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This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The objective of this paper is to present the contribution of a new dielectric constant characterisation for the modelling of radar backscattering behaviour. Our analysis is based on a large number of radar measurements acquired during different experimental campaigns (Orgeval'94, Pays de Caux'98, 99). We propose a dielectric constant model, based on the combination of contributions from both soil and air fractions. This modelling clearly reveals the joint influence of the air and soil phases, in backscattering measurements over rough surfaces with large clods. A relationship is established between the soil fraction and soil roughness, using the Integral Equation Model (IEM), fitted to real radar data. Finally, the influence of the air fraction on the linear relationship between moisture and the backscattered radar signal is discussed.

Soil moisture and roughness parameters play a key role in hydrological and climate studies. Considerable effort has been devoted to the study of radar backscattering responses from natural surfaces, in active microwave remote sensing [

Secondly, past experimental studies have been designed to estimate surface moisture only, by adding different hypotheses to the surface roughness description. A linear relationship between surface moisture and backscattered radar signals has been proposed [

In general, for agricultural soils with rough surfaces, we observe clods with a large air fraction between them. This air fraction is not taken into account when estimating the dielectric constant. In fact, with the gravimetric approach, and thetaprobe or TDR measurements, we neglect this effect and analyse the soil fraction only. In the present study, we propose a new modelling process for the dielectric constant, in order to include the effects of the air fraction. Our calculation of the dielectric constant is based on the assumption of a composite ground, with both soil and air fractions. Section 2 describes the experimental data used for this work, recorded during three experimental campaigns (Orgeval'94, Pays de Caux'98, Pays de Caux'99). Section 3 describes IEM modelling, using dielectric constant modelling based on the introduction of both “air” and “soil” phases. It presents an analysis of the relationship between soil fraction and radar signal behaviour, and its influence on the relationship between radar signal and soil moisture. Finally, our conclusions are presented in Section 4.

In this study, data was acquired during three experimental campaigns (Orgeval'94, Pay de Caux'98, 99,), over agricultural watersheds. For each one of these, SAR images (RADARSAT-1, SIR-C) were acquired with different configurations (

The objective of this experimental campaign was to characterize the effect of soil roughness on radar measurements. The Orgeval watershed is located to the east of Paris (France; Lat. 48° 51′N and Long. 3° 07′E). The experimental campaign was conducted by the CETP (Centre d'étude des Environnements Terrestre et Planétaires) and the CEMAGREF (Centre d'Etude de Machinisme Agricole, du Génie Rural et des Eaux et Forets). The Orgeval'94 campaign was run concurrently with the SIRC/XSAR (1.25 GHz, 5.3GHz and 9.25 GHz) missions [

The soil composition is relatively constant over the whole basin: 17% clay, 78% silt, and 5% sand. Simultaneous ground measurements were carried out in eight bare soil fields. The soil moisture content remained high and constant over the watershed (about 0.35 cm^{3}/cm^{3}), such that the soil roughness and tilling practices were the only remaining factors, which could influence the backscattered radar signals.

The Pays de Caux'98, 99 experimental campaign was designed to characterize the agricultural soil roughness and its effects on erosion and runoff in the North of France. The test site was the Blosseville watershed located in the Pays de Caux, in Northern France (long. 0°50′ W, lat. 49°47′ N). The loamy soils of the northern European loess belt are sensitive mainly to soil structure degradation, and are commonly exposed to erosion caused by concentrated runoff. Within that framework, an intensive research program was carried out in the region of the Pays de Caux. The site's soil features are: (1) a very homogenous loamy texture (13% clay, 65% loam, and 22.5% sand), (2) approximately 50% of the fields are bare, or nearly bare. RADARSAT-1 measurements were recorded in 1998 and 1999, over more than 10 large (more than 100m x 100m each) test fields.

The rms heights (

The present study is focussed on a particular radar configuration: HH polarization and C band (5.3 GHz) operating mode, for the radar acquisitions. IEM is used as a reference, for the simulation of backscattering coefficients. It is the most used model in backscatter studies of bare soil ([

The dielectric constant is introduced into IEM, through the Fresnel reflection coefficients, _{0}, between the air (region 0) and the soil layer (with permittivity

Water content is converted to a dielectric constant, by using a dielectric mixing model ([_{i}_{i}

Zribi and Deschambre [^{2}/

As can be seen in

In this study, rather than trying to simulate the heterogeneity resulting from the presence of air, with an accurate 3D backscattering model, we introduce a modification to the modelling of the dielectric constant. We consider a dielectric, two-phase mixing model [_{soil}) and _{soil} in the mixing formula, yielding:

In order to retrieve the variations of _{soil} for our database, it was decided to fit IEM to the radar data, in the HH and C band configurations.

_{soil} parameter varies as a function of the roughness parameter Zs. A correlation can be observed between the soil fraction and surface roughness (correlation coefficient R^{2} equal to 0.49). This could be explained simply by the fact that, with increasing roughness, we have an increase in the number and size of clods and thus a higher probability of encountering a higher air fraction. We propose the following empirical relationship between Zs and _{soil}, derived from the fitted data:

Real data fitted to this model shows a very high portion of air (even superior to 0.7) for high roughness values. This is due, firstly to our use of a single dielectric constant and the hypothesis of homogeneous soil texture, and secondly, to the use of a surface model, which is not necessarily well adapted to the backscattering estimation, over these surfaces.

