## 1 Introduction  
A positive impact on hydrology as well as on modern agricultural practices can be achieved by monitoring spatial and temporal dynamics of some land surface variables such as soil water content, \(m_{\mathrm{v}}\), and vegetation. Despite the fact that synthetic aperture radar (SAR) allows acquiring in all weather conditions, unassessed strengthenings of the relations among backscattering, \(\sigma^{\circ}\), at different frequencies and polarizations and soil-vegetation variables (SVV) are limiting the operational application of SAR. Indeed, SAR configuration controls the wave-target interactions [1; 2] and, thus, affects models' assessments depending on its frequency, polarization and acquisition geometry. The dependence of bare soils \(\sigma^{\circ}\), \(\sigma^{\circ}\)s, on both water content and surface roughness was modeled by several authors [1; 2; 3; 4; 5]. However, the need of a prior knowledge of the soil surface roughness could reduce the feasibility of SAR techniques [4; 6; 7; 8]. Indeed, reliable roughness measures are hardly achievable: (i) in situ measurements with contact methods (e.g., grid board [9]) are point based and usually not representative at plot scale; (ii) innovative methodologies (e.g., non-contact ultrasonic profiling) are capable of describing wide areas but still economically expensive (i.e., requiring airborne acquisitions). Over vegetated areas an additional \(\sigma^{\circ}\) contribution, \(\sigma^{\circ}\)v, needs to be taken into account. Several authors, investigated \(\sigma^{\circ}\)v by setting up theoretical models [10; 11; 12] schematizing the vegetation as simple targets of known geometry (such as plates and cylinders). Simple empirical models, avoiding a rigorous mathematical and geometrical simulation of the canopy, are often based on ratios of bands acquired at different polarizations [13; 14; 15; 16]. The need of a priori characterization of vegetation structure (hardly achievable through in situ campaigns) reduces the operational use of SAR in agriculture. In recent years, several researches focused on \(m_{\mathrm{v}}\) quantification (over both bare, B, and vegetated, V, soils) explored different SAR configurations and approaches by testing (Table 1): (i) the use of temporal indices; (ii) the integration of passive microwaves and in situ data; (iii) different \(\sigma^{\circ}\) models; (iv) the conjunct use of complex statistical models (such as Bayesian approach); (v) empirical fitting and ratio methods (refer to the Appendix A for symbols and acronyms). There were several approaches: empirical, EA; semi-empirical, SEA; theoretical, TA; polarimetric, PA; statistical SA, these latter employing Neural Networks, polarimetric indices or, channels ratio. Some authors calibrated \(\sigma^{\circ}\) models such as: IEM (Integral Equation Model [4]), WC (Water-Cloud model [17]); GO (Geometrical Optics [4]); Dubois [1]; Oh [2; 3]; RTM (Radiative Transfer Model); MIMICS (Michigan Microwave Canopy Scattering model [18]). Several authors separated soil and vegetation contributions by exploiting more than two polarizations (single frequency), by parameterizing the WC through in situ data. All these approaches are usually based on regression analyses among \(\sigma^{\circ}\) and SVV (i.e., soil roughness, water content, fractional cover and leaf area index). It is well known that SAR configuration (acquisition geometry, frequency and polarization) plays a fundamental role in the \(\sigma^{\circ}\) vs. SVV relationship; thus it is expected that modifications of some SVV change also the spatial correlation between data acquired with different configurations. Based on this evidence, this paper firstly aims to quantify the strength of the relation among \(\sigma^{\circ}\) and four SVV (dynamic and single regression analyses) over bare and vegetated soils, over a wide range of cultivars and for different SAR configurations.