*3.2. Cross-Validation with PALSAR-2 Quadruple Observation Products*

The relationship between CyGNSS reflectivity Γ values and PALSAR-2 backscatter σ0 values was differentiated depending on the specular point incidence angles and effective scattering area (Tables S2 and S3). Positive relationships between the Γ values and σ<sup>0</sup> values were found with 0–10◦ incidence angles (Figures S2–S6a,b; Table S2). For specular points obtained at 10–70◦, the correlations became negative, with a few exceptions observed for a fine specular point group (i.e., for incidence angles of 30–35◦, the square root value of the effective scattering area is smaller than 6 km, Table S2, Figure 9). The spatial inundation rates and Γ values showed mostly positive correlations among the groups with incidence angles of 10–50◦. In contrast, negative correlations tended to be dominant for low-end incidence angle groups of 0–10◦ and high-end incidence angle groups of 50–70◦ (Table S2, Figure S2). In such high-/low-end incidence angle groups, the double bounce factor tended to show the most significant co-relationship with the Γ values among the 7-component scatterings (odd/double/volume scatterings listed in Table S1 and shown in Figures S3–S5. The remaining component analysis results are not shown in this paper since the correlations were weaker than those of the odd/double/volume scatterings. In contrast, for the middleincidence-angle groups (10–50◦), the volume diffusion results tended to show the most significant correlations with the Γ values (Table S2, Figures S3–S5). Among the PALSAR-2 HH/HV/VV backscatters, HV tended to show the most significant correlations with the Γ values (Table S2, Figure S6).

**Figure 7.** Samples of nonnormalized Γ values in 2020 (**a**–**d**) and 2021 (**e**–**h**). The left-hand side scenes are snapshots obtained in dry seasons (**a**,**c**,**e**,**g**). The right-hand side scenes are snapshots obtained in rainy seasons (**b**,**d**,**f**,**h**).

**Figure 8.** PALSAR-2 data-based rice map ((**a**); white pixels indicate rice paddies), PALSAR-2 databased rice floodability map (**b**) and inundation detection snapshot obtained by PALSAR-2 above one of the study sites [Thot not, Can Tho city, Vietnam, on 6 May 2016 (69 days after sowing)] with the corresponding aerial photo (**c**); CF: Continuously inundated paddy; AWD: Alternate wetting and drying paddy; the temporal water level dynamics of these blocks are presented in the referenced literature [21,26,27]).

The CyGNSS reflectivity Γ and PALSAR-2 backscatter data series showed a highly nonlinear relationship, and this was one of the causes of the low Pearson correlation coefficients (Table S2). Particularly for the relationship between the Γ values and the PALSAR-2-based spatial inundation percentages, three domains with unique characteristics were found (Figure S2g,m). First, for the specular points whose Γ values are approximately smaller than −20 dB, relatively high inundation percentages were found (Figure S2g,m; domain shown by the green arrow). In such a domain, the Γ values tended to show a linearly positive correlation with the inundation percentages. Second, for specular points with Γ values between approximately −20 dB and 0 dB, specular points with 0% spatial inundation percentages were detected (Figure S2g,m; domain shown by the red arrow). In this domain, the Γ values tended to correspond to upwardly convex negative nonlinear correlations. Finally, for the specular points with Γ values greater than approximately 0 dB (Figure S2g,m; domain shown by the blue arrow), relatively high inundation percentages were detected. In this domain, the Γ values tended to show upwardly convex positive nonlinear correlations.

**Figure 9.** Two-dimensional scatterplots between the CyGNSS reflectivity Γ (dB) and PALSAR-2 based spatial inundation percentage (**a**) and PALSAR-2 back scatters σ<sup>0</sup> (dB) values ((**b**) HV, (**c**) odd scattering, (**d**) volume diffusion, (**e**) double bounce) at specular points with 30–35◦ incidence angles. The statistical analysis results representing these relationships are described in Table S2.

Since the relationship between the CyGNSS reflectivity Γ and PALSAR-2 backscattering σ0 values was also highly nonlinear (Figures S3–S6), a quadratic polynomial fitting analysis was carried out to survey the direction of convexity (downwardly convex, linear, or upwardly convex; Table S3). Although the relationship was mostly downwardly convex for the groups with incidence angles of 0–60◦, an upwardly convex nonlinear relationship became dominant for groups with incidence angles of 5–15◦ and 60–70◦ (Table S3, Figures S3–S6). In contrast, for the middle-incidence-angle groups (15–60◦), downwardly convex nonlinear relationships represented the majority.

#### **4. Discussion**
