4.1. IEM model

α<sup>1</sup> ¼ arctan

lim f ! hight frequency

46 Soil Moisture

3.2.3. Hybrid decomposition

cycle:

solve the undetermined equation system).

0

BB@

α<sup>1</sup> ¼ arctan

2σHHVV � σVVVV � σHHHH þ

2σHHVV þ σVVVV � σHHHH þ

frequency, the α<sup>1</sup> is approximated using the IEM model as

2f hhf ∗ vv � f vv � � � � <sup>2</sup> � <sup>f</sup> hh � � � � 2 þ

0

BBBB@

2f hhf ∗ vv þ f vv � � � � <sup>2</sup> � <sup>f</sup> hh � � � � 2 þ

priori information to enhance the accuracy of soil moisture retrieval.

½ �¼ Tv <sup>f</sup> <sup>v</sup>

<sup>V</sup><sup>11</sup> <sup>¼</sup> <sup>A</sup><sup>p</sup> <sup>þ</sup> <sup>1</sup> � �<sup>2</sup>

<sup>2</sup> <sup>þ</sup> <sup>2</sup>A<sup>2</sup> p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>2</sup> <sup>þ</sup> <sup>4</sup>j j <sup>σ</sup>HHVV

<sup>2</sup> <sup>þ</sup> <sup>4</sup>j j <sup>σ</sup>HHVV

þ 4 f hhf ∗ vv

þ 4 f hhf ∗ vv

� � � � 2

� � � � 2

2

1

CCA

1

CCCCA

(31)

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(30)

2

ð Þ σVVVV � σHHHH

ð Þ σVVVV � σHHHH

� � q

� � q

f vv � � � � <sup>2</sup> � <sup>f</sup> hh � � � �

f vv � � � � <sup>2</sup> � <sup>f</sup> hh � � � �

! r

! r

<sup>2</sup> � �<sup>2</sup>

<sup>2</sup> � �<sup>2</sup>

In Allain [28], the IEM model is used to simulate the backscattering coefficients. It is found that α<sup>1</sup> tends to be invariable with respect to the radar frequency higher than 8 GHz. At such high

where the fhh and fhh are the parameters in the IEM model. In this case, the α<sup>1</sup> is independent of surface roughness and mainly depends on the soil dielectric constant. The potential of α<sup>1</sup> for the soil moisture retrieval is investigated in Baghdadi et al. [18] using the C-band RADARSAT-2 data, indicating it is possible to discriminate two soil moisture levels or provide necessary a

The eigen-based decomposition is more empirically used for soil moisture retrieval, as it is inherently a mathematical approach. In contrast, the model-based decomposition based on the Bragg and Fresnel scattering models is more physically used. Recently, the combination between the model-based and eigen-based decompositions results in the hyper-decomposition [1]. Firstly, the volume scattering component is removed using the model-based decomposition. Then, the remaining ground scattering is decomposed using the eigen-based decomposition. This process overcomes the requirement of assumption on the dominant surface or dihedral scattering mechanism in the ground component (in that case, we need to assume the β or α to be constant in order to

Furthermore, as the vegetation shape and structure vary with the phenological growth, the limited volume scattering model is not sufficient to capture this complex variability. Thus, the dynamic volume scattering is developed [1], which is suitable for the entire crop phenological

V∗

V<sup>11</sup> V<sup>12</sup> 0

<sup>12</sup> V<sup>22</sup> 0 0 0 V<sup>33</sup> The IEM model can be used to simulate the backscattering coefficients from incidence angle θ and soil parameters (surface roughness ks, correlation length kl, and soil moisture mv). Two surface roughness conditions (Gaussian or exponential) are considered to compute the corresponding backscattering coefficients. Regarding the applicability of IEM model, some studies show reasonable agreements between measurements and the model [30, 31]. However, the disagreements between measurements and model predictions are frequently observed [32–36], because the IEM model backscattering behavior depends on the autocorrelation function (ACF). Furthermore, the measurement of correlation length l is difficult to be accurate enough, since this parameter is dependent on the profiler length as well as the number of repetition in the surface roughness measurements [37, 38].

