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The objective of this study is to improve the performance of semi-empirical radar backscatter models, which are mainly used in microwave remote sensing (Oh 1992, Oh 2004 and Dubois). The study is based on satellite and ground data collected on bare soil surfaces during the Multispectral Crop Monitoring experimental campaign of the CESBIO laboratory in 2010 over an agricultural region in southwestern France. The dataset covers a wide range of soil (viewing top soil moisture, surface roughness and texture) and satellite (at different frequencies: X-, C- and L-bands, and different incidence angles: 24.3° to 53.3°) configurations. The proposed methodology consists in identifying and correcting the residues of the models, depending on the surface properties (roughness, moisture, texture) and/or sensor characteristics (frequency, incidence angle). Finally, one model has been retained for each frequency domain. Results show that the enhancements of the models significantly increase the simulation performances. The coefficient of correlation increases of 23% in mean and the simulation errors (RMSE) are reduced to below 2 dB (at the X and C-bands) and to 1 dB at the L-band, compared to the initial models. At the X- and C-bands, the best performances of the modified models are provided by Dubois, whereas Oh 2004 is more suitable for the L-band (r is equal to 0.69, 0.65 and 0.85). Moreover, the modified models of Oh 1992 and 2004 and Dubois, developed in this study, offer a wider domain of validity than the initial formalism and increase the capabilities of retrieving the backscattering signal in view of applications of such approaches to stronglycontrasted agricultural surface states.

The backscattering electromagnetic models of bare soils aim to reproduce the interactions between the electromagnetic wave and the surface. They are considered a useful tool to understand the processes (single, multi-or volume scattering) in the backscattering coefficient that microwave antennas record, in perspective of the inversion of soil parameters such as the top soil moisture, texture, and surface roughness [

The most commonly used approximate models based on a physical description of the backscattering processes are the small-perturbation model, Kirchhoff model, which is declined using two approximations according to the roughness level (geometric optic or physical optic for low or high roughness, respectively), and Integral Equation Model (IEM) [

With the availability of satellite SAR data that have been acquired over the past 20 years in the L-band (Alos 1 or 2), C-band (Ers 1 or 2, Radarsat 1 or 2, Envisat, Sentinel- 1a/b…), and X-band (TerraSAR-X, Tandem-X, Cosmo-skymed constellation…), it is now possible to independently evaluate and improve these semi-empirical models (developed at least 12 years ago) in different wavelength domains in terms of the estimation of surface soil parameters (moisture, texture or roughness).

In this context, the objective of this study is to address the performances of three semi-empirical models (Oh 1992, Oh 2004 and Dubois) over a wide range of soil surface conditions and propose an improvement of the models using an original method based on the reduction of their residues. Initially developed and applied in mathematics and statistic domains, the analyze and the reduction of the residues is fundamental in modeling approaches and can significantly improve the performances of models by removing the effect of physical characteristics non-taken into account in the initial formalism. The application of such method on backscattering model (used in remote sensing) is unique, especially regarding the surface descriptors and/or satellite characteristics.

This work is based on the multi-spectral SAR satellite images acquired by TerraSAR-X, Radarsat-2 and Alos-PALSAR over agricultural surfaces, which are characterized by their specific top soil moisture, surface roughness and texture [

The study area is located in southwestern France near Toulouse (

The top soil moisture, surface roughness and texture were measured over a network of 37 agricultural fields when the soils were bare [

The dielectric constant of the soil was measured at each satellite overpass using mobile theta probe sensors. The volumetric soil moisture of the first five centimeters was derived from the in situ calibration function of [^{3}・m^{−3} (

The soil roughness was measured using a 2 m pin profilometer at each change of surface state (e.g., transition from a prepared soil to a harrowed or plowed soil), that is, 1 - 6 times on the surveyed fields depending on the agricultural practices. Two profiles were collected in the directions parallel and perpendicular to the tillage orientation. The two standard statistical parameters (i.e., the standard deviation of roughness heights and the autocorrelation length, abbreviated as h_{rms} and lc, respectively) were calculated from each profile. During the experiment, 117 roughness measurements were collected over the surface states that ranged from smooth (after the soil preparation for the crop sowing) to highly rough conditions (after a deep plowing). The roughness values in the semi-empirical model (abbreviated as kh_{rms}, where k corresponds to the wave number) were 0.55 - 12.57 (

The soil texture measurements included sampling the surface (0 - 25 cm depth) in a

circle of 15 meters radius, with 16 sub-samples. Along the transect of the soil moisture, 2 - 8 samples were obtained depending on the length of the transect and the observed behavior of the top soil moisture. Over the study area, the soil content was dominated by silt, whose mean value was 52%, followed by the fractions of clay and sand (24%). Nevertheless, a high variability was observed, and the 146 measurements show that the clay, silt and sand contents were 9% - 58%, 22% - 77%, and 4% - 53%, respectively (

