*2.3. PALSAR-2 Datasets, Corresponding Preprocessing Methods and Cross-Validation Scheme with CyGNSS Data*

PALSAR-2 s quadruple observation datasets (Lv. 1.1; 40–50 km observation widths, 70 km observation length; 307 scenes; August 2018–December 2021, Table S1) containing observations of the Mekong Delta were prepared after the radiometric and polarimetric calibration factors of the PALSAR-2 standard product were updated (on 24 March 2017 [30]). The high-spatial-resolution (4.3 m azimuthal resolution and 5.1 m range resolution at a 37◦ incidence angle) quadruple data were decomposed to characterize the microwave scattering pattern in inundated paddy soils and non-inundated paddy soils at different rice growth stages. The phase and polarimetry data in PALSAR-2 s quadruple observation datasets were converted into a coherency matrix; a refined Lee filter (7 × 7 window) was applied to ease speckle noise; and the data were then decomposed with Singh 7 components [31]. The digital number of the HH/HV/VH/VV microwave data was used in the backscatter reflectivity calibration expressed in Equation (5):

$$
\sigma^0 = 10 \cdot \text{Log}\_{10} < I^2 + Q^2 > -105.0 \tag{5}
$$

where *σ*<sup>0</sup> is the backscattering coefficient, *I* is the value of the imaginary component and *Q* is the value of the quadrature component of the digital numbers. The value of −105 is the calibration factor noted in the literature [30]. An inundation detection classification task (i.e., to determine whether the field water level was higher than the soil surface or not) was conducted with a support vector obtained in the previous supervised classification study [9] during ground observation collection (a total of 624 ROIs considering different rice growth stages), as mentioned above in Section 2.1. The backward geocoding of the abovementioned products was conducted by the Newton–Raphson method with ellipsoidal height data (DEM: Shuttle Radar Topography Mission 3 (SRTM3) version 4 and the EGM2008 geoid model) and the ALOS-2 orbital data (3D-spline-interpolated on every azimuth line).

The cross-validation was conducted with the PALSAR-2 preprocessed quadruple data and the CyGNSS specular points Lv. 2 data product following the calibration described in Section 2.2; these data were observed over the same locations as the PALSAR-2 geocoded images within ±3 days of the PALSAR-2 observation date. First, the PALSAR-2 data were spatially downsampled to a 500 m resolution, and then the precision index of each corresponding specular point was calibrated over the geocoded PALSAR-2 images. Finally, each weighted mean of PALSAR-2 signals (e.g., the 7-component scattering intensities, *σ*0, and the spatial inundation rate) was further weighted based on the precision index derived value over the PALSAR-2 image, and the results were compared with the CyGNSS reflectivity Γ data.

These SAR data processes were necessary for the robust validation to compensate for the footprint size difference of the inundation status that was observed between the ground point observations and the GNSS-R data that were detected from space.
