## 3 Methodology
### Extraction of Surface Water by the SMDPSO Method  
The SMDPSO method extracts water bodies in two main steps. First, the water probability image is obtained from the multispectral data by the proposed spectral matching method. Then, the water pixels are identified from the water probability image by using the DPSO method [20]. The purpose of surface water bodies extraction based on FY-3/MERSI images is to solve the problem of pixels or discrete image pixels. However, the basic particle swarm optimization (PSO) is mainly used to solve the problem of continuous space, but it cannot solve the problem of discrete space. Therefore, we applied discrete binary PSO [37; 38]. By selecting standard spectra from the FY-3/MERSI image to calculate the water probability, the water probability image was divided into 4x4 blocks. For each different block, a spectral matching algorithm based on discrete particle swarm optimization was used to extract the land surface water [18; 19]. The flow chart is shown in Figure 3.  
Because NDWI makes full use of the regularity of surface water reflection spectral curves, it has a good response to water bodies. Thus, the value of the NDWI is introduced into the calculation of water probability. The water probability image of the study area obtained by calculations is shown in Figure 4.  
To make the DPSO algorithm more sensitive to various surface types in the process of extracting land surface water, the image is roughly classified based on the mean value \(\upmu\) and standard deviation \(\sigma\) of the pixel water probability. The judgment conditions and flow charts of the four coarse classifications are shown in Figure 5.  
The high \(\upmu\)/\(\sigma\) value of rough classification 1 indicates that the block has a high probability of water homogeneity or a low standard deviation, and the pixel feature of the block is likely to be a homogeneous land surface water body or a homogeneous non-water surface. The comparatively lower \(\upmu\)/\(\sigma\) values of rough classifications 2, 3, and 4 indicate that the block has a lower water probability mean value or a higher standard deviation, and the pixel features of the block are more likely to be mixed features. In the rough classification of a low \(\upmu\)/\(\sigma\) value, three categories were classified according to the size of the water probability value. Classification 2 has a highest water probability mean value, indicating that the pixel feature of this block is more likely to be the boundary between water and land and also more likely to be the boundary between small water and vast land areas. Classification 3 offers a medium water probability mean value, indicating that the block is more likely to have small tributaries and that more water probability information from other types is mixed in the block. Classification 4 provides the lowest water probability mean value and a relatively high-water probability standard deviation, indicating that it is more likely to be a mixed block of non-water land, such as the boundary between bare land and vegetation, and the boundary between buildings and vegetation. A rough classification diagram of the Poyang Lake research area is shown in Figure 6.  
Figure 4: Water probability (normalized difference water index (NDWI)) map of the Poyang Lake area. Figure 3: The flow chart of spectral matching based on discrete particle swarm optimization (SMDPSO). In the code for DPSO, the position vectors of all the particles form position matrix X. The pixels in the block are divided into two categories: water and non-water. The velocity vectors of all particles form the velocity matrix V. The particle objective function value is then calculated. The optimal particle history and global optimal solution are obtained, and the particle velocity and particle position are updated. Next, the fitness value of the particles is calculated, and the historical optimal and global optimal solutions of the particles are updated.