TerraSAR-X (TS-X, 29 images), Radarsat-2 (RS-C, 22 images), and Alos-PALSAR (AP-L, 3 images), which operate in the X-band (f = 9.65 GHz, λ = 3.1 cm), C-band (f = 5.405 GHz, λ = 5.5 cm) and L-band (f = 1.27 GHz, λ = 23.6 cm), respectively. The TerraSAR- X images were acquired with HH polarization at incidence angles of 27.3˚ - 53.3˚ using two beam modes (StripMap (SM) and SpotLight (SL)), which were characterized by a pixel spacing of approximately 3 and 1.5 m, respectively [

The model is based on the relationships that calculate the backscattering coefficients in HH, VV and HV polarizations from the polarization ratios (denoted p and q), sensor characteristics and surface parameters (Equations (1) - (8)).

Mission | Mode | Acquisition Date | Pass | Incidence | Pixel | Polarization states |
---|---|---|---|---|---|---|

Angle (˚) | Size (m) | |||||

TS-X | SpotLight | 03/15/10 | D | 28.7 | 2 | HH |

TS-X | SpotLight | 04/14/10 | A | 32.3 | 2 | HH |

TS-X | SpotLight | 04/08/10; 04/30/10; 08/29/10 | A | 45.5 | 1.75 | HH |

TS-X | SpotLight | 03/05/10; 05/21/10; 07/15/10; 08/17/10 | D | 53.3 | 1.5 | HH |

09/30/10; 10/11/10; 10/22/10 | ||||||

11/02/10; 11/13/10; 11/24/10 | ||||||

TS-X | StripMap | 02/21/10; 03/26/10; 05/09/10; 05/20/10 | D | 27.3 | 2.75 | HH |

07/14/10; 08/16/10; 09/29/10; 10/10/10 | ||||||

10/21/10; 11/12/10; 11/23/10 | ||||||

TS-X | StripMap | 09/15/10 | A | 31.8 | 2.75 | HH |

TS-X | StripMap | 02/27/10; 07/31/10 | D | 41.7 | 3 | HH |

RS-C | FQ5 | 03/05/10; 11/24/10 | A | 23.3 - 25.3 | 4.7 × 4.9 | Full |

RS-C | FQ6 | 10/21/10; 11/14/10 | D | 24.6 - 26.5 | 4.7 × 4.7 | Full |

RS-C | FQ10 | 02/26/10; 04/15/10; 05/09/10; 09/30/10 | A | 29.1 - 30.9 | 4.7 × 5.1 | Full |

RS-C | FQ11 | 03/26/10; 08/17/10 | D | 30.2 - 32.0 | 4.7 × 5.5 | Full |

RS-C | FQ15 | 03/15/10; 04/08/10; 05/02/10; 08/30/10; 10/17/10 | A | 34.3 - 36.0 | 4.7 × 4.8 | Full |

RS-C | FQ16 | 05/20/10; 07/31/10; 10/11/10 | D | 35.4 - 37.0 | 4.7 × 5.1 | Full |

RS-C | FQ20 | 11/03/10 | A | 39.1 - 40.7 | 4.7 × 4.8 | Full |

RS-C | FQ21 | 02/20/10; 03/16/10; 07/14/10 | D | 40.1 - 41.6 | 4.7 × 5.1 | Full |

AP-L | FBS | 02/27/10; 04/14/10 | A | 38.7 | 6.2 | HH |

AP-L | FBD | 05/01/10 | A | 38.7 | 12.5 | HH/HV |

where

The ratio p refers to the co-polarizations (_{rms}), and Fresnel reflection from the surface at nadir (Г_{0}) by non-linear relationships.

The Fresnel coefficients (Г_{0}, Г_{H} and Г_{V}) are derived from the dielectric constant values of the soil (ε_{r}) (Equations (6) - (8)), which are derived from the top soil moisture and texture measurements (clay, silt and sand contents) using the relationships described by [

In their study of 2004, [_{rms}), top soil moisture (m_{v}). Based on a larger dataset than that available in 1992, the authors show that the expression of ratio q is independent of the surface moisture [

The backscattering coefficients are calculated according to the following relationships:

The formalism proposed by [_{rms}) and dielectric constant (ε_{r}). The latter can be determined based on the relationships proposed by [

