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## Sensitivity of radar signal to soil roughness

Many studies (Aubert et al., 2011a; Baghdadi and Zribi, 2016; Baghdadi et al., 2008a; Gorrab et al., 2015a) showed that the backscattering radar signal for bare soil increases with the rms surface height (Hrms) according to the logarithmic or exponential law. Then after certain LHrmsHrmsZg thresholds, the backscattering radar signal becomes constant (Figure II.5). This threshold after which the signal becomes constant depends on the wavelength and the radar’s incidence angle. According to several studies, the radar signal rapidly saturates with the soils roughness (Hrms) when the wavelength and or the incidence angle are weak. This saturation of the radar signal occurs when kHrms is higher than 1 (where k is the radar wave number = 2π/λ) (Figure

II.5). Moreover, this saturation corresponds to Hrms values of 4 cm in L-band, 1 cm in Cband and around 0.5 cm in X-band (Baghdadi and Zribi, 2016). Figure II.5 also illustrates the dynamic weakness of the radar backscattering coefficient in two cases, first in the case of weak incidence angles (variation of 7 dB for 20º-25º, Figure II.5a), than in the case of strong incidence angles (variation of 10 dB for 45º-50º, Figure II.5b).

**Sensitivity of the radar signal to soil moisture**

The radar signal approximately follows a logarithmic law with soil moisture. Moreover, this logarithmic function represented approximately as a linear function for soil moisture between 10 and 35 vol. % (Figure II.6). When the soil moisture increases than about 35 vol. %, the radar signal stabilizes and starting to decrease with the increasing of the soil moisture. So that, the estimation of soil moisture is difficult after 35 vol. % (e.g. Baghdadi et al., 2007; Holah et al., 2005).

**SAR data processing**

Before processing the SAR images, the data are radiometrically calibrated, which allows the backscattering coefficient (°) to be extracted from the signal intensity of each pixel. This calibration enables to carry out multi-temporal analysis of different images (using either the same, or different sensors, but the same radar frequency, incidence angle and polarization). The pixel-by-pixel interpretation of SAR images are extremely difficult because of the presence of speckle noise. It is due to the coherent interference of waves reflected from many elementary scatterers. Due to these reasons, soil surface characteristics are always estimated over homogeneous sectors including several pixels, or at the scale of single fields (which helps to reduce the speckle effect). The mean backscattering coefficients are calculated from calibrated SAR images, by averaging the linear intensity values of all pixels within the field (or sub-field). The reduction in speckle noise and the improvement in the quality of backscattering estimations are thus highly dependent on the size of homogeneous units used (Joughin et al., 1993; Lee et al., 1994).

**Radar backscattering modeling and evaluation**

The radar backscattered models have been the subject of many studies based on theoretical or experimental research. In general, there are several classes of models: empirical, semi-empirical and physical models. These models will be briefly discussed in chapter three.

**Modeling of radar backscattering on bare soils**

The modeling of the radar backscattered signal was developed in order to link and analyze the radar signal’s sensitivity to the physical parameters of the soil surface (roughness and water content in particular) as a function of SAR configurations (mainly radar wavelength, incidence angle and polarization) (Baghdadi and Zribi, 2016; Baghdadi et al., 2004, 2006a, 2011b, 2015, 2016a; Beckmann and Spizzichino, 1987; Fung et al., 1992; Rice, 1951; Ulaby et al., 1986).

The empirical models require calibration using in situ measurements and SAR observations acquired (Baghdadi et al., 2004, 2006a, 2011b, 2015, 2016a; Dubois et al., 1995; Oh, 2004; Oh et al., 1992, 1994, 2002). In addition, the range of validity of the empirical models is limited to the range of variations in the data used for model calibration.

In addition, the physical models are based on laws of the resolution of Maxwell’s equations, with physical approximations limiting their areas of validity. The disadvantages of these models are the complexity of implementations and require many parameters in simulations. The development of these models have been the goal of several studies such as (Chen et al., 2003; Fung, 1994; Fung et al., 1992; Ulaby et al., 1986). In the IEM model (Fung et al., 1992), the discrepancy between SAR simulations and SAR measurements is mainly related to the description of surface roughness which is an important input to SAR backscattering models (Baghdadi et al., 2011b; Mattia et al., 2003; Verhoest et al., 2008). The surface roughness is described by three parameters: the standard deviation of the height (Hrms), the correlation length (L) and the shape of the correlation function (Fung et al., 1992). The correlation length is usually measured with an uncertainty which introduces an error on simulated backscattering coefficients (Baghdadi et al., 2000; Davidson et al., 2000; Le Toan et al., 1999; Lievens et al., 2011). A few studies proposed a semi-empirical calibration of SAR backscattering models in order to reduce the uncertainty on SAR simulations (Baghdadi et al., 2002b, 2004, 2006a, 2011a, 2011b, 2015; Rahman et al., 2007) . In Baghdadi et al. (2002b, 2004, 2006, 2011a, 2011b, 2015) the method consisted of replacing the measured L by a fitting parameter, so-called Lopt, which was found to be related to Hrms (Lopt increases with Hrms). Lopt is a function of Hrms (linear, exponential, or power calibration) which depends on SAR parameters (incidence angle, polarization and frequency). This calibration reduces IEM’s input soil parameters (Hrms and mv instead of Hrms, L and mv). Rahman et al.

