estimation difficulty) on the global soil water potential. Following these assumptions, total soil water potential head or

 y  y

*z p sma* (4)

 y

=+++ +

**Table 1.** Different unit systems for expressing soil water potential (adapted with permission from [4]).

T-2 J kg-1

Chemical potential *μt* Energy per mass L2

138 Groundwater - Contaminant and Resource Management

hydrostatic pressure, capillarity, solute, air pressure, and swelling [5].

potential (*ψ*) which is represented by the sum of its active components:

yy

the gravitational force field on the energy of soil water.

quantifies the effect of solutes on the energy of soil water.

hydraulic head is when expressed per unit weight:

the effect of the capillarity and adsorption on the energy of soil water.

effect of the air pressure in soil porous system on the energy of soil water.

water.

 y **Tensiometer** is a measuring device used to determine matric water potential (*ψm*) in the vadose zone. The device consists of an airtight glass or plastic tube filled with water and connected to a porous cup at the bottom. Tensiometers are placed in the soil and the water inside the tube comes into equilibrium with the soil solution (i.e. it is at the same pressure potential as the water held in the soil matrix). Then, the reading is collected from the pressure gauge (water or mercury) at the top of the device. Typically, the measurement range is 0–80 centibars. These devices are easy to use and inexpensive. They require a close contact with surrounding soil around porous cup that might sometimes be hard to achieve, for example, on swelling or coarse soil types. More details about this method can be found in [6].

**Piezometers** are used to measure hydrostatic potential (*ψp*) and positive pressure head (*h*), since they are used below water table. A piezometer is a hollow plastic tube installed in the soil, which is open to the atmosphere at the top and located in the saturated soil at the bottom. The bottom of the tube has perforated screened section which allows water to enter the piezometer. Water rises in the tube until the hydrostatic pressure of the water inside the tube is the same as hydrostatic pressure of surrounding soil water. Hydrostatic pressure can be calculated from the water level readings in the piezometer.

**Thermocouple psychrometers** are used to measure soil matric potential based on the relative humidity of the water vapour in the soil [7]. At equilibrium, the vapour water potential is equal to the liquid water potential. Since the vapour and liquid are at the same elevation, the components of the soil water potential measured by the psychrometer are the sum of the matric and osmotic potential, assuming atmospheric air pressure. The unit consists of a measuring device and soil sensor, which is buried into the soil (ceramic cup) and connected via cable to a measuring device. Electrical circuit (thermocouple) is used to measure temperature. The output of the psychrometer is expressed in voltage, which represents the difference in temperature measured in the ceramic cup and the reference (constant) temperature. If the soil is dry, the output voltage will be greater. A calibration equation is used to convert readings to water potential.

**Electrical resistance sensors** measure the electrical resistance of a porous block that is in contact with surrounding soil. Electrical resistance between electrodes embedded in a porous medium (block) is proportional to its water content, which is related to the soil water matric potential of the surrounding soil. Electrical resistance decreases as the soil and the block lose water. The most common sensor is a gypsum block. The block is part of a simple DC circuit and buried in the soil. Cable is connecting the block and a voltage measuring device. These sensors are not very accurate [8] and are best suited to manage irrigation systems if precise measurements are not needed.

Soil water constants are used to describe water content across different water potential range in soil and are related to the energy required to extract water from soil (**Figure 1**).

*Maximal water capacity* (SWMAX) is the maximal water content of soil, that is, at (or near) saturation. The potential energy gradient is downward through the soil profile, mainly due to gravity forces and through macropores.

*Field capacity* (FC) is the amount of water that remains 2–3 days after the saturation of a soil with water after gravity movement of water has largely ceased. The water is held in the soil at tension of -0.33 bar (pF 2.0) by matric forces (in micro‐ and mesopores). Water held between saturation and field capacity is subject to free drainage over short time periods, and it is generally considered unavailable to plants.

*Permanent wilting point* (PWP) is the lowest amount of water in the soil at which matric forces hold water too tight for plant extraction (-15 bar or pF 4.2).

*Available field capacity* (aFC) or plant available water (PAW) is the difference between field capacity (FC) and wilting point of a soil. It is considered as water available for plants to extract from the soil moisture zone. Plant available water is mostly located in soil micro‐ and meso‐ pores.

**Figure 1.** Scheme of the mayor soil water constants: maximal water capacity, field capacity, permanent wilting point and plant available water depending on the soil water potential range.

#### **2.3. Soil water retention curve**

Soil water retention curve represents the relationship between the water content (*θ*), and the soil water potential (*h*). In the literature, different names could be found such as soil water characteristic curve, capillary pressure saturation relationship, and/or pF curve. The water retention curve provides information on how tight water is held in soil porous system and how much energy would need to extract it from the different pores. The main characteristics of soil water retention curves are visible from **Figure 2** where the *x*‐axis shows the relative water content in the soil (*θ*), while the *y*‐axis shows pressure head (*h*). If the pressure head values are close to 0, the soil is almost completely saturated, as *θ* decreases, the binding force is getting stronger (more energy is needed to extract water from the soil). At the low‐pressure head values (close to the border wilting point pF 4.2 or -15,000 cm), the water that is retained in the soil is located in the smallest pores.