In previous studies, the authors define the range of values for which the performance of the models is optimal (_{rms} values (proposed by the author) and h_{rms} in the X-, C- and L-bands are provided (X-h_{rms}, C-h_{rms} and L-h_{rms}, respectively, which correspond to the TerraSAR-X, Radarsat-2 and Alos-PALSAR data). The confidence intervals regarding the surface roughness are notably similar for the two models proposed by Oh (slightly larger in the case of Oh 2004) and significantly wider than the model of Dubois, which is limited to low roughness levels (with values of kh_{rms} less than 2.5). In contrast, a wider confidence interval of the top soil moisture is associated with the model of Dubois, 35% m^{3}・m^{−3}, followed by Oh 2004 (25.1% m^{3}・m^{−3}) and Oh 1992 (22% m^{3}・m^{−3}). According to the incidence angle, the domain of validity is 10˚ - 70˚ regarding the models proposed by [

The method of evaluation and improvement of semi-empirical backscattering models is presented in _{rms}, TSM, Clay, Sand, and θ of the image)) to identify different methods

Models | kh_{rms} | X-h_{rms} [cm] | C-h_{rms} [cm] | L-h_{rms} [cm] | TSM [%] | Inc. Ang. [˚] | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | Min | Max | |

Oh 1992 | 0.10 | 6.00 | 0.05 | 2.97 | 0.09 | 5.31 | 0.38 | 22.56 | 9.0 | 31.0 | 10.0 | 70.0 |

Oh 2004 | 0.13 | 6.98 | 0.06 | 3.45 | 0.11 | 6.17 | 0.49 | 26.24 | 4.0 | 29.1 | 10.0 | 70.0 |

Dubois | - | 2.50 | - | 1.24 | - | 2.21 | - | 9.40 | - | 35 | 30.0 | - |

to improve the models. The equations of the modified models are described and evaluated in the last section (4.2). The models were implemented and evaluated on two independent databases. From a random selection, one half of the samples was used for training (S_{TRAINING}), and the remainder was used for validation (S_{VALIDATION}) (except in the L-band because of the limited quantity of data).

The semi-empirical models exhibit a wide range of performances, as illustrated by the values of the coefficient of correlation (0.31 - 0.80) (

Figures 5(a)-5(c) illustrate the best result of the comparison between simulated and estimated backscattering coefficients for the X-, C- and L-bands. The simulations in the domains of validity (as defined by the authors) are shown in black; otherwise, they are in blue. In those examples, the theoretical domains of validity limit the applicability of the model to 59% (n = 168, in the X-band), 78% (n = 174, in the C-band) and 66% (n = 10, in the L-band) of the observed surface conditions. Nevertheless, the distinction of the simulations based on the domains of validity appears difficult, particularly in the case of Oh’s models, where the two sets of points (blue or black) have fairly similar dispersions. Regarding the model of Dubois, the simulations inside or outside the domain

of validity are clearly separable and associated with an underestimation or overestimation of the backscattering coefficient values, respectively (the results in the X- and C- bands are not shown here).

The behaviors of the residues of the models (_{rms}_{ }(with a decreasing trend from 0.3 to 2.4 dB per unit of kh_{rms}), which confirms that the description of the surface roughness is poor in radar backscatter models. Moreover, the increase of this bias with the frequency (illustrated by the Oh 1992 and Dubois models) underlines the sensitivity of the backscattering coefficients to the roughness states, particularly in the L-band. Other important dynamics constitute interesting levers to reduce the model bias, such as the trends with the incidence angle (particularly for the model of Dubois). Finally, the low sensitivity between the residues and the top soil moisture can be overlooked if this parameter is not a key descriptor of bare soils.

Those sensitive parameters were corrected in the modified version of the three models (displayed in red in

As an example, _{rms} and the Dubois model. The behaviors of the model residues are not necessarily homogenous and linear, as in the case of the relationship between the incidence angle and the residues of the Dubois model in the X-band (_{rms} and the residues,

The modified semi-empirical models were statistically evaluated on validation samples, which represent 50% of the total samples (

of the considered frequency. In the X-band, the coefficient of correlation is 0.69 for the models proposed by Oh in 1992 and Dubois (versus 0.59 before the modification), and the errors on the backscattering coefficients are equal to 1.47 and 1.41 dB, respectively (2.33 and 4.79 dB before the correction). In the C-band, different models show similar performances, where r is approximately 0.64 (they were 0.32 - 0.45), and the RMSE is less than 2 dB (20% in relative value). These errors were 2.16 - 3.66 dB depending on the considered model (

In the L-band, the coefficient of correlation also increases (r is larger than 0.84 for the models proposed by Oh, whereas it is 0.80 before the correction) (

In the following sections, only the best modified models are described for each wavelength (Dubois in the X- and C-bands; Oh 2004 in the L-band).

