## 1 Introduction  
Soil moisture is a key variable in hydrogeological monitoring; it can reflect infiltration and runoff, thus indicating precipitation distribution in the region [1; 2]. Soil moisture controls the balance of surface energy and influences atmosphere formation through latent heat flux and sensible heat flux. In agricultural management, soil moisture content is an important measure of rational water resource utilization. In hydrological models, climate models, and agricultural management, soil moisture is entered the model as a parameter. Soil moisture parameter acquisition mainly involves remote sensing optical data (e.g., Aqua satellite) and microwave remote sensing data (e.g., Soil Moisture and Ocean Salinity satellite). The inversion data is the surface parameters obtained by the algorithm through the band information of the image. Optical data have high spatial resolution, which can meet the spatial resolution requirements of research, but inversion accuracy is not high due to the influence of weather factors and the vegetation canopy [3; 4; 5]. In passive microwave remote sensing, Soil Moisture Active Passive (SMAP) at the L-band can penetrate the soil surface and obtain high-precision data products [6; 7]. However, these data demonstrate low spatial resolution, which can be improved via a downscaling process. The spatial resolution of soil moisture data based on the L-band (i.e., passive microwave) cannot satisfy watershed scale studies. Therefore, it is essential to identify a simple and feasible downscaling approach for this problem. Several downscaling methods have been developed throughout the past decade, which can be classified into three categories: (i) regression methods based on the use of topography and soil depth information [8; 9]; (ii) methods based on the combination of coarse resolution passive microwave data with fine-scale optical data and a surface process model [10]; and (iii) methods based on the combination of passive microwave data with a downscaling factor, such as the Surface Temperature and Vegetation Index [11]. The regression method involves scale conversion by establishing the functional relation of the characteristic quantities (e.g., vegetation index, land surface area, and surface temperature) of different images [12; 13]. This method retains the integrity of image radiation information while reducing scale, which benefits the application of results in other models [14]. However, this class of methods must follow the premise that the functional relation is essentially identical on all scales [15]; in addition, functional relationships must be determined through a single land-cover type. Methods based on fine-scale optical data and a surface process model must obtain the evaporative fraction (EF) and actual evaporative fraction (AEF), which are used in the energy balance model. Then, the method is implemented using a surface energy balance model to decouple the effects of external factors (i.e., land use, soil depth, and meteorological forcing) on the relationships between the parameters of the energy balance model and surface soil moisture. These methods comprehensively consider land-cover type, soil evaporation efficiency, and non-linear relationships, rendering the results of pixel decomposition more similar to the actual value with an error of 0.012 m\({}^{3}\)/m\({}^{3}\). However, these methods must obtain additional parameters to support accurate scaling results, and complex calculations are required. In practical applications, these methods are highly accurate, but do not meet hydrogeological monitoring requirements due to the operational complexity [16; 17; 18]. Methods based on a combination of passive microwave data and downscaling factors consider the surface temperature and vegetation coverage index and establish the relative soil moisture index, but have two fundamental differences [19]: (i) it is unnecessary to have an EF and AEF; and (ii) a simple energy balance model can be used in place of a complex surface process model.