# Crop Water Content of Winter Wheat Revealed with Sentinel-1 and Sentinel-2 Imagery
## 2 Materials and Methods
### Modeling Method  
Compared with fully polarized SAR data, the dual-polarized Sentinel-1 data lacks necessary polarization information when, and therefore cannot effectively obtain information about vegetation canopy water content. However, previous studies have found that single-polarized or dual-polarized SAR data can express soil water content information in areas covered by vegetation [35]. In this study, the correlation between SAR polarization index with crop water content and soil water content was analyzed. The result found that the SAR polarization index and soil water content information generally had a better and significant relationship. Therefore, multiple SAR polarization indices were constructed based on the Sentinel-1 data and the index with the highest correlation with soil water content was selected as the input parameter in the water cloud model. The water cloud model was fitted to the sample points of the modeling set to obtain a model for monitoring winter wheat plant water content. During construction of the SAR polarization index, the mask file of the study area was firstly used to extract the winter wheat planting area in Gaocheng District, and then the percentiles of VH and VV in the statistical area were counted. According to previous studies, the \(\sigma^{0}\) value of the 5% quantile represents the minimum humidity of the soil (\(\sigma^{0}\)dry) and the \(\sigma^{0}\) value of the 95% quantile represents the maximum humidity of the soil (\(\sigma^{0}\)wet) [24]. The resulting enhanced soil moisture indices were VHen and VVen, respectively (Formulas (2) and (3)). Then, the enhanced SAR polarization index was constructed based on VHen and VVen. \[\mathrm{VH}_{\mathrm{en}}=\frac{\sigma^{0}_{\mathrm{vh}}-\sigma^{0}_{\mathrm{ vh\ dry}}}{\sigma^{0}_{\mathrm{vh\ wet}}-\sigma^{0}_{\mathrm{vh\ dry}}} \tag{2}\]  
\[\mathrm{VV}_{\mathrm{en}}=\frac{\sigma^{0}_{\mathrm{vv}}-\sigma^{0}_{\mathrm{ vv\ dry}}}{\sigma^{0}_{\mathrm{vv\ wet}}-\sigma^{0}_{\mathrm{vv\ dry}}} \tag{3}\]  
where \(\sigma^{0}_{\mathrm{vh}}\) is the VH backscatter coefficient of the sample points, \(\sigma^{0}_{\mathrm{vv}}\) is the VV backscatter coefficient of the sample points, \(\sigma^{0}_{\mathrm{vh\ dry}}\) is the VH backscatter coefficient of the minimum humidity of the soil, \(\sigma^{0}_{\mathrm{vh\ wet}}\) is the VH backscatter coefficient of the maximum humidity of the soil, \(\sigma^{0}_{\mathrm{vv\ dry}}\) is the VV backscatter coefficient of the maximum humidity of the soil, \(\sigma^{0}_{\mathrm{vv\ wet}}\) is the VV backscatter coefficient of the maximum humidity of the soil. For Sentinel-2, the correlations between different vegetation indices and water content of winter wheat based on the Sentinel-2 data (Table 2) was calculated. Five vegetation indices with high correlation coefficients were selected for gray relational analysis (GRA) [36]. Using the results of the GRA, we determined the factors (Vegetation water content index) for modeling the water content of winter wheat crop. A multiple linear regression model for constructing water content of winter wheat crop by least squares method was used. Then, the model would be used for water content estimation of winter wheat crop.