2.1. Soil moisture

Ocean Salinity (SMOS) satellite was launched in 2009, followed by the Soil Moisture Active and Passive (SMAP) satellite launched in 2015 although the radar component failed to send the signal back. These two missions used the microwave band, considering the dependence of the emissivity on the target dielectric constant and the penetration ability at long frequency. The microwave is found to be an appropriate frequency for monitoring the soil moisture, as it is not influenced by the cloud, and can operate day/night. Nevertheless, the passive radiometer signal is limited by the coarse spatial resolution. In contrast, the radar signal is characterized by higher spatial resolution and longer revisit time. Thus, it is appropriate to employ the radar signals for the soil moisture at a scale of agricultural fields. The polarimetric radars such as the ALOS PALSAR and RADARSAT-2 provide a full coherency or covariance matrix, which contain more information than the single-channel radar system. The PolSAR allows to extract the scattering mechanisms, which are useful for the land classification and geophysical param-

The soil moisture retrieval from the microwave remote sensing data is mainly influenced by the vegetation, surface roughness, and soil texture. However, over the agricultural fields, the crop characteristics vary with the phenological growth, leading to the complexity to model the vegetation influences on the soil moisture retrieval. For instance, the quality of the polarimetric soil moisture retrieval approach is highly dependent on the volume scattering model, which is used to remove the vegetation scattering contribution in the full polarized radar signal. To address this issue, several adaptive volume scattering models were developed at L-band [1] and C-band [2] for tracking the dynamic of crop growth. Both the retrieval accuracy and retrieval rate are enhanced by the dynamic volume scattering models. In contrast, in the radiative transfer models, the vegetation effect is often simulated by the vegetation optical depth, which is subsequently related to the vegetation water content and the normalized

Within this context, this chapter provides a review of the model-based polarimetric decomposition approach, radiative transfer models, and combined active-passive methods for soil moisture retrieval over the vegetated agricultural fields. Particularly, different adaptive volume scattering models for the polarimetric decomposition are compared, and the optimal application conditions are drawn for the soil moisture retrieval. This chapter gives readers an

2. Soil and vegetation parameters influencing the microwave signals

SAR system transmits polarimetric waves toward the targets and receives the backscattering signals after the interaction with ground and ground targets. This technique is of great importance for agricultural managers to monitor the soil properties and surface conditions of the agricultural fields. For example, the retrievals of soil status information from SAR can be used to identify areas at risk of erosion by water and wind. Thus, in this study, we propose to investigate soil moisture and surface roughness as two important parameters describing the

overview of the soil moisture retrieval models at microwave band.

eter retrievals.

30 Soil Moisture

differential vegetation index (NDVI).

Soil is considered as three-phase materials: liquid phase, solid particles, and air phase. The liquid phase can be categorized into two types: the bound water and free water. Bound water is comprised of the water molecules contained in the first few molecular layers surrounding the soil particles. They are tightly held by the soil particles due to the influence of osmotic and matric forces [3, 4]. As the distance away from the soil particle surface increases, the matric forces decrease; thus the water molecules located far from the soil particle are able to move within the soil medium, which is referred as free water. Nevertheless, the criterion to separate bound water and free water is to some extent arbitrary. The amount of bound water located in the first few layers is determined by the surface area of the soil particles, which depends on the distribution of soil particle size. According to the distribution of soil particle size, different soils can be categorized into different soil textures. The solid particles are the second phase, which make up the soil skeleton. The void space between soil particles may be full of water if the soil is saturated or may be full of air if the soil is dry or may be partially saturated. The water percent hold in the soil particles is considered as soil moisture. There exist several expressions for soil moisture representation, and the frequently used approaches are the volumetric soil moisture mv and gravimetric soil moisture mg. The relationship between the volumetric soil moisture mv and gravimetric soil moisture mg is established by the water density r<sup>w</sup> and total mass density rb: mv ¼ mg � rb=rw, where mv is measured using time-domain reflectometry (TDR) and mg is used to calibrate the TDR measurements. Nevertheless, the soil texture must be taken into account in order to determine the soil capability for stocking water.

### 2.1.1. Soil texture

Soil texture is reported to have great effects on the dielectric behaviors over the entire microwave frequency range and is most significant at frequencies around 5 GHz [5]. Different soil textures can be qualitatively classified used both in field and laboratory measurements based on their physical properties. The classes are distinguished by the "textural feel" which can be further clarified by separating the relative proportions of sand, silt, and clay using grading sieves. The classes are then used to determine the crop suitability and to approximate the soil responses to environmental conditions [6]. Different soil elements which determine the specific soil texture are separated and based on the specific ranges of particle diameter d [7]:


Soil texture classification is based on relative combination of sand, silt, and clay. Clay particles are microscopic in size and are highly plastic at moist condition. The presence of silt and/or clay creates a fine texture soil, which impedes water and air movements. Sand-sized particles are visible with the naked eye.

