## 5 Discussion  
Based on the LME model, we explored the potential for soil moisture retrieval over Poyang Lake ungauged zone using time series Sentinel-1 images. Although several algorithms have been proposed to retrieve soil moisture maps operationally from Sentinel-1 data recently, our method is different in that it assumes a linear SM-\(\sigma^{0}\) relationship varied with both time and space. The accuracies of three LME models developed using different polarized \(\sigma^{0}\) images (Table 3) all meet the ESA requirement for GMES soil moisture product (\(\leq\)5%). Moreover, after validating the model predicted soil moisture  
Figure 7: Soil moisture index maps for six selected dates. indices against those calculated with ground measurements, the performance statistics achieved are comparable with those from the existing similar studies [59; 60], with the overall R\({}^{2}\) and cross-validated R\({}^{2}\) being 0.68 and 0.64, respectively. The LME model has been widely used to account for daily variations of the AOD-PM\({}_{2.5}\) relationship and shows good performance in model predictions. Since parameters that influence the AOD-PM\({}_{2.5}\) relationship exhibit much less spatial variability than temporal variability, the LME model without the site effect shows similar performance when compared with the full LME model [34]. In contrast, the SM-\(\sigma^{0}\) relationship varies strongly in space and accounting for the site effect in the LME model is necessary to improve the predicted soil moisture accuracy, as shown in Table 4. However, when predicting soil moisture maps over the whole study area, the site-specific intercept was not available for each grid. Therefore, a relative soil moisture index was proposed to correct for site effect. The derived soil moisture indices of each site capture the temporal dynamics of the measured soil moisture indices well (Figure 4), which are usually of greater interest than their absolute values in some applications [61]. It is necessary to investigate the prediction uncertainties that are associated with this work. Possible sources of error are as follows: (1) soil moisture ground measurements. With a limited number of observation sites under which the main land cover class is cropland, it is difficult to fully characterize the soil moisture patterns over the study area. Besides, measurement errors of the DZN1 sensors also contribute to the uncertainties; (2) Different spatial scales between in situ points and satellite pixels. While soil moisture measurements that are used to calibrate the SM-\(\sigma^{0}\) relationship are collected at point scale, the collocated backscattering coefficients represent the average condition of the whole grid cell; (3) Different observation depths between the DZN1 sensor and C-band radar. Ground measurements that are used in this study are taken at the depth of 0-10 cm, whereas the penetration depth of C-band microwaves is about 0.5-2 cm [62]. This difference could bring uncertainties during the calibration and validation phases; (4) The LME model. Under the assumptions of a linear SM-\(\sigma^{0}\) relationship and \(\sigma^{0}\) as the single predictor, the developed LME model introduces uncertainties. Multiple factors affect the spatial variability and the temporal dynamic of soil moisture and most of these factors are interrelated, making it difficult to model all of the predictors. Despite the uncertainties, the LME model that is developed in this study shows a better and more robust performance when compared with the linear fixed effects model (Figure 5). By allowing the SM-\(\sigma^{0}\) relationship to change temporally and spatially, the LME model accounts for other factors to some extent, such as vegetation and surface roughness. More predictors, such as NDVI and soil texture, can be added to the LME model to further study the spatial variation of the SM-\(\sigma^{0}\) relationship. Due to its simplicity, the model can be easily transferred to other regions with multi-temporal SAR images and soil moisture measurements.