## 5 Evaluation of Scale Effects in the Validation of GOCI-Derived SSC
### Proposed Method for Scale Effect Evaluation  
To address these issues, a scale effect evaluation method for validating GOCI SSC results in highly dynamic waters--based on the CV of HJ CCD SSC within the corresponding GOCI pixel--is proposed. The procedure is as follows:  
1. Apply appropriate atmospheric correction and SSC inversion models to retrieve the spatial distribution of SSC from both the GOCI image and the nearly simultaneous HJ CCD image and perform preliminary validation with a limited number of in situ data points. 2. Resample the 30 m HJ CCD SSC data to a 500 m resolution using two approaches: (a) compute the mean SSC over a 17 \(\times\) 17 window corresponding to each 500 m GOCI pixel (denoted as HJ-Avg SSC); (b) use the central pixel's SSC value from the corresponding 17 \(\times\) 17 HJ CCD window (denoted as HJ-Center SSC). 3. Calculate the CV of SSC for each 17 \(\times\) 17 HJ CCD window corresponding to a GOCI pixel and stratify the CV values into different intervals. 4. Within each CV interval, perform regression analyses between GOCI SSC and both HJ-Avg SSC and HJ-Center SSC, determining the RMSE, R\({}^{2}\), and MRE for each relationship. 5. Compare the regression results for the two resampling approaches to evaluate the influence of scale effects within different CV intervals. The distribution of the CV of the HJ CCD SSC in the corresponding windows ranges from 0 to 0.74. Regression analysis conducted across all CV values (for both resampling approaches) yielded the results shown in Figure 10: the regression between HJ-Center SSC and GOCI SSC produced an RMSE of 107.06 mg/L (approximately 18.9% of the mean GOCI SSC) and an R\({}^{2}\) of 0.7268, while the regression between HJ-Avg SSC and GOCI SSC resulted in an RMSE of 82.15 mg/L (about 14.7% of the mean GOCI SSC) and an R\({}^{2}\) of 0.8392. The differences between these regressions suggest that scale effects play a role, although when all data points are considered together, the scale effect is not pronounced. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sensor**} & \multirow{2}{*}{
\begin{tabular}{c} **Spatial** \\ **Resolution (m)** \\ \end{tabular} } & \multirow{2}{*}{**Imaging Time**} & \multicolumn{3}{c}{**SSC (mg/L)**} \\ \cline{4-5}  & & & **Field Measurement** & **Image Inversion** & **R.E. (\%)** \\ \hline HJ CCD & 30 & 10:39 & 993.20 & 827.9 & 16.65 \\ GOCI & 500 & 10:29 & 721.3 & 27.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of SSC validation results between HJ CCD and GOCI at the measured station. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sensor**} & \multirow{2}{*}{
\begin{tabular}{c} **Spatial** \\ **Resolution (m)** \\ \end{tabular} } & \multirow{2}{*}{**Imaging Time**} & \multicolumn{3}{c}{**SSC (mg/L)**} \\ \cline{4-5}  & & & **Field Measurement** & **Central Pixel** & **3 \(\times\) 3 Window** & **17 \(\times\) 17 Window** \\ \hline HJ CCD & 30 & 10:39 & 993.2 & 875.7 & 827.9 & 702.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of SSC from different HJ CCD windows with SSC measured at the station. To further investigate the scale effects under varying degrees of spatial heterogeneity, the CV values were divided into eight intervals: 0-0.07, 0.07-0.08, 0.08-0.10, 0.10-0.15, 0.15-0.20, 0.20-0.25, 0.25-0.30, and 0.30-0.74. Figure 11 displays sample SSC pixels and the regression relationships between the two resampled HJ CCD SSC and GOCI SSC for each interval. It is evident that as the CV increases, the internal variability of HJ CCD SSC becomes more pronounced, and the correlation between the HJ CCD and GOCI SSC decreases progressively. Figure 11: _Cont._  
Figure 10: Regression relationships between two different scales of HJ CCD SSC and corresponding GOCI SSC: (**a**) the regression between HJ-Center SSC and GOCI SSC; (**b**) the regression between HJ-Avg SSC and GOCI SSC.