Soil water constants are used to describe water content across different water potential range

*Maximal water capacity* (SWMAX) is the maximal water content of soil, that is, at (or near) saturation. The potential energy gradient is downward through the soil profile, mainly due to

*Field capacity* (FC) is the amount of water that remains 2–3 days after the saturation of a soil with water after gravity movement of water has largely ceased. The water is held in the soil at tension of -0.33 bar (pF 2.0) by matric forces (in micro‐ and mesopores). Water held between saturation and field capacity is subject to free drainage over short time periods, and it is

*Permanent wilting point* (PWP) is the lowest amount of water in the soil at which matric forces

*Available field capacity* (aFC) or plant available water (PAW) is the difference between field capacity (FC) and wilting point of a soil. It is considered as water available for plants to extract from the soil moisture zone. Plant available water is mostly located in soil micro‐ and meso‐

**Figure 1.** Scheme of the mayor soil water constants: maximal water capacity, field capacity, permanent wilting point

Soil water retention curve represents the relationship between the water content (*θ*), and the soil water potential (*h*). In the literature, different names could be found such as soil water characteristic curve, capillary pressure saturation relationship, and/or pF curve. The water retention curve provides information on how tight water is held in soil porous system and

in soil and are related to the energy required to extract water from soil (**Figure 1**).

gravity forces and through macropores.

140 Groundwater - Contaminant and Resource Management

generally considered unavailable to plants.

pores.

hold water too tight for plant extraction (-15 bar or pF 4.2).

and plant available water depending on the soil water potential range.

**2.3. Soil water retention curve**

**Figure 2.** Water retention curve example for loam, sand, and clay texture soil based on soil hydraulic parameters taken from [9].

Coarser textured soils (sandy) lose water more quickly than fine textured soils (clay) as a direct reflection of the size distribution of pores in the soil. As most of the pores in the coarser soils have greater diameter, water will percolate during small negative soil water potential, while in the finer textured soils (clay, loam, silty loam), water drainage occurs at very high values of negative soil water potential.

**Hysteresis** in soil is defined as the difference in the relationship between the water content of the soil and the corresponding water potential obtained under wetting and drying process. Soil water retention curve is usually developed by going from high to low water content producing drying curve. However, if the measurements started from saturated conditions (e.g. pressure plate), this would produce wetting curve. It means that water content in the drying (or drainage) curve of water potential is larger than water content in the wetting curve for the same value of water potential.

Most common methods for soil water retention curve estimation are pressure plate and pressure cells, although there are other methods to determine its shape like hanging water column, suction tables, or soil freezing.

**Pressure plate** has a range for measuring water retention curve (*h*=0 to -15,330 cm) and usually can provide very accurate measurements in the wet range. The pressure plate was introduced in the 1930s by Richards [10]. Device is used to make indirect measurements of soil pressure head (matric potential) by imposing a known pressure potential on saturated soil samples until free water no longer flows from the system. When the sample comes to equilibrium, its water potential will be equivalent to the applied pressure.

**Pressure chambers** are usually used to estimate the dryer part of soil water retention curve. Pressure chambers that hold a single intact soil sample are called pressure (tempe) cells and are usually used for *h* range from 0 to -1000 or even -3000 cm. The cell consists of plastic housing, a porous ceramic plate at the bottom, a metal ring to secure the soil sample and a rubber sealing between the housing and the ring. The positive known pressure is applied to the sample to extract water and the sample is weighted at specific pressure values (when equilibrium is reached).

The shape of water retention curve can be explained using a wide range of mathematical expressions [11–13]. However, most common expression used is the van Genuchten‐Mualem one [14]:

$$\theta\left(h\right) = \theta\_r + \frac{\theta\_s - \theta\_r}{\left(1 + \left|\alpha h\right|^n\right)^m} \text{ for } h < 0 \tag{6}$$

$$\theta\left(h\right) = \theta\_s \text{ for h} \ge 0 \tag{7}$$

$$K\left(h\right) = K\_s S\_e^l \left(1 - \left(1 - S\_{e^\*}^{\frac{1}{m}}\right)^m\right)^2 \tag{8}$$

$$S\_e = \frac{\theta - \theta\_r}{\theta\_{s-}\theta\_r} \tag{9}$$

$$\text{Term} = 1 - \frac{1}{n}; n \ge 1 \tag{10}$$

where *θr* and *θ<sup>s</sup>* denote residual and saturated volumetric water content [L3 L-3], respectively, *Ks* is the saturated hydraulic conductivity [LT-1], *Se* is the effective saturation, *α* [L-1] and *n* [-] are the shape parameters, and *l* [-] is a pore connectivity parameter. The pore connectivity parameter value is usually taken from an average for many soils (l=0.5) [15].

