State of the art in monitoring and modeling soil moisture at various

Ref: C0699
State of the art in monitoring and modeling soil moisture at
various scales for irrigation purposes
Nunzio Romano, Dept. of Agriculture, Division of Agricultural, Forest and Biosystems Engineering, University of Napoli Federico II, IT-80055, Portici (NA), Italy
Abstract
Soil moisture is a key state variable for understanding processes evolving in the hydrologic
cycle and, in particular, for developing good management practices of irrigation water. Recently, the techniques for monitoring water content in soil are receiving considerable attention and are undergoing substantial changes and improvements. In this paper, the major
methods to measure soil water content are reviewed from the more classic to a few new
ones, but with the central thread to frame them within model applications that exploit the
measured datasets. The various traditional and more up-to-date methods are reviewed by
the central thread of techniques developed to measure soil moisture interwoven with applications of modeling tools that exploit the observed datasets.
Keywords: soil moisture, irrigation, soil-water budget model, space-time scales.
1
Introduction
Measurement of soil moisture is of great importance in many investigations and applications
pertaining to agriculture, hydraulic engineering, hydrology, meteorology, and soil mechanics.
In the field of agronomy and forestry, the amount of water contained in the soil affects plant
growth and diffusion of nutrients toward the plant roots, as well as acts on soil aeration and
gaseous exchanges with direct consequences on root respiration. Also, continuous monitoring of soil moisture can support the setting up of optimal strategies for the efficient and sustainable use of irrigation water and feeds the topic of precision agriculture. In hydrology,
moisture conditions in the uppermost soil horizon play an important role in determining the
amount of incident water - either precipitation or irrigation water - that becomes overland flow
and runoff. Evapotranspiration processes, transport of solute and pollutants, numerous hydraulic (e.g., water holding capacity, hydraulic conductivity) or mechanical (e.g., consistency,
plasticity, strength) soil characteristics, all depend on soil moisture. Soil water content is also
known to be an important variable in modeling hillslope instability and landslides.
1.1
Definitions
Soil water content is generally defined as the ratio of the mass of soil water, Mw, to the mass
of dried soil, Ms, or as the volume of soil water, Vw, per unit total volume of soil, VT, which is
the sum of the volume of solid particles (Vs), the volume of soil water (Vw), and the volume of
soil air (Va). In both cases, however, the computation of the soil water content value depends
on the definition of the dry soil condition. As the interest of practical applications relies largely
upon the determination of the magnitude of relative changes in soil water contents at a certain location, by tradition the dry soil condition refers to the standard condition obtained in the
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laboratory by extracting water from the soil sample placed in an oven at a temperature of
approximately 100 to 110 degrees Celsius (°C), until variations in the sample weight are no
longer noticed. Although the choice of this range of temperatures is indeed somewhat arbitrary, keeping the soil sample in the oven for an adequate duration and at the average temperature value of 105 °C, guarantees evaporation of the “free” water from the soil (Romano,
1999). Moreover, this standard condition can be easily attained using a commercial oven.
Soil water content on a volumetric basis, θ, is defined by the dimensionless ratio between the
soil water volume, Vw, to the total soil volume, VT, as follows:
V
θ  w
(1).
VT
Especially when subjecting a soil sample to chemical analyses, one prefers to express the
soil water content on a mass basis as follows:
M
θM  w
(2).
Ms
For a rigid soil, if ρb=Ms/VT denotes the oven-dry bulk density and ρw=Mw/Vw is the density of
liquid water, the volumetric soil water content, θ, and the gravimetric soil water content, θM,
are related by the following expression:
ρ
θ  θM b
(3).
ρw
1.1.1
The concept of available soil-water for irrigation purposes
Especially for irrigation scheduling purposes, soil moisture conditions within the plant rooting
zone are often described by relying on the concept of soil moisture availability for plant
growth, the so-called “plant-available soil water content”, PAWC for short (see Figure 1).
PAWC is computed by the difference between the values of the volumetric soil water content
at field capacity, θFWC (upper soil moisture limit), and at permanent wilting, θPW (lower soil
moisture limit), hence PAWC = θFWC–θPW (Romano & Santini, 2002).
