# Data-Free Area Detection and Evaluation for Marine Satellite Data Products
## 2 Materials and Methods
### Methods
#### 2.3.1 Data Pre-Processing  
The Level 1 data of GOCI, MODIS and OLCI were pre-processed to obtain the remotely sensed water reflectance (\(\rho_{w}\)) of the images after radiometric calibration, atmospheric correction, geometric correction and sea-land separation. The spectral curves of the sample library should be standardized to be able to fit the other post-processing processes of the remote sensing images. Thus, the reflectance of water (\(\rho_{w}\)) was converted into remote sensing reflectance (\(R_{rs}\)). In ocean remote sensing, \(\rho_{w}=\rho_{f}\)[43]. By neglecting the optical  
Figure 2: Framework and technical methods.  
thickness of gaseous aerosols, such as ozone and water vapor [44], \(\tau=0\). The remote sensing reflectance (\(R_{rs}\)) can be obtained as follows:  
\[R_{rs}=\frac{\rho_{w}}{\pi\tau_{0}}, \tag{1}\]  
\[\tau_{0}=\exp(-\tau{\rm cos}\theta_{0}/2), \tag{2}\]  
where \(\tau_{0}\) is the diffuse transmission ratio, \(\tau\) is the aerosol optical thickness and \(\theta_{0}\) is the solar zenith angle.  
Level 2 data were geometrically corrected to convert the data-free area into vector data. The \(R_{rs}\) image obtained using Equation (1) was cropped to obtain the \(R_{rs}\) image data corresponding to the spatial location of the data-free area only.  
The wave spectral data of the data-free area showed that the ocean coverage objects at the spatial location of the data-free area were mostly composed of clean water, turbid water, green tide algae, clouds and sea ice. Thus, the five marine coverage types that are most common in the ocean and that may have an impact on the missing data were selected as the targets of this study. The spectral differences between the categories of the five marine coverage objects were large. Consequently, Spectral Angle Mapper Classification (SAM) was chosen as the identification classification method. The correctness of the standard spectral curve, which is the core of the algorithm, was particularly important in the study.  
The traditional endmember extraction methods, such as the pixel purity index (PPI, i.e., based on the principle of convex geometry). The basic principle is to form a single-row body in the feature space, with its endmembers located at the vertices of the single-row body [45]. In practical applications, an MNF dimensionality reduction transformation is usually performed on the data before the endmembers are extracted using PPI. Then, the result is integrated into an N-dimensional visualization window for endmember extraction. However, this method is mainly applicable to hyperspectral data. It is also a supervised algorithm with many steps, suggesting a complex process, and it entails high subjectivity [46]. As the spectral resolution of the multispectral data is already much lower than that of hyperspectral data and because its band information is less, the information is no longer suitable for dimensionality reduction processing. Moreover, the dimensionality reduction transformation of MNF does not apply to multispectral data. Therefore, in this study, we separately extracted the endmembers to determine the corresponding spatial locations before selecting the spectral library samples. Then, the standard spectral data obtained by the method were identified and classified by their higher accuracy and better robustness.