## 3 Results
### Validation and Evaluation of Reconstruction Results  
Both overall reconstrution using the ordinary DINEOF algorithm and stratified reconstruction employing the CS-DINEOF algorithm were performed on the refined 2019 chl-a dataset of the Bohai Sea region. Specifically, the algorithm was configured as follows: the maximum number of EOFs \(k_{max}\) was set to 20, the iterative convergence threshold was established at \(\varepsilon=1.0~{}\times~{}10^{-3}\), and the maximum iteration steps _iter_ was set to 300. As defined in Section 2.3.3, RMSE, r, SNR and MAE were used to evaluate the reconstruction accuracy between the reconstructed values and the original values at cross-validation points. Table 3 summarizes the reconstruction performances across four validation parameters. Compared to the ordinary DINEOF algorithm, the CS-DINEOF algorithm successfully reduced the RMSE and MAE from 0.2562 mg/m\({}^{3}\) and 0.1769 mg/m\({}^{3}\) to 0.2281 mg/m\({}^{3}\) and 0.1020 mg/m\({}^{3}\), respectively. Simultaneously, r and SNR increased from 0.8910 and 15.0174 to 0.9606 and 18.0380, respectively. These results indicate that the proposed CS-DINEOF algorithm could significantly enhance the reconstruction accuracy. On the other hand, we note that there was a relatively modest improvement in RMSE, compared with the more significant improvements in the other three parameters. This issue comes from the high sensitivity of RMSE to large biases in the reconstruction of potential extreme values or outliers within the dataset. With regard to computational time (CT), the experiments demonstrate the CS-DINEOF method has a substantial advantage over the ordinary DINEOF algorithm. Because of the stratification process, the size of each sub-dataset is markedly reduced, resulting in accelerated matrix computation. With the same aforementioned computational configurations, the CT of the CS-DINEOF method is approximately 228.9% faster than that of the ordinary DINEOF method, greatly enhancing the reconstruction efficiency. Figure 6 presents four examples of chl-a images with gaps (indicated by black spaces) on 15 February, 26 April, 22 September, and November 28 in 2019, covering four days from different seasons, with SMRs of 78.47%, 31.66%, 18.98%, and 53.46%, respectively. Figures 7-10 show the reconstructed results using the DINEOF and CS-DINEOF methods, along with zoomed-in views of local details. As shown in Figures 7,b, 8,b, 9a,b and 10a,b for data from different seasons with varying missing rates, both DINEOF and CS-DINEOF  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Imaging Time** & **Original Images** & **Original Pixels** & **Valid Images** & **Valid Pixels** \\ \hline
00:16 & 352 & 300,364 & 110 & 274,988 \\
01:16 & 350 & 300,364 & 164 & 279,265 \\
02:16 & 342 & 300,364 & 174 & 279,941 \\
03:16 & 329 & 300,364 & 166 & 280,676 \\
04:16 & 343 & 300,364 & 182 & 280,889 \\
05:16 & 350 & 30  
Figure 8: The reconstruction results using (**a**) ordinary DINEOF and (**b**) CS-DINEOF on 26 April 2019. Specific local area is marked with red box in (**a**,**b**), and the corresponding zoomed-in views are shown in panels (**c**,**d**). Figure 9: The reconstruction results using (**a**) ordinary DINEOF and (**b**) CS-DINEOF on 22 September 2019. Specific local area is marked with red box in (**a**,**b**), and the corresponding zoomed-in views are shown in panels (**c**,**d**). Figures 7c,d, 8c,d, 9c,d and 10c,d offer zoomed-in views of specific local areas marked with red frames in Figures 7a,b, 8a,b, 9a,b and 10a,b. Compared to the ordinary DINEOF method, the reconstructed results of the CS-DINEOF method not only reveal more local details (Figure 7c,d) but also exhibit smoother transitions (Figure 8c,d) and higher spatial coherence (Figures 9c,d and 10c,d) of chl-a distribution. These comparisons demonstrate the natural advantage of the stratified reconstruction strategy employed in the CS-DINEOF algorithm.