Figure 1: Schematic illustration of the PAWC concept.
The concept of the amount of soil water that is available to the plants was historically introduced for agronomic purposes to help farmers better decide the irrigation scheduling for their
crops. This concept soon became the basis of most bucket-type simplified models developed
to compute the hydrologic balance and to evaluate the dynamics of soil moisture (Romano et
al., 2011). The permanent wilting point, θPW, represents the soil water content at which a
plant wilts completely and is no longer able to recover its turgor and biological activity when
placed in a humid environment. A working definition of the permanent wilting point is based
on the volumetric soil water content at the matric suction head, h, of 150 m (or, at the matric
suction pressure of approximately 1.5 MPa). This low matric pressure head is often considered as a reference point to characterize, on average, the amount of soil water when a plant
wilts permanently, although for different plant species the matric pressure potential at permanent wilting in the bulk soil can range from about 0.8 MPa to 3 MPa (e.g., xerophytic
plants) and even more. It should be noted, however, that the shape of the soil water retention
function at very low matric pressure heads is such that the soil water content varies little
even for relatively large changes in matric pressure heads around the conventional value of
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150 m. In contrast, the soil water content at field capacity, θFWC (field capacity, for short), is
assumed as the average volumetric soil water content in a uniform soil profile at which the
redistribution process, following an infiltration event, proceeds so slowly that draining rates
become virtually negligible.
The definition of field capacity, θFWC, is a somewhat tricky question. This hydrologic variable
is definitely not a constitutive soil characteristic, but rather it should be viewed as a processbased parameter being determined using specifically-designed field experiments (for a comprehensive discussion on this matter, the reader is directed to the paper by Romano & Santini, 2002). However, for practical reasons the field capacity value, θFWC, is often associated
with the point of the soil water retention function at the matric suction head of 3.30 m, as an
average between those matric values being mostly associated with coarser soils (0.50 m to
1.00 m matric suction heads) and with finer-aggregated soils (4.00 m to 6.00 m matric suction heads). Strictly speaking, the latter (simplified) method can only be used if the soil profile
is uniform from the hydraulic viewpoint over the soil depth investigated for the root system
under study. Moreover, the concept of field capacity is applicable only to the unsaturated
zone, and therefore the amount of water held in the soil at field capacity will vary as the saturated portion of the soil profile increases or decreases. The use of the “plant-available soil
water content, PAWC” concept to identify the soil moisture is preferred since it provides a
somewhat clearer identification of the soil volume (i.e., the rooting zone) where soil moisture
is effective from both the monitoring and modeling purposes. This soil volume is connected
to the evapotranspiration processes and can be assumed as the uppermost soil layer delimited between the soil surface and the lower end of the plant rooting zone.
In a study to evaluate the impact exerted by different parameterizations of the soil water content at field capacity on determining the soil water budget, Romano et al. (2011) showed that
the approach to estimate θFWC at a specific point of the water retention function, commonly
known as the soil water content at the matric suction head of 3.30 m, can yield poor hydrologic predictions using a single-layer bucket model, especially if coarser textured soils predominate and the local climate has distinct seasonal features, as occurs in Mediterranean
climates. In general, these authors warn about deriving the value of θFWC with excessively
simplistic methods if a bucket-type hydrologic model is used, and demonstrate that the field
drainage experiment is superior for determining this soil parameter.
1.2
Scale issues
We will also frame the present topic within the question of scale. Reference will be mostly
made here to the spatial scale, although the time scale will also be addressed when needed.
Following the framework proposed by Blöschl & Sivapalan (1995), scale can be schematically considered as a characteristic dimension made up by the triplet of “support”, “spacing”,
and “extent” (see Figure 2).
Figure 2: The scale triplet (after Blöschl & Sivapalan, 1995).
