# Data-Free Area Detection and Evaluation for Marine Satellite Data Products
## 3 Results
### Data Product Analysis and Evaluation
#### 3.2.2 Continuity of Ocean Color Information  
The year-round presence of clouds over the ocean leads to the inevitable existence of data-free areas in ocean color products [4]. Given this circumstance, users often focus on the quality of the continuity of product ocean color information in the spatial and temporal patterns, i.e., the discrete problem of the data-free areas of the products [59; 60]. Our findings indicate that a single missing rate indicator cannot sufficiently reflect the overall quality status of products, and it is only applicable to the quality assessment of single-view images. Figure 11: Schematic of the abnormal missing areas and proportions over four seasons (month by month): (a) area and (b) percentage. In other words, the existing quality evaluation method is highly restrictive, and it presents certain limitations in visually describing the quality status of products to be unified in time and space. Thus, we attempted to find a suitable indicator for describing the quality condition of the continuity of the product as a whole, which can also be called the missing spatiotemporal dispersion indicator. The data containing the spatiotemporal information of data-free areas should be initially obtained prior to the calculation of the missing spatiotemporal dispersion indicators. In this study, we further attempted to fuse the missing information of each product with temporal and spatial data into a single scene image to be able to obtain the corresponding index parameters. First, the data-free area information is binarized (0 for data-free area; 1 for data-available area). Then, the spatiotemporal image results of the inter-annual data-free area of a corresponding product are calculated as follows:  
\[M= \begin{cases}1&(Data-free\;area)\\ 0&(Other\;area)\end{cases} , \tag{10}\]  
\[I=\frac{\sum_{i}^{4}M_{i}}{M_{max}-M_{min}}, \tag{11}\]  
where \(M\) is the result of the binarization of each view image, and I is the spatiotemporal image of the data-free area. The results are shown in Figure 12.  
The spatiotemporal image obtained via calculation can visually depict the main distribution of the data-free areas in the Yellow Sea and Bohai Sea. GOCI and MODIS have high missing amount percentages for Bohai Bay, Laizhou Bay, Liaodong Bay of the Bohai Sea and the Yangtze River Delta of the Yellow Sea. Furthermore, GOCI was completely missing information in the Yangtze River Delta. The obtained results suggest that the data-free areas in these regions are mostly composed of turbid water near the shore. For example, the missing location of OLCI is usually in the middle of the sea, as opposed to the other two types of data, OLCI is missing to a lesser extent on the nearshore. The missingness is mostly due to the influence of clouds. The above method of directly evaluating the spatiotemporal distribution of data-free areas is called subjective evaluation, which is a common evaluation method in the field of remote sensing. This method is convenient and intuitive but susceptible to the influence of subjective factors, and the obtained results are not comprehensive and cannot unify the evaluation standards [61]. In ensuring that the evaluation of the three kinds of data is objective, quantified indicators are selected to correlate the spatiotemporal dispersion of the data in this study. Standard deviation reflects the degree of dispersion of a dataset. A large standard deviation represents a large degree of dispersion of the data in the dataset. The standard deviation of the spatiotemporal image map constructed in this study reflects the dispersion degree of the data-free area. As the standard deviation becomes larger, the spatiotemporal  
Figure 12: Schematic of the spatiotemporal image of the data-free area: (**a**) GOCI, (**b**) MODIS and (**c**) OLCI. dispersion of an image becomes stronger. As shown in Table 7, the spatiotemporal dispersion of the data-free area in OLCI is better than those in the other two products, followed by MODIS and GOCI. Information entropy is also known as Shannon entropy [62].