The hydraulic conductivity characterizes the ability of a soil to transmit water and as such is inversely related to the resistance to water flow [16]. The hydraulic conductivity decreases as soil becomes unsaturated and smaller quantity of pore space is filled with water. The unsatu‐ rated hydraulic conductivity function shows the dependency of the hydraulic conductivity on the various ranges of water content or pressure head. Hydraulic conductivity of saturated soil is much higher in coarser texture soils (sand) compared with clay or loam texture soils.

The fitting of soil water retention curve data can be obtained by optimizing some of the parameters used in the equation. This requires non‐linear optimization method. The RETC (RETention Curve) program [17] may be used to predict the hydraulic conductivity from observed soil water retention data assuming that one observed conductivity value (not necessarily at saturation) is available. The program also permits one to fit analytical functions simultaneously to observed water retention and hydraulic conductivity data.

## **2.4. Soil hydraulic properties estimation**

Most common methods for soil water retention curve estimation are pressure plate and pressure cells, although there are other methods to determine its shape like hanging water

**Pressure plate** has a range for measuring water retention curve (*h*=0 to -15,330 cm) and usually can provide very accurate measurements in the wet range. The pressure plate was introduced in the 1930s by Richards [10]. Device is used to make indirect measurements of soil pressure head (matric potential) by imposing a known pressure potential on saturated soil samples until free water no longer flows from the system. When the sample comes to equilibrium, its water

**Pressure chambers** are usually used to estimate the dryer part of soil water retention curve. Pressure chambers that hold a single intact soil sample are called pressure (tempe) cells and are usually used for *h* range from 0 to -1000 or even -3000 cm. The cell consists of plastic housing, a porous ceramic plate at the bottom, a metal ring to secure the soil sample and a rubber sealing between the housing and the ring. The positive known pressure is applied to the sample to extract water and the sample is weighted at specific pressure values (when equilibrium is

The shape of water retention curve can be explained using a wide range of mathematical expressions [11–13]. However, most common expression used is the van Genuchten‐Mualem

> ( ) for h 0 (1 ) *s r <sup>r</sup> <sup>n</sup> <sup>m</sup> h*

a

( ) for h 0 *<sup>s</sup>*

 q

( ) <sup>1</sup>

*e*

*S* q q

where *θr* and *θ<sup>s</sup>* denote residual and saturated volumetric water content [L3

parameter value is usually taken from an average for many soils (l=0.5) [15].

<sup>2</sup> (1 (1 ) )

*r*

*Ks* is the saturated hydraulic conductivity [LT-1], *Se* is the effective saturation, *α* [L-1] and *n* [-] are the shape parameters, and *l* [-] is a pore connectivity parameter. The pore connectivity

*s r*

q q-

q q

*h*

<sup>+</sup> (6)

*h* = ³ (7)


<sup>1</sup> *m n* <sup>1</sup> ; >1 *<sup>n</sup>* = - (10)

L-3], respectively,

*l m <sup>m</sup> K h KS S* = -- *s e <sup>e</sup>* (8)


column, suction tables, or soil freezing.

142 Groundwater - Contaminant and Resource Management

reached).

one [14]:

potential will be equivalent to the applied pressure.

q

 q

q

Modelling of water flow and solute transport in soils is predefined with hydraulic properties of studied soil system. Soil hydraulic properties can be obtained directly by conducting laboratory or field measurements and experiments. However, these techniques can be costly and time‐consuming which have resulted in different method for the estimation of soil hydraulic properties. It is possible to estimate these properties from soil information, which are widely available or easy to measure. Mathematical functions to estimate soil hydraulic parameters from basic soil information, such as soil texture, soil organic matter content, bulk density, etc. are called pedotransfer functions (PTFs). Large databases, including soil hydraulic properties and corresponding textures, bulk densities, organic matter content, field capacity, wilting point etc., are available for different soil types. One example is program ROSETTA [18] that predicts parameters of van Genuchten‐Mualem functions. Soil hydraulic parameters are used in agricultural, environmental, and hydrological modelling in which the number of parameters needed depends on simulated processes and used model. Some models require knowledge of the shape of soil water retention curve (SWAP, HYDRUS). Other models, for example, the SWAT model, require water retention values at given matric potentials. Direct point predictions for given matric potentials can lead to more accurate estimations than if water retention values of these matric potentials are derived from predicted SWRC (parameter estimation). Therefore, it is important to have both point predictions and parameter estima‐ tions. It is also well known that the performance of prediction models is highly dependent on the quality of the data set (number and type of measured properties, sample size and its heterogeneity) used for their development.