^{2}|, on a linear scale, in HH polarization, in the L (1.25 GHz) and C (5.3GHz) bands, as a function of the volumetric moisture parameter _{s}_{soil}. We clearly observe the strong influence of this parameter on the Fresnel coefficient, with increasing values of |^{2}| for a low air fraction. This could explain, in particular, the strong variations in radar signal observed as a result of variations in moisture, from one field to another. In fact, the saturation of |^{2}| (on a logarithmic scale) and of the resulting backscattered signal, at high moistures, will occur more rapidly when the air fraction is low. This is the reason for which backscattering simulations generally predict saturation, before it occurs in real measurements [

^{0}), and the mean soil surface volumetric moisture (_{s}

As described in the Introduction, the coefficients describing the linear relationship between moisture and radar signal are often different from one watershed to another and also from one year to another. For example, with ERS/SAR (VV polarisation, 23° incidence angle), the slope is equal to 0.33 for [_{s}_{1}=5%, _{s2}_{s3}_{s4}_{s5}_{s6}_{soil} parameters: _{1}, v_{2}, _{3}, _{4}, _{5}, and _{6}, estimated from a uniform distribution between the values 0.6 and 1. These lead to infinite cases, which could be observed at real agricultural sites. We then simulated backscattering coefficients with IEM for different situations, by mixing one _{soil} parameter (between 0.6 and 1) with one moisture value (_{l}, _{sj}

The influence of the air fraction can thus be clearly observed in the behaviour of the backscattered radar signals. This effect is more significant for low moistures, with a variation equal to 3 dB for a moisture value of 5%, and 2dB for a moisture value of 30%, in the C band (

This result explains the high variation of linear relationship between soil moisture and radar signal, due just to the presence of the air fraction in the estimation of dielectric constant. This is in agreement with the other experimental studies showing this variation [

In this paper we deal with a scientific question, often neglected in our previous studies, related to the computation of the dielectric constant used in backscattering models for the estimation of soil roughness or moisture. For real agricultural soils, particularly for medium or rough surfaces, we have observed the presence of a significant air fraction that could be present between clods, or below clods. This portion could have a significant influence on the dielectric constant. In this study, based on a large experimental campaign involving moisture, roughness and radar measurements, we propose modelling of the dielectric constant in which both a soil fraction and an air fraction are used. The fitting of an IEM to real radar data clearly shows that an increase in roughness leads to an increase in the air fraction. However, this fraction could also be correlated to the time since the soil was last worked. Generally, for new soil tillage, we observe the presence of larger quantities of air between embedded clods, and with rainfall and runoff, the percentage of air decreases. Therefore, the _{soil} parameter probably decreases with the age of the tillage. This effect could explain some of the differences in behaviour observed in the correlation between radar signals and soil moisture. These results illustrate the difficulty to analyse backscattering behaviour over natural surfaces. In future studies, first, it will be very interesting to estimate experimentally the percent of air fraction for different types of soil (large ploughed, ploughed, cloddy, smooth soils, etc) in order to propose a correction of dielectric constant computation, for each case of surface. Second, the consideration of volume diffusion in surface backscattering models needs to be more discussed and estimated, particularly for surfaces with large air fraction percent.

This work was financed by the French CNES/TOSCA program. The authors would like to thank the European Space Agency (ESA) for providing us with the radar images free of charge.The authors also wish to thank the BRGM, CEMAGREF and CETP teams for their logistical support during the field campaigns.

Roughness parameters of the test fields.

Inter-comparison between radar signal measurements and backscattering simulations as a function of soil roughness.

Illustration of real agricultural soils.

Clod illustration, showing soil and air fractions.

Variation of the _{soil} parameter (soil fraction) as a function of the soil roughness parameter Zs.

Illustration of variations in |^{2}|, as a function of soil moisture, for different values of the _{soil} parameter (_{soil}=1, _{soil} =0.9, _{soil} =0.8, _{soil} =0.7, _{soil} =0.6),

Illustration of IEM simulations, with a classical computation of the dielectric constant, for different values of roughness, as a function of soil moisture.

Illustration of the effects of air fraction on the linear relationship between soil moisture and simulated radar signals, lines corresponding to ten linear relationship cases, with for each one, as input, successive surface moisture values (5%, 10%,15%, 20%, 25% and 30%) with six _{soil} parameters (_{1}, _{2}, _{3}, _{4}, _{5}, and _{6}) estimated from a uniform distribution between the values 0.6 and 1.

Details of radar data acquisition.

Orgeval 94 | SIR-C | 12/04/94 - 18/04/94 | HH |

Pays de Caux 98 | RADARSAT | 24/02/98 |
HH 39° |

Pays de Caux 99 | RADARSAT | 07/02/99 |
HH 23° |