In the X-band, three correction functions (denoted C_{1-Dubois}_{ }=f (θ), C_{2-Dubois} = f (TSM) and C_{3-Dubois} = f (kh_{rms})) were applied to the initial Dubois model to reduce the error from the incidence angle, top soil moisture and standard deviation of roughness heights (Equations (16) - (19)):

In the C-band, the errors from the incidence angle, top soil moisture and standard deviation of roughness heights were also reduced by applying three correction functions to the initial Dubois model (denoted C_{1-Dubois}_{ }= f (θ), C_{2-Dubois}_{ }= f (TSM) and C_{3-Dubois}_{ }= f (kh_{rms})) (Equations (20) - (23)):

In the L-band, the Oh 2004 model was modified (C_{1-Oh2004} = f (TSM) and C_{2-Oh2004} = f (kh_{rms})) according to the sensitivities observed with the top soil moisture and standard deviation of roughness heights (Equations (24) - (26)):

The domains of validity of the three modified models were extended according to kh_{rms}, the top soil moisture and the incidence angle point of view (_{rms} values for the modified Dubois model. Initially, limited to values below 2.50, the modified model can be applied over a larger range of roughness (to 12.57, which corresponds to an h_{rms} of 6.22 cm). It is slightly improved regarding the incidence angle (27.3˚ - 70.0˚ instead of 30.0˚ - 70.0˚) and not improved in terms of the surface soil moisture. In the C-band, the domain of validity of kh_{rms} for the modified Dubois model also strongly increased (limited now to 9.72, compared to 2.50 initially). No difference was observed for the domain of validity of the top soil moisture, but the lower limit of incidence angle is now 24.3˚ instead of 30.0˚. The increase of the domain of validity widens the possibilities of applications of the semi-empirical models to various agricultural surface states observed after tillage practices [

Finally, unlike the X- and C-bands, the limited sampling in the L-band (n = 15) does not enable the extension of the domain of validity of the models. Indeed, the observed roughness levels, with kh_{rms} values of 0.33 - 1.44, are circumscribed within the limits defined by the authors (0.13 - 6.98). Regarding the incidence angle, all images were acquired at a single value of 38.7˚. Only the top soil moisture had a slightly larger range of values than the initial Oh 2004 model: 3.8-33.3% instead of 4.0% - 29.1%.

This study aimed to improve the performances of three semi-empirical models (Oh 1992, Oh 2004 and Dubois) using a SAR multi-frequency (X-, C- and L-bands) database, which was acquired over an agricultural area with a wide variability of bare soil surface states. The proposed methodology consisted in identifying and correcting the residues of the models, depending on the surface properties (roughness, moisture, texture) and/or sensor characteristics (frequency, incidence angle). The results show that the correction of the residues is significant, especially regarding to the incidence angle, top soil moisture and soil roughness, for which the signal sensitivity is equal to 0.13 dB by, 0.06 dB by % m^{3}・m^{−3} and 1.25 dB by m m^{−1} in mean, respectively. Finally, the modified models perform better than the initial formalisms, and the best modified model has been retained for each frequency domain: Dubois for X- and C-bands, and Oh 2004 for L-band. After correction of the residues, the correlations were improved between simulations and observations (from 0.59 to 0.69 in the X-band, from 0.44 to 0.65 in the C-band, and up to 0.84 in the L-band), whereas the RMSE and biases were reduced (RMSE < 2 dB in the C- and X-bands and 1 dB in the L-band), highlighting the pertinence of the method. Moreover, the domains of validity were strongly increased for the modified models because the original formalism did not consider all information carried by the main input variables (standard deviation of roughness heights and top soil moisture) to simulate the backscattering coefficients, which explains the poor initial results. The extension of the domains of validity is particularly notable in the X- and C-bands with maximum kh_{rms} values of 12.57 and 9.72 for the Dubois model, which corresponds to an increase by a factor 5 and 4, respectively.

The results offer new perspectives for the inversion of soil parameters from microwave models, particularly with the ongoing and future satellite missions (Sentinel-1A/ B, Alos-2, Terrasar-X…). In a near future, this approach could be extended to physical-based models such as the IEM (Integral Equation model) widely used in microwave remote sensing.

The authors wish to thank the ESA (European Space Agency), DLR (German Space Agency), CSA (Canadian Space Agency), JAXA (Japan Aerospace eXploration Agency), SOAR Project and CNES (Centre National des Etudes Spatiales) for their support, funding and satellite images (proposal HYD0611 and SOAR-EU and Categorie-1 ESA project no. 6843). In addition, the authors wish to thank the farmers (Mr. Blanquet, Mr. Bollati, Mr. Brardo, Mr. Pavan and Mr. Peres) for their time and precious discussion and the people who helped for collecting the ground data.

Fieuzal, R. and Baup, F. (2016) Improvement of Bare Soil Semi-Empirical Radar Backscattering Models (Oh and Dubois) with SAR Multi-Spectral Satellite Data (X-, C- and L-Bands). Advances in Remote Sensing, 5, 296-314. http://dx.doi.org/10.4236/ars.2016.54023