*3.3. The Retrieval Algorithm of Soil Moisture*

In this study, the soil moisture retrieval algorithm of the linear regression equation proposed by Chew et al. [11] was based on the assumption that the surface reflectivity obtained from CYGNSS data is linearly correlated with the soil moisture of SMAP, and this linear correlation presents spatial variation and does not vary with time. The spatial resolution of CYGNSS is much smaller than the SMAP product, and the surface reflectivity varies depending on land cover and topography. Therefore, to effectively attenuate the effects of vegetation cover and topography, surface reflectivity corrected by the proposed method and soil moisture products of SMAP were sampled on a 3 × 3 km grid using the nearest neighbor sampling method [33–35], and thus soil moisture was retrieved. Among them, the nearest neighbor sampling method did not change the original pixel values of the SMAP products during resampling. The SMAP products of the 36 × 36 km grid were sampled into the 3 × 3 km grid, i.e., all 3 × 3 km grids within a 36 × 36 km grid have the same values. The expression was as follows:

$$\mathcal{S}M\_{\text{CYGNSS},t} = \mathcal{J} \cdot \left(\Gamma\_t - \overline{\Gamma\_{\text{cal}}}\right) + \overline{\mathcal{S}M\_{\text{SMAP},\text{cal}}} \tag{7}$$

*SMCYGNSS,t* is the soil moisture retrieved with CYGNSS, Γ*<sup>t</sup>* is the corrected surface reflectivity of CYGNSS and Γ*cal* and *SMSMAP*,*cal* are the mean values of corrected surface reflectivity from CYGNSS and soil moisture products of SMAP during the modeling time, respectively. *β* is the slope, representing the slope of the SMAP products and corrected surface reflectivity after removing *SMSMAP*,*cal* and Γ*cal* at the modeling time. If there were less than three sampling points of CYGNSS in a 3 × 3 km grid, the *β* of the grid was not calculated. The value of *β* will be used to estimate the soil moisture during the validation period. Soil moisture retrieval was performed for the 3 × 3 km grid according to the above process, and then the soil moisture result of 3 × 3 km were aggregated and averaged to the 36 × 36 km grid. The mean values for soil moisture of all 3 × 3 km within the 36 × 36 km grid were used as the retrieval values of soil moisture of the final 36 × 36 km grid.