σ VV�pola volume ¼ σ

σ HV�pola

σ HH�pola

σ HV�pola

σ VV�pola dihedral ¼ 0 HH�pola

volume ¼ ω 0:044ωτ � 0:018ð Þ ωτ

accounted, which can be quantified as [8]

dihedral ¼ 1:9ω 1 þ 0:9ωτ þ 0:4ð Þ ωτ

exp �0:84 ks ð Þ<sup>2</sup>

exp �2:9 ks ð Þ<sup>2</sup>

model for vegetation covered lands.

soils and attenuated by the vegetation itself:

the optical depth τ<sup>p</sup> and incidence angle θ:

TBp ¼ EpγpTsoil þ ð Þ 1 � ω 1 � γ<sup>p</sup>

γ<sup>p</sup> ¼ e

dihedral ¼ 0:013ω 1 þ 7:85ωτ þ 7:9ð Þ ωτ

5. Soil and vegetation emission model

volume ¼ 0:74ω 1 þ 0:54ωτ � 0:24ð Þ ωτ

cos θ � �j j <sup>R</sup>HH

cos θ � � j j <sup>R</sup>HH

<sup>2</sup> <sup>þ</sup> <sup>0</sup>:006ð Þ ωτ

2 cos θ

<sup>2</sup> <sup>þ</sup> j j <sup>R</sup>VV <sup>2</sup> � �0:5 cos <sup>θ</sup>

To collect sufficient emitted energy at microwave bands, satellite radiometer uses large footprint, resulting in coarse spatial resolution. Based on the measured brightness temperature, two typical models are applied for the soil moisture retrieval: L-band Microwave Emission of the Biosphere (L-MEB) and Land Parameter Retrieval Model (LPRM). The former was mainly developed for the L-band such as the SMOS mission, while the latter was mostly used at high frequency but can be also applied to L-band. All these models were based on a simple τ-ω

Vegetation effect: The τ-ω model is formulated to account for the vegetation effect on the brightness temperature. It simulates the TB at polarization p (h or v) as the incoherent summation of (i) the soil emission attenuated by the vegetation, (ii) vegetation direct upwelling microwave emission, and (iii) vegetation downwelling emissions which are reflected by the

where Tsoil and Tvege are soil and vegetation effective temperatures, respectively. The soil emissivity Ep = (1 � Rp) is computed from the soil reflectivity (Rp). The vegetation attenuation on the soil emission is modeled through a vegetation transmissivity γ<sup>p</sup> which is a function of

� �Tvege <sup>þ</sup> ð Þ <sup>1</sup> � <sup>ω</sup> <sup>1</sup> � <sup>γ</sup><sup>p</sup>

�τp<sup>=</sup> cos ð Þ <sup>θ</sup> and <sup>τ</sup><sup>p</sup> <sup>¼</sup> bp � VWC (36)

� �TvegeRpγ<sup>p</sup> (35)

At the moderate or high frequency such as C- and X-bands, the dihedral scattering is negligible. However, at low frequency such as L-band, the dihedral scattering component must be

<sup>3</sup> h i <sup>1</sup> � exp ð Þ �11:7τ<sup>=</sup> cos <sup>θ</sup> � � cos <sup>θ</sup>

<sup>2</sup> h i <sup>1</sup> � exp ð Þ �1:93τ<sup>=</sup> cos <sup>θ</sup> � � exp �1:37τ<sup>1</sup>:<sup>12</sup><sup>=</sup> cos <sup>θ</sup> � �

<sup>2</sup> h i <sup>1</sup> � exp ð Þ �9:62τ<sup>=</sup> cos <sup>θ</sup> � � exp �1:02τ<sup>1</sup>:<sup>38</sup><sup>=</sup> cos <sup>θ</sup> � �

<sup>2</sup> h i <sup>1</sup> � exp ð Þ �2:12τ<sup>=</sup> cos <sup>θ</sup> � � cos <sup>θ</sup>

Soil Moisture Retrieval from Microwave Remote Sensing Observations

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

(33)

49

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To overcome the limitations of IEM model, Baghdadi proposed in [35, 36, 39] a calibration procedure for HH, VV, and HV polarization channels, respectively. It is assumed that the disagreements between IEM model and actual datasets are due to the selection of autocorrelation function and the in situ correlation length measurements. Therefore, after fitting a large set of experiment datasets, a calibration parameter lc is built for different polarization channels at different incidence angles in order to take the place of measured correlation length l. The calibration parameter lc given in [40] for C-band is described with respect to RMS surface height s and incidence angle θ:


By replacing the measured correlation length with this calibration parameter, the agreement between the IEM model simulation and actual radar measurement is reported to be improved [35, 40].