This scale triplet may refer to either the measuring or modeling issues, and can be applied to
both the spatial and temporal dimensions. If, to fix the ideas, we consider the spatial scale of
soil moisture observations, “support” (or, grain) is the volume in which the average value of
soil moisture is obtained, “spacing” is the distance between the sensors (being also related to
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the sampling concept), and “extent” represents the entire domain over which the measurements are carried out. When dealing with measuring issues, the term “scale” is very often
identified with its “support” component. A modeler, instead, uses the word “scale” more
commonly with reference to the “extent” of the spatial grid where the simulated outputs are
computed. Even if it would be highly desirable to have the measuring scale commensurate
with the modeling scale (i.e., the scale at which the simulation results are obtained or of interest), unfortunately a mismatch in scale between observations and simulations often occurs. A mismatch may occur also between the previous two types of scales and the scales of
the spatial and temporal evolution of the phenomenon under study.
2
Monitoring and modeling soil moisture at local scale
Several methods have been proposed to determine the water content in soil, especially under field conditions. Basically, soil water content can be measured by direct or indirect methods. At the local scale in space, the “support” of soil moisture measurements should be
linked mostly to a characteristic length of the soil volume investigated by the sensor probe,
usually ranging from about 0.10 m to 0.50 m, whereas from the modeling point of view the
support is that of a vertical soil profile or a plot, thus ranging from about 1 m up to 10 m. In
summary, I conveniently assume herein the local scale to exhibit a characteristic (average)
spatial length of 100 m.
2.1
Direct method
The most widely used direct method to measure the water content in soil is the thermogravimetric method, often assumed as a reference procedure because it uses precise devices, which nowadays are also quite inexpensive (Romano, 1999). However, it necessarily
entails the destruction of the soil sample and hence the inability to repeat the measurement
in the same sampling location. This method consists of collecting a disturbed or undisturbed
soil sample (usually about 100-200 grams taken by an auger or a sampling ring) from the
appropriate soil depth, weighing it, and sealing it carefully in order to prevent water evaporation or moisture gain prior to analysis. The soil sample is then placed in an oven and dried at
105°C. The residence time in the oven should be such that a stable weight is attained, and it
depends not only on the type of soil and the size of the sample, but also on the efficiency and
load of the oven. Common residence times in an oven are approximately 12 hours if a
forced-draft oven is used, or approximately 24 hours when using a convection oven. On
completion of the drying phase, the sample is removed from the oven, cooled in a desiccator
with active desiccant, and weighed again. Even though θM is quite straightforward to measure, it is worth noting that we are usually interested in determining the volumetric soil water
content, which involves the conversion of θM into θ and the measurement of the oven-dry
bulk density, ρb. The latter requirement makes direct determination of soil moisture a rather
demanding task and unfortunately increases the levels of uncertainty associated with the
direct technique. This is because, in practice, measuring ρb entails collection at the fixed
depth of an undisturbed soil core, commonly using a stainless steel cylinder, to be able to
have a known volume, which should also have a size commensurate with the representative
elementary volume of the soil type under study. Therefore, a source of errors in using the
thermo-gravimetric method is related to the coring phase, with the associated unavoidable
disturbances to the soil core during field operations. Soil core sampling also requires time (i)
to push slowly by hand the metallic cylinder into the soil while removing the soil around the
cylinder to limit the lateral friction, and then (ii) to carefully extract from the sampling point the
cylinder with the soil core inside. Overall, thermo-gravimetry is a generally-accepted reference method for comparisons since in practice it is the only method providing a direct measurement of soil water content. The methods that will be reviewed in the following section
should more properly be grouped into the sensing methods, insofar as they do not measure
the soil water content, but rather a correlated variable. Indirect methods entail the measurements of some soil physical or physico-chemical properties that are highly dependent on soil
water content. In general, they do not involve destructive procedures and use equipment that
can also be placed permanently in the soil, or remote sensors located on airborne platforms
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or satellites. Indirect methods are well suited for carrying out measurements on a repetitive
basis and also enable data to be recorded automatically, but in almost all of the cases they
require the knowledge of accurate calibration curves.