(2007) proposed a method for deriving L through the IEM. In this method, the radar signal is modeled as a function of only Hrms and L, and the contribution of soil moisture on backscattering coefficients is ignored (dry soil). Thus, L could be estimated by inverting the IEM.

**Estimation of soil parameters using radar backscattering on bare soils**

For bare soil, many studies have shown the potential of radar data to retrieve soil parameters (moisture and roughness) (Aubert et al., 2011; Baghdadi and Zribi, 2006; Baghdadi et al., 2002a, 2007, 2008a, 2012a; Le Hégarat-Mascle et al., 2002; Zribi et al., 2005b). The SAR signal increases with increasing soil moisture for values between 0 and 35% (Aubert et al., 2011a; Baghdadi et al., 2007; Gorrab et al., 2015a; Holah et al., 2005). Beyond this threshold, the backscattering coefficients tend to saturate and then decreases with increasing soil moisture (Holah et al., 2005). Most bare soil moisture estimation studies have used SAR data in X and C bands and the results show a precision on the estimation of soil moisture between 3 and 6 vol.% (Aubert et al., 2011; Baghdadi et al., 2012, 2016b; El Hajj et al., 2014; Paloscia et al., 2013; Srivastava et al., 2003, 2009; Zribi et al., 2011). Moreover, in C-band, the accuracy of the soil moisture estimates depends on the effect of surface roughness and of the sensor incidence angle. On the other hand, in X-band, the effect of roughness on the accuracy of the soil moisture estimation is negligible and the quality of estimates is slightly better with low incidence angle (RMSE < 1 vol.%) (Aubert et al., 2011a, 2013; Galarneau et al., 2001; Hégarat-Mascle, 2000; Quesney et al., 2000). Thus, the accuracy of the moisture estimates in X-band is twice as well as that obtained in C-band data (3 vol.% in the X-band compared with 6 vol.% in the C-band) (Baghdadi and Zribi, 2016).

Baghdadi et al. (2002a) analyzed the potential of synthetic aperture radar (SAR) data for monitoring roughness states over bare agricultural fields using one ERS image (23°) and two RADARSAT images (39° and 47°). The relationships between the backscattering coefficient, incidence angle, soil surface roughness and row direction have been examined in order to determine the best SAR configuration for such monitoring. The result showed a strong dependence of incidence angle on the discrimination between radar return over areas of different surface roughness. The influence of soil roughness on radar return is more sensitive at a high incidence angle (47°), over the influence of other soil parameters, making it possible to differ and map various surface roughness classes (smooth, medium and rough) over agricultural fields.

### The Semi-Empirical Oh Model

Oh (2004) and Oh et al. (1992b, 1994, 2002) developed between 1992 and 2004 several versions of a semi empirical backscattering model. Basing on theoretical models, scatterometer measurements and airborne SAR observations, the Oh model is built over a wide variety of bare soil surfaces. The Oh model relates the co-polarized ratio p (= 0 HH / 0 VV ) and the cross-polarized ratio q (= 0 HV / 0 VV ) to incident angle (θ), wave number (k), standard deviation of surface height (Hrms), correlation length (L), and soil moisture (mv) or dielectric constant ( r ).

#### The Physical Integral Equation Model (IEM)

The Integral Equation IEM is a physical model (Fung, 1994), where the soil is characterized by the dielectric constant ( r ), the standard deviation of surface height (Hrms), the form of the correlation function, and the correlation length (L). The IEM also takes into account the sensor parameters such as the incidence angle (θ), the polarization (pq with p,q = H or V), and the radar wave number (k = 2π/λ where λ is the wavelength). The IEM has a validity domain that covers the range of roughness values that are commonly encountered for agricultural surfaces: kHrms ≤ 3.

