5. Soil and vegetation emission model

since this parameter is dependent on the profiler length as well as the number of repetition in

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

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

The Oh model is established based on theoretical scattering models [9], scatterometer measurements, and airborne polarimetric SAR datasets (in L-, C-, and X-band, respectively) under different roughness and soil moisture conditions at incidence angles ranging from 10 to 70�. This

As a first-order radiative transfer solution, the WCM model expresses the total backscattering

volume. The surface scattering can be modeled using the bare soil moisture model such as the previous IEM and Oh models. The vegetation two-way attenuation on the surface scattering

The vegetation layer is assumed to be comprised of homogenous water particles with a uniform distribution, and volume scattering component can be expressed from vegetation

signals as the summation of surface and volume scattering components, σ<sup>0</sup>

HV to soil parameters (including s, l, ε) and radar system parameters (including the

VV and the cross-polarized ratio <sup>q</sup> <sup>¼</sup> <sup>σ</sup><sup>0</sup>

HV=σ<sup>0</sup>

total <sup>¼</sup> <sup>Γ</sup><sup>2</sup>

volume <sup>¼</sup> <sup>0</sup>:75<sup>ω</sup> <sup>1</sup> � <sup>Γ</sup><sup>2</sup> cos <sup>θ</sup>. Accounting the

σ0 surfaceþ

VV and

HH=σ<sup>0</sup>

the surface roughness measurements [37, 38].

• For HH polarization: lc <sup>¼</sup> <sup>0</sup>:<sup>162</sup> <sup>þ</sup> <sup>3</sup>:006 sin 1 ð Þ :23<sup>θ</sup> �1:<sup>194</sup><sup>s</sup>

• For VV polarization: lc <sup>¼</sup> <sup>1</sup>:<sup>281</sup> <sup>þ</sup> <sup>0</sup>:134 sin 0 ð Þ :19<sup>θ</sup> �1:<sup>59</sup><sup>s</sup>

• For HV polarization: lc <sup>¼</sup> <sup>0</sup>:<sup>9157</sup> <sup>þ</sup> <sup>1</sup>:2289 sin 0 ð Þ :1543<sup>θ</sup> �0:<sup>3139</sup><sup>s</sup>

height s and incidence angle θ:

model relates the co-polarized ratio <sup>p</sup> <sup>¼</sup> <sup>σ</sup><sup>0</sup>

wave number k and local incidence angle θ).

power is modeled by <sup>Γ</sup><sup>2</sup> <sup>¼</sup> exp ð Þ �2τ<sup>=</sup> cos <sup>θ</sup> .

scattering albedo and optical depth such as σ<sup>0</sup>

polarization leads to the following empirical volume power [8]:

[35, 40].

48 Soil Moisture

4.2. Oh model

absolute σ<sup>0</sup>

σ0

4.3. Water cloud model

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 model for vegetation covered lands.

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 soils and attenuated by the vegetation itself:

$$T\mathcal{B}\_p = E\_p \gamma\_p T\_{\text{soil}} + (1 - \omega) \left(1 - \gamma\_p\right) \mathcal{T}\_{\text{rege}} + (1 - \omega) \left(1 - \gamma\_p\right) \mathcal{T}\_{\text{vege}} \mathcal{R}\_p \gamma\_p \tag{35}$$

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

$$
\gamma\_p = e^{-\tau\_p/\cos(\theta)} \quad \text{and} \quad \tau\_p = b\_p \cdot V \text{WC} \tag{36}
$$

At L-band, the vegetation scattering albedo ω is assumed to be close to zero and independent of the polarization and incidence angle [41].

Surface roughness effect: assuming the surface scattering over the interface between soil and air, the rough soil reflectivity Rp was obtained from the smooth surface reflectivity rp:

$$R\_p = \left[ (1 - Q) \cdot r\_p + Q \cdot r\_q \right] \cdot \exp\left( -H\_r \cos^{N\_p}(\theta) \right) \tag{37}$$

where rp is the Fresnel coefficients for h and v polarizations:

$$\begin{aligned} r\_{lt} &= \left| \frac{\cos \theta - \sqrt{\varepsilon\_r - \sin^2 \theta}}{\cos \theta + \sqrt{\varepsilon\_r - \sin^2 \theta}} \right|^2 \\\\ r\_v &= \left| \frac{\varepsilon\_s \cos \theta - \sqrt{\varepsilon\_s - \sin^2 \theta}}{\varepsilon\_s \cos \theta + \sqrt{\varepsilon\_s - \sin^2 \theta}} \right|^2 \end{aligned} \tag{38}$$

model output. For instance, the following cost function was constructed [45] by using both the

� � � � �

2

þ γ �

<sup>p</sup> ð Þ X are the simulated radar and radiometer signals. The γ is a tuning parameter to

balance the radar and radiometer signals in the optimization process. The increase of γ represents the enhanced contribution of the radiometer signals for the soil moisture retrieval. The airborne Passive-Active L-band Sensor (PALS) data were collected during the SMAPVEX12 and SMAPVEX16 campaigns, providing an opportunity to develop the active-passive soil

For the spaceborne platform, such as the condition of the original SMAP mission, the radar and radiometer signals have different spatial resolutions. In this case, the radar signal with fine spatial resolution is used to disaggregate the radiometer signal with coarse resolution to obtain TB data with moderate resolution, considering the correlation between the radar and radiometer signals. Then, the emission model was applied to the disaggregated brightness tempera-

1 College of Environmental and Resource Sciences, Zhejiang University, Hangzhou, China

[1] Jagdhuber T, Hajnsek I, Papathanassiou KP. An iterative generalized hybrid decomposition for soil moisture retrieval under vegetation cover using fully polarimetric SAR. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. 2015;8(8):

[2] Huang X, Wang J, Shang J. An integrated surface parameter inversion scheme over agricultural fields at early growing stages by means of C-Band polarimetric RADARSAT-2 imagery. IEEE Transactions on Geoscience and Remote Sensing. 2016;54(5):2510-2528

<sup>2</sup> 2

<sup>X</sup> TBdata

� � � � �

<sup>p</sup> are the real data from the radar and radiometer, respectively. σsimu

<sup>p</sup> � TBsimu

Soil Moisture Retrieval from Microwave Remote Sensing Observations

TBdata p

<sup>p</sup> ð Þ X

� � � � �

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

3

5 (40)

pq ð Þ X

51

pq � <sup>σ</sup>simu

σdata pq

pq ð Þ X

radar and radiometer signals:

pq and TBdata

moisture retrieval approaches.

Author details

Hongquan Wang1,2\*

References

3911-3922

where σdata

and TBsimu

<sup>C</sup>ð Þ¼ <sup>X</sup> <sup>0</sup>:<sup>5</sup> <sup>X</sup> <sup>σ</sup>data

4

� � � � �

ture to retrieve the soil moisture at a moderate spatial resolution.

\*Address all correspondence to: hongquan.wang@usherbrooke.ca

2 CARTEL, University of Sherbrooke, Sherbrooke, QC, Canada

The parameter Q quantifies the polarization mixing degree due to the surface roughness and is neglected at L-band [42, 43]. Np represents the dependence of roughness on incidence angle. Furthermore, the effective surface roughness parameter Hr is associated to the measured surface roughness in a conventional way:

$$H\_r = 4k^2s^2\tag{39}$$

with wave number k and surface RMS height s. However, the clear general relationship between Hr and measured surface roughness is still uncertain. In the literature, different empirical relationships were established to link the Hr parameter to surface RMS height and the autocorrelation length [44]. The Hr parameter is also found to be influenced by soil moisture, but it is reported to be mainly valid for the sandy soils [42].