2.2
Indirect methods
Indirect measurement techniques that account for the effects exerted by water content in the
soil on its dielectric properties have become increasingly popular for irrigation scheduling,
mainly because of the present availability of advanced electronic components in various devices. One method pertaining to this category is the well-known time domain reflectometry
(TDR) which enables the apparent relative dielectric permittivity of soil to be determined by
monitoring the travel time it takes for a fast-rise-step voltage pulse to propagate along a
transmission line connected to a suitable probe placed in the soil at the selected measuring
depth. This time depends on the dielectric properties of the system surrounding the probe,
hence on the soil water content. A coaxial cable connects the probe to the TDR instrument,
which provides the step voltage pulses and also analyzes the reflected waveform with a time
resolution of nanoseconds. An overview of the theoretical background and the operating
principle of the TDR lies far beyond the scope of the present article, and the reader is referred to specific papers or chapters related to this technique (e.g., Robinson et al., 2008;
Vereecken et al., 2008). It is worth mentioning here that, through examination of the dielectric
behavior of a wide range of mineral soils, Topp et al. (1980) found that a third-order polynomial regression equation fits very well the paired data points of volumetric soil water content,
θ, and TDR-measured dielectric permittivity of various porous media.
The other dielectric-based technique employed to estimate the volumetric water content at
the local scale considers the soil as the component of a capacitor. Unlike TDR, the capacitance technique basically determines the soil’s apparent relative dielectric permittivity by
measuring the charge time of a capacitor embedded into the soil, which serves as a dielectric
medium. Even though improvements have been made to the TDR technique, there is no
doubt that nowadays the major technical progress is being achieved with the use of capacitance sensors. One of the reasons for the widespread use of the capacitance sensors is essentially due to their lower costs, in terms of both time and financial resources, compared to
the use of the TDR technique, although obviously at the expense of a worsening in accuracy
and precision of the soil moisture measurements. The capacitance technique basically belongs to the family of frequency-domain techniques, and the greater measuring errors associated with its use depend mainly on the frequency of the electromagnetic field imposed by
the instrument. The voltage oscillation frequency of some capacitance sensors is around 2030 MHz, but for others it reaches higher values of approximately 80-100 MHz and even up to
300 MHz. That said, these frequencies are smaller than those at which the TDR method operates (up to 2-3 GHz), which makes the measurements of the complex soil dielectric permittivity by a capacitance method much more prone to be affected by soil temperature and salinity. It should be evident from the preceding discussion that reliable assessment of the calibration curve for a capacitance sensor is a question of prime importance for their use in studies dealing with soil moisture monitoring (e.g.,Mittelbach et al., 2012).
Figure 3: Examples of TDR (left) and capacitance (right) probes.
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Strictly speaking, the TDR and capacitance dielectric-based techniques do not lead to point
soil moisture measurements (only the gamma-ray attenuation technique should be considered as such), but rather they average the soil water content over a soil volume which mainly
depends on the length and shape of the probe buried in the soil (see Figure 3 showing different TDR and capacitance probes).
A survey of the literature reveals that many types of soil moisture models have been developed, mainly depending on the background and knowledge of the single research groups, to
represent soil hydrologic behavior and the basic processes of precipitation, evapotranspiration, runoff, and drainage. Such models are also used to interpret a specific scientific question or solve a prescribed practical problem. In the following, the two most widespread soil
moisture models are presented and their main features briefly discussed.
The most widely adopted model of soil moisture dynamics at the local scale, or rather at the
point scale, is the well-known equation of Richards, obtained as a combination of the mass
balance equation and Darcy’s law (e.g., Romano et al., 1998):
  hz,t   
 hz,t 
 

 1   Sh
(4),
Ch
 K h 
t
z 
 z

which is written here in its one-dimensional and matric suction head form. In this equation,
time, t, and vertical coordinate, z (taken positive downward), are the independent variables,
whereas matric suction head, h, is the dependent variable. Model parameters are the soilwater capacity function, C(h)=dθ/dh, which can be readily obtained from knowledge of the
soil-water retention function, θ(h), and the hydraulic conductivity function, K[θ(h)]. The sink
term, S(h), describes the root water uptake as a function of matric pressure head. When
tackling practical problems under specified initial and boundary conditions, the Richards
equation has to be solved numerically, chiefly because of its inherent nonlinear nature. In
some cases, as for the infiltration into initially very dry soils, solving the Richards equation
through numerical schemes may require specifically-designed algorithms in order to attain a
prefixed level of computational efficiency or to avoid numerical instabilities.