#### 2.1.2. Soil permittivity

The complex dielectric constant describes the behaviors of nonconductor in the electrical field. A number of factors affect the dielectric constant, such as wave frequency, temperature, and salinity of the matter. The dielectric constant represents the maximum capability to store, absorb, and conduct electric energy for a given matter. It is a measure of the medium response to the electromagnetic wave and is defined as ε<sup>a</sup> ¼ ε 0 <sup>a</sup> � iε 00 <sup>a</sup> ¼ ε<sup>0</sup> ε 0 <sup>r</sup> � iε 00 r � �, where ε<sup>a</sup> represents the absolute complex permittivity, ε 0 <sup>a</sup> and ε 00 <sup>a</sup> are the real and imaginary parts of εa, and <sup>ε</sup><sup>0</sup> <sup>¼</sup> <sup>8</sup>:<sup>85</sup> � <sup>10</sup>�<sup>12</sup>ð Þ <sup>F</sup>=<sup>m</sup> is the vacuum permittivity. <sup>ε</sup> 0 <sup>r</sup> is referred as the relative permittivity and considered as the dielectric constant of the specific medium. ε 00 <sup>r</sup> is referred as the absorption capabilities of the medium and is relative to its conductivity and dielectric loss. For most natural medium, the condition ε 0 <sup>r</sup> ≫ ε 00 <sup>r</sup> is satisfied.

The relative dielectric constant of water is around 80, much larger than those of solid soil (2–5) and air (around 1) [3]. Hence, the permittivity of natural soils which are mixtures of three matters is influenced largely by water content. It is viable to measure the dielectric constant in order to infer the soil water content. However, under very dry soil conditions, the real part of the dielectric constant ε 0 <sup>r</sup> ranges from 2 to 4, and the imaginary part ε 00 <sup>r</sup> is below 0.05 [8]. This low dielectric constant results in the soil moisture underestimation by TDR instruments, because the water is tightly bounded to the surface of soil particle, and it causes only a relatively small increase of soil permittivity which cannot be detected by TDR. On the contrary, as the water content continues to increase, above the specific transition soil moisture value (free water becomes dominant in soils), the soil permittivity will increase rapidly.

In addition, assuming the propagating wave attenuates exponentially in soils, the penetrating depths δ<sup>p</sup> of microwave into the soil (skin depth) can be calculated as [9, 10]

$$\delta\_p = \frac{\lambda \sqrt{\varepsilon\_r}}{2\pi \varepsilon\_r''} \tag{1}$$

Inversely, the soil moisture is deduced from the soil permittivity measurements by a similar

ε 0

This model does not consider the imaginary part of dielectric constant, and the main restriction is that the used frequency must be less than 1 GHz. The in situ soil moisture measurements

Hallikainen model: A more applicative conversion model is proposed by [5], and the soil permittivity is modeled as a function of soil moisture and soil texture in a two-order polyno-

where ai, bi, and ci (i = 1, 2, 3) are the complex coefficients for difference wave frequency between 1.4 and 18 GHz. Thus, both the real and imaginary parts of soil permittivity can be modeled. The S and C represent the percentage of silt and clay components, respectively.

Mironov model: The soil dielectric constant depends on the soil water content, temperature, texture, and wavelength. In the past decades, the semiempirical models in [4, 11] were mainly used for both the active and passive microwave remote sensing of soil moisture. Furthermore, Mironov dielectric model [12] considers the difference between the bound water and free water in the soil layers, which is found to be better for soil moisture retrieval at L-band.

<sup>r</sup> � <sup>5</sup>:<sup>5</sup> � <sup>10</sup>�<sup>4</sup>

<sup>ε</sup><sup>r</sup> <sup>¼</sup> <sup>ð</sup>a0 <sup>þ</sup> a1S <sup>þ</sup> <sup>a</sup>2CÞ þ ð Þ b0 <sup>þ</sup> <sup>b</sup>1S <sup>þ</sup> <sup>b</sup>2C mv <sup>þ</sup> ð Þ c0 <sup>þ</sup> <sup>c</sup>1S <sup>þ</sup> <sup>c</sup>2C mv2 (4)

ε 0 2

<sup>r</sup> <sup>þ</sup> <sup>4</sup>:<sup>3</sup> � <sup>10</sup>�<sup>6</sup>

Soil Moisture Retrieval from Microwave Remote Sensing Observations

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33

ε 0 3

<sup>r</sup> (3)

three-order polynomial equation:

using TDR are based on this model.

mial form:

mv ¼ �5:<sup>3</sup> � <sup>10</sup>�<sup>2</sup> <sup>þ</sup> <sup>2</sup>:<sup>92</sup> � <sup>10</sup>�<sup>2</sup>

Figure 1. The penetrating depth in terms of radar frequency and soil moisture.

