## 1 Introduction  
Soil moisture is a crucial state variable in the fields of hydrology, climatology, ecology, and agriculture [1; 2; 3; 4]. With the development of remote sensing (RS) technology, large-scale monitoring of soil moisture has become a reality without expensive in situ monitoring networks. As an active microwave that can monitor soil moisture at a spatial resolution of meters to tens of meters under almost all weather conditions, synthetic aperture radar (SAR) is a promising data source to monitor soil moisture with relatively high prediction accuracy [5; 6]. In recent years, as SAR satellite sensors develope from the earlier Seasat, ERS-1/2, JERS-1, RADARSAT-1 and other single-polarization space-borne sensors to the more recent ENVISAT/ASAR, SIR-C/X-SAR, ALOS/PALSAR, Sentinel-1, RADARSAT-2, TerraSAR-X, Cosmo-Skymed, GF-3, ALOS-2 multiband, and multipolarization satellite sensors, SAR has been widely used for soil moisture inversion [7; 8; 9; 10; 11]. According to the land cover class, the methods of soil moisture inversion using SAR data can be classified into two types: methods applied to bare soils [9; 10; 11] and methods for soils covered by vegetation [12; 13; 14; 15; 16; 17]. For soil moisture inversion of soils with vegetation coverage, the key question is how to eliminate the effect of vegetation coverage on the backscattering coefficient. MIMICS and water-cloud models are currently used to describe the backscattering. Because of the complexity of the MIMICS model, the use of the water-cloud model became common [18; 19]. [PERSON] [20] developed an inversion approach to estimate surface soil moisture using sentinel-1/2 data based on the calibration of the water-cloud model. For soil moisture inversion of bare soil, the main problem is how to handle the soil surface roughness. Unsuccessful roughness parameterization has become the main source of error that affects the accuracy of soil moisture inversion. Currently, there are four conventional methods to parameterize the surface roughness [21]. The first method is change-detection analysis under the assumption of constant roughness. [PERSON] et al. [22] offered a solution strategy to estimate soil moisture using multiangle radar images without ancillary data. The second method is calibrating soil roughness parameters. [PERSON] et al. (2002) developed a calibrated integral equation model (CIEM), which used the empirical correlation length _lopt_ to replace the correlation length _l_[23]. The third method is combining the semiempirical relations between the correlation length and root mean square height (_Hrms_). [PERSON] et al. (2014) proposed a new description of soil surface roughness for soil moisture [24]. The fourth method is using prior knowledge of the roughness state. [PERSON] et al. (2002) used prior information on the surface roughness of a given area to invert soil moisture [25]. There are other alternative approaches to the roughness problem, such as multiscale processes [26; 27], two-dimensional surface roughness characterization [28; 29], and polarization decomposition data usage [30; 31]. There are also radar backscatter models that can correctly model the radar signal for a wide range of soil parameters in bare surface soil [32], which can be physical, semiempirical, or empirical. The most popular physical models are the integral equation model (IEM) [33], an IEM calibrated by [PERSON], which is called the calibrated integral equation model (CIEM) in this paper [23; 34; 35; 36; 37; 38], and the advanced integral equation model (AIEM) [39]. This paper intensively exploits the surface roughness by combining the change-detection analysis under the assumption of constant roughness and the calibrating soil roughness parameters. The approach attempts to use the backscattering of VV and VH polarizations and CIEM to invert soil moisture and surface roughness in bare soil. The surface roughness parameter can often be expressed as _Hrms_ and the correlation length \(l\).