3
Monitoring and modeling soil moisture at larger scales
Sensing methods that elaborate on the signal of electromagnetic waves but measure soil
water contents over a relatively larger control volume, are the hydro-geophysical techniques
of indirectly electrical resistivity tomography (ERT), ground penetrating radar (GPR), and
electromagnetic induction (EMI). These measurement techniques enable soil water content
to be obtained at a support scale that is intermediate between the typical small support of the
TDR, capacitance, and ring oscillator probes, and the much larger support offered by airborne-based remote sensing techniques (Robinson et al., 2012). The ERT technique basically consists in measuring values of the bulk soil electrical conductivity (ECb) and relating them
to the soil water content (Samouëlian et al., 2005). Even though electrical resistivity tomography is largely applied to field conditions, especially its two-dimensional version, a threedimensional ERT monitoring technique has also been used successfully developed at the
local scale of a laboratory soil column for assessing, for instance, a solute transport process
or a soil water balance in the rooting zone. Time-lapse non-invasive 3D electrical tomography (ERT) is recently applied to monitor soil-plant interactions in the root zone and gain a
better understanding for modeling exchanges of fluxes in the soil-vegetation-atmosphere
system. Ground penetrating radar (GPR) is another technique that, although initially developed and used in other scientific and technical sectors, is now also widely used for soil moisture monitoring. Huisman et al. (2003) and Slater and Comas (2009) have provided comprehensive reviews of this technique. However, almost all of these measurement techniques
have to rely on robust inverse modeling procedures. Therefore, the integration of measurements in a fully coupled hydro-geophysical inversion seems a useful way forward to feed
comprehensive root-zone water balance modeling tools with a suitable amount of good quality data.
The description of near-surface soil moisture dynamics at relatively large scales can be obtained through a bucket scheme with an integrated spatial view, it being a zero-dimensional
model, and usually at the daily time-scale. This scheme assumes the soil as a reservoir to be
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intermittently filled by water, it being rainfall or irrigation events in the form of randomly distributed shots (Poisson process). Soil water storage capacity is emptied by surface runoff,
deep drainage, and evapotranspiration processes. With reference to a single-layer bucket
model, the non-linear differential equation of water balance for a soil layer of depth Zr is written as follows (Rodríguez-Iturbe and Porporato, 2004):
dst 
(5),
 Ist , t   Est   Tst   Lst 
n Zr
dt
which should be viewed as a stochastic water balance model because of the stochastic representation of the rainfall or irrigation inputs. Soil thickness Zr is the control volume, commonly represented by the hydrologically active soil profile from the soil surface up to the end of
the rooting zone. In this equation, n is soil porosity, s (0≤s≤1) is the degree of soil saturation
(i.e. the volumetric soil water content, θ, normalized by soil porosity, n) averaged over the
entire rooting zone, I is rainfall rate infiltrating into the soil, E is actual evaporation rate, T is
actual transpiration rate, and L is leakage rate from the bottom end of the bucket. It is worth
noting that evaporation, E, transpiration, T, and leakage, L, rates are considered only as a
function of average soil saturation, s, whereas the losses due to surface runoff are generated
only when the bucket is completely full, i.e. under full saturation in the soil. This model assumes that only a fraction of the incoming precipitation is able to infiltrate into the soil when
the rainfall depth exceeds the storage capacity of the soil profile. The relationship
I[s(t),t]=min[r, n·Zr(1-s)] accounts for the dependence of infiltration rate, I, on rainfall depth, r,
and the degree of soil saturation, s, in the sense that rainfall infiltration is equal either to rainfall depth or to soil storage capacity, whichever is less.