**Table of contents :**

1. Articles published

2. International Conferences

**I. Chapter 1: Introduction **

I.1 Context

I.2 State of art

I.2.1 Remote sensing data for soil characterization

I.2.2 Potential of radar data for monitoring soil conditions

I.3 Plan of the thesis

**II. Chapter 2: Generalities **

II.1 Introduction

II.2 Radar remote sensing

II.2.1 Instrumental Parameters

II.2.1.1 Radar frequency

II.2.1.2 Polarization

II.2.1.3 Incidence angle

II.2.2 Radar backscattering coefficient

II.3 Description of soil parameters

II.3.1 Soil moisture

II.3.2 In situ measurements

II.3.2.1 The gravimetric method

II.3.2.2 The TDR (Time Domain Reflectometry)

II.3.3 Surface roughness

II.4 Radar signal sensitivity to soil parameters

II.4.1 Sensitivity of radar signal to soil roughness

II.4.2 Sensitivity of the radar signal to soil moisture

II.5 SAR data processing

II.6 Radar backscattering modeling and evaluation

II.6.1 Case of bare soil

II.6.1.1 Modeling of radar backscattering on bare soils

II.6.1.2 Estimation of soil parameters using radar backscattering on bare soils

II.6.2 Case of soil with vegetation cover

II.7 Conclusion

**III. Chapter 3: Evaluation of radar backscattering models **

III.1 Introduction

III.2 Dataset

III.2.1 Study Areas

III.2.2 Satellite Data

III.2.3 Field Data

III.2.4 Soil texture

III.3 Description of the Backscattering Models

III.3.1 The Semi-Empirical Dubois Model

III.3.2 The Semi-Empirical Oh Model

III.3.3 The Physical Integral Equation Model (IEM)

III.3.4 IEM Modified by Baghdadi (IEM_B)

III.3.5 The Advanced Integral Equation Model

III.4 Results and Discussion

III.4.1 Evaluation of the Dubois Model

III.4.2 Evaluation of the Oh Model

III.4.3 Evaluation of the IEM

III.4.4 Evaluation of IEM Modified by Baghdadi (IEM_B)

III.4.5 Evaluation of the Advanced Integral Equation Model (AIEM)

III.5 Conclusions

**IV. Chapter 4: A New Empirical Model for Radar Scattering from Bare Soil Surfaces**

IV.1 Introduction

IV.2 Dataset description

IV.3 Validation and analysis of the Dubois model

IV.3.1 Description of Dubois model

IV.3.2 Comparison between simulated and real data

IV.4 New empirical model

IV.4.1 Methodology

IV.4.2 Comparison between Dubois model and new model

IV.4.3 Results and discussion

IV.4.3.1 Performance of the new model

IV.4.3.2 Behaviour of the new model

IV.5 Conclusion

**V. Chapter 5: Estimation of soil roughness using neural networks from sentinel-1 SAR data **

V.1 Introduction

V.2 Dataset

V.2.1 Synthetic dataset

V.2.2 Real dataset

V.2.2.1 Study sites

V.2.2.2 . SAR Satellite images

V.2.2.3 In situ measurements

V.3 Methodology for estimating soil moisture

V.3.1 Neural Networks

V.3.2 Methodological overview

V.4 Results and discussion

V.4.1 Synthetic dataset

V.4.1.1 Estimation of mv

V.4.1.1.1 Using the IEM model

V.4.1.1.1.1 Use of VV polarization alone

V.4.1.1.1.2 Use of VH polarization alone

V.4.1.1.1.3 Use of VV and VH polarizations together

V.4.1.1.2 Using Baghdadi model

V.4.1.1.2.1 Use of VV polarization alone

V.4.1.1.2.2 Use of VH polarization alone

V.4.1.1.2.3 Use of VV and VH polarizations together

V.4.1.1.3 Conclusion

V.4.1.2 Estimation of Hrms

V.4.1.2.1 Using IEM model

V.4.1.2.2 Using Baghdadi model

V.4.2 Real dataset

V.4.2.1 Estimation of soil moisture (mv)

V.4.2.1.1 Using the IEM model

V.4.2.1.2 Using Baghdadi model

V.4.2.2 Estimation of surface roughness (Hrms)

V.4.2.2.1 Using the IEM model

V.4.2.2.2 Using Baghdadi model

V.4.2.2.3 Discussion

V.4.3 Estimation of Hrms and mv both at very high spatial resolution ʺVHSRʺ

V.4.3.1 Synthetic dataset

V.4.3.1.1 Estimation of mv

V.4.3.1.1.1 Using the IEM model

V.4.3.1.1.2 Using Baghdadi model

V.4.3.1.1.3 Discussion

V.4.3.1.2 Estimation of soil roughness ʺHrmsʺ

V.4.3.1.2.1 Using the IEM model

V.4.3.1.2.2 Using Baghdadi model

V.4.3.1.2.3 Discussion

V.4.3.2 Real dataset

V.4.3.2.1 Estimation of soil moisture (mv)

V.4.3.2.1.1 Using the IEM model

V.4.3.2.1.2 Using Baghdadi model

V.4.3.2.2 Estimation of surface roughness (Hrms)

V.4.3.2.2.1 Using the IEM model

V.4.3.2.2.2 Using Baghdadi model

V.5 Conclusions

VI. General conclusion and perspectives

VI.1 General conclusion

VI.2 Perspectives

Annex 1: Results on soil roughness estimates using synthetic dataset generated from the IEM model

Annex 2: Results on soil roughness estimates using synthetic dataset generated from Baghdadi model

List of figures and tables

List of figures

List of tables

**References**