It is noted that as the wavelength increases, the penetrating depth increases, as shown in Figure 1 for L-, C-, and X-band, respectively. Meanwhile, for a given wavelength, the penetrating depth decreases as soil moisture increases.

#### 2.1.3. Conversion between soil moisture and soil dielectric constant

Topp model: The soil permittivity is expressed as a three-order polynomial function in Topp model [4], which is only available for wave frequency between 20 MHz and 1 GHz:

$$
\hat{\varepsilon}\_r = 3.03 + 9.3mv + 146mv^2 - 76.7mv^3 \tag{2}
$$

Figure 1. The penetrating depth in terms of radar frequency and soil moisture.

clay creates a fine texture soil, which impedes water and air movements. Sand-sized particles

The complex dielectric constant describes the behaviors of nonconductor in the electrical field. A number of factors affect the dielectric constant, such as wave frequency, temperature, and salinity of the matter. The dielectric constant represents the maximum capability to store, absorb, and conduct electric energy for a given matter. It is a measure of the medium response

tion capabilities of the medium and is relative to its conductivity and dielectric loss. For most

The relative dielectric constant of water is around 80, much larger than those of solid soil (2–5) and air (around 1) [3]. Hence, the permittivity of natural soils which are mixtures of three matters is influenced largely by water content. It is viable to measure the dielectric constant in order to infer the soil water content. However, under very dry soil conditions, the real part of

<sup>r</sup> ranges from 2 to 4, and the imaginary part ε

low dielectric constant results in the soil moisture underestimation by TDR instruments, because the water is tightly bounded to the surface of soil particle, and it causes only a relatively small increase of soil permittivity which cannot be detected by TDR. On the contrary, as the water content continues to increase, above the specific transition soil moisture value

In addition, assuming the propagating wave attenuates exponentially in soils, the penetrating

<sup>δ</sup><sup>p</sup> <sup>¼</sup> <sup>λ</sup> ffiffiffiffi ε 0 r p 2πε<sup>00</sup> r

It is noted that as the wavelength increases, the penetrating depth increases, as shown in Figure 1 for L-, C-, and X-band, respectively. Meanwhile, for a given wavelength, the penetrat-

Topp model: The soil permittivity is expressed as a three-order polynomial function in Topp

<sup>r</sup> <sup>¼</sup> <sup>3</sup>:<sup>03</sup> <sup>þ</sup> <sup>9</sup>:3mv <sup>þ</sup> <sup>146</sup>mv<sup>2</sup> � <sup>76</sup>:7mv<sup>3</sup> (2)

model [4], which is only available for wave frequency between 20 MHz and 1 GHz:

(free water becomes dominant in soils), the soil permittivity will increase rapidly.

depths δ<sup>p</sup> of microwave into the soil (skin depth) can be calculated as [9, 10]

<sup>r</sup> is satisfied.

0 <sup>a</sup> and ε 00

and considered as the dielectric constant of the specific medium. ε

0 <sup>r</sup> ≫ ε 00 0 <sup>a</sup> � iε 00 <sup>a</sup> ¼ ε<sup>0</sup> ε 0 <sup>r</sup> � iε 00 r

0

� �, where ε<sup>a</sup> represents

<sup>r</sup> is referred as the absorp-

<sup>r</sup> is below 0.05 [8]. This

(1)

<sup>a</sup> are the real and imaginary parts of εa, and

00

00

<sup>r</sup> is referred as the relative permittivity

are visible with the naked eye.

to the electromagnetic wave and is defined as ε<sup>a</sup> ¼ ε

<sup>ε</sup><sup>0</sup> <sup>¼</sup> <sup>8</sup>:<sup>85</sup> � <sup>10</sup>�<sup>12</sup>ð Þ <sup>F</sup>=<sup>m</sup> is the vacuum permittivity. <sup>ε</sup>

0

ing depth decreases as soil moisture increases.

2.1.3. Conversion between soil moisture and soil dielectric constant

ε 0

the absolute complex permittivity, ε

natural medium, the condition ε

the dielectric constant ε

2.1.2. Soil permittivity

32 Soil Moisture

Inversely, the soil moisture is deduced from the soil permittivity measurements by a similar three-order polynomial equation:

$$
\Delta m = -5.3 \times 10^{-2} + 2.92 \times 10^{-2} \varepsilon\_r^{'} - 5.5 \times 10^{-4} \varepsilon\_r^{'2} + 4.3 \times 10^{-6} \varepsilon\_r^{'3} \tag{3}
$$

This model does not consider the imaginary part of dielectric constant, and the main restriction is that the used frequency must be less than 1 GHz. The in situ soil moisture measurements using TDR are based on this model.