Unlike the Richards equation, the bucketing approach incorporates a more simplistic representation of near-surface soil moisture dynamics, partly because it does not fully resolve the
local vertical variations in soil water contents and therefore it should be viewed as a lumpedparameter hydrologic model. The Richards equation is mainly applied to problems at the
point/local spatial scale, especially when the soil moisture simulations require a detailed description of the water uptake by plant roots (Carminati, 2012), or to improve our understanding of the processes evolving in the soil-vegetation-atmosphere system (Santini & Romano,
1996; Romano et al., 2012). Yet, this equation is being increasingly utilized to resolve problems of observations obtained at a certain scale (for example, at the farm, district, or regional
levels).
Moving toward a larger scale is hampered, among various other factors, by the inherently
high soil heterogeneity that, in turn, greatly affects the nonlinear nature of the spatial variability of soil water content measurements. Moreover, this task involves the use of some statistical/stochastic/geostatistical methods and also drags with itself inevitable error propagations
and inherent uncertainties. An example helping to frame this question is the long-standing
problem of soil hydraulic characterization over a relatively large land area. Hopmans et al.
(2002) interestingly argued that the data obtained by performing laboratory experiments on a
number of soil cores or soil columns can be successfully employed to determine effective
hydraulic parameters at the larger spatial scale of interest.
Figure 4: Schematic of the cosmic-ray soil moisture monitoring method.
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By exploiting the basic working principle of the well-known conventional down-hole neutron
scattering technique, a “new” above-ground neutron-based soil moisture sensing equipment
has been recently developed that relies on the measurement of background neutrons emitted
naturally from soil: the cosmic-ray method (Ochsner et al., 2013). This non-invasive method
is definitely a fundamental breakthrough, something that is going to have a significant impact
in the monitoring and modeling of soil moisture status over an area of approximately few tens
of hectares (see the schematic in Figure 4).
In terms of soil moisture monitoring, the cosmic-ray method allows average soil water content to be determined to a soil depth of about 0.50-0.70 m and over a circular area with radius of about 300 m by measuring high energy neutron count rates with a probe located a few
meters above the soil surface, with a small, known correction for atmospheric humidity. Although the cosmic-ray method suffers from the same problem as the conventional neutron
scattering method with respect to the enlargement of the measuring volume as the soil becomes drier and drier, it is an emerging opportunity also in modeling terms and operates at
an intermediate spatial scale between point grid sampling and the footprint of a satellite image. On the one hand, the area-average (aggregate) effective soil moisture determined by
the cosmic-ray method can give valuable insight into identifying effective parameters and
suitable aggregation schemes to estimate area-average fluxes. On the other hand, it provides a means for validating satellite remote sensing products.
4
Concluding remarks
Unlike in the past, the present-day availability of newly developed sensing techniques, such
as offered by a wireless network of low-cost sensors, enables soil moisture data to be obtained at both a high spatial and temporal resolution more efficiently and cost-effectively. The
investigations described recently in the papers by Mittelbach and Seneviratne (2012) and
Rosenbaum et al. (2012) are helpful examples of the great potential offered by the new technologies applied to soil moisture sensing and to identifying the structure of space-time variability exhibited by the local-scale measured values. These activities can also be viewed as a
sound response to the need to validate effectively the recent generation of water balance
models. Many studies have raised the important question that the applications of such models in, for example, precision agriculture require data that describe accurately the spatial and
temporal variations of significant variables, such as soil moisture, in many locations in a distributed manner.
Monitoring and modeling issues go on chasing each other continuously in many scientific
disciplines. The important advances gained many years ago in the soil physics theory and in
the analytical and numerical solutions of the equations governing the flow of water and the
transport of solutes in soil have stimulated interest in conducting various experiments in the
laboratory or under field conditions to corroborate the theories and to evaluate the simulations provided by computer models. More recently, instead, we are witnessing a new momentum to produce even more efficient techniques and sensing equipment that open up a
variety of scenarios in monitoring near-surface soil moisture. Mention has already been
made about the progressive technological improvement of the capacitance probes for measuring soil water contents in situ and their use in wireless sensor networks to improve our understanding of the spatial and temporal evolution of this variable at the local scale.
5
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