Hallikainen model: A more applicative conversion model is proposed by [5], and the soil permittivity is modeled as a function of soil moisture and soil texture in a two-order polynomial form:

$$\boldsymbol{\varepsilon}\_{r} = (\mathbf{a}\_{0} + \mathbf{a}\_{1}\mathbf{S} + \mathbf{a}\_{2}\mathbf{C}) + (\mathbf{b}\_{0} + b\_{1}\mathbf{S} + b\_{2}\mathbf{C})\mathbf{m}\mathbf{v} + (\mathbf{c}\_{0} + \mathbf{c}\_{1}\mathbf{S} + \mathbf{c}\_{2}\mathbf{C})\mathbf{m}\mathbf{v}^{2} \tag{4}$$

where ai, bi, and ci (i = 1, 2, 3) are the complex coefficients for difference wave frequency between 1.4 and 18 GHz. Thus, both the real and imaginary parts of soil permittivity can be modeled. The S and C represent the percentage of silt and clay components, respectively.

Mironov model: The soil dielectric constant depends on the soil water content, temperature, texture, and wavelength. In the past decades, the semiempirical models in [4, 11] were mainly used for both the active and passive microwave remote sensing of soil moisture. Furthermore, Mironov dielectric model [12] considers the difference between the bound water and free water in the soil layers, which is found to be better for soil moisture retrieval at L-band.

### 2.2. Surface roughness

Besides the soil moisture, the surface roughness is another important factor that affects the backscattering SAR signature, because it determines how the incidence wave interacts with the surface. There exist several ways to describe the natural surface roughness, and two frequently used methods are mentioned here: the fractal geometry theory and the statistical description.

roughness, while the correlation length l (with autocorrelation function) is to characterize the

Suppose a surface in the x-y plane and the height of point (x, y) are assumed to be z(x, y) above the x-y plane. A representative surface with dimensions Lx and Ly is segmented statistically,

> ð Ly=<sup>2</sup>

z x; y � �dxdy (7)

Soil Moisture Retrieval from Microwave Remote Sensing Observations

http://dx.doi.org/10.5772/intechopen.81476

z<sup>2</sup> x; y � �dxdy (8)

(9)

35

(10)

�Ly=<sup>2</sup>

ð Ly=<sup>2</sup>

�Ly=<sup>2</sup>

Consequently, the standard deviation of the surface height within the area Lx X Ly is

The formulation above can be reduced to a discrete condition. The surface profiles are digitized into discrete values zi(xi) at spacing rate Δx which is satisfied the criterion Δx < 0.1λ as

q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>z</sup><sup>2</sup> ð Þ� <sup>z</sup><sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

N � 1

<sup>2</sup> � <sup>N</sup>ð Þ <sup>z</sup>^ <sup>2</sup>

�Ly=<sup>2</sup> <sup>z</sup> <sup>x</sup>; <sup>y</sup> � �z x <sup>þ</sup> <sup>ξ</sup>; <sup>y</sup> <sup>þ</sup> <sup>ζ</sup> � �dxdy

�Ly=<sup>2</sup> <sup>z</sup><sup>2</sup> <sup>x</sup>; <sup>y</sup> � �dxdy (11)

ð Lx=2

�Lx=2

ð Lx=2

�Lx=2

s ¼

described in [3]. The standard deviation s for discrete condition is formulated as

s

P<sup>N</sup> <sup>i</sup>¼<sup>1</sup> ð Þ <sup>z</sup><sup>i</sup>

<sup>N</sup> is the mean surface height and N is the number of samples.

For the horizontal surface roughness description, the surface autocorrelation function (ACF) has to be determined. The autocorrelation function r characterizes the independence of two

Ð Ly=<sup>2</sup>

In the discrete case, the autocorrelation function for a spatial displacement xi = (j � 1)Δx is

s ¼

Ð Lx=<sup>2</sup> �Lx=2 Ð Ly=<sup>2</sup>

Ð Lx=<sup>2</sup> �Lx=2

horizontal roughness [9, 17].

which is centered at the original point.

and the second moment is given by

defined as

where ^z ¼

defined as

P<sup>N</sup> <sup>i</sup>¼<sup>1</sup> zi

points at a distance ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>ξ</sup><sup>2</sup> <sup>þ</sup> <sup>ζ</sup><sup>2</sup> <sup>p</sup> :

rð Þ¼ ξ; ζ

The average height of the surface is given by

<sup>z</sup> <sup>¼</sup> <sup>1</sup> LxLy

<sup>z</sup><sup>2</sup> <sup>¼</sup> <sup>1</sup> LxLy
