## 2 Materials and Methods
### ESTARFM_p Fusion Model  
Unlike terrestrial areas, coastal Chl-a is affected by hydrodynamic conditions, wind, nutrient concentration, etc., and changes rapidly. The simple global linear fitting scheme of the ESTARFM cannot accurately reflect the relationship between the two Chl-a datasets. In addition, the original multi-band data provide sufficient ground feature information, so the ESTARFM has sufficient data to obtain the reflectance relationship between sensors and make accurate predictions on the target date, while the single band of Chl-a cannot. Therefore, the relationship between the Chl-a product in different datasets is difficult to determine. Applying the same solution as the ESTARFM may lead to large deviations or even wrong values. To obtain the fused Chl-a of the target date more accurately, this paper adopted the idea of segmented fitting and numerical conversion. The Chl-a concentration retrieved by different observation systems is the expression of the true Chl-a concentration at a fixed time and location, so the assumption of a relationship (Equation (4)) between different datasets is valid. The GOCI and Landsat data were segmented according to the Chl-a concentration range, and the relationship between the two Chl-a data could be described more accurately using the method of segmented fitting. In addition, due to the rapid changes in chlorophyll, this paper used the corresponding numerical conversion method to solve this problem for the target date. This solution avoids calculation errors caused by using a conversion coefficient with a fixed spatial position when the Chl-a data change. The main steps are as follows:  
(1) Data segmentation: Since the relationship between different Chl-a data is difficult to determine, the unified linear relationship cannot accurately reflect its changes; by segmenting the data and using the local fitting method, the change in the conversion coefficient can be described more accurately. The number of segments and the spacing between segments are determined by the statistical characteristics of the data. A larger number and smaller interval between segments can describe the relationship more accurately. However, in this way, the number of fitting data is limited, and the influences of bad pixels are enlarged, which affects the stability of the fitting result. Thus, gradient accumulation was used as a threshold for controlling segmentation. \[\sum_{i=1}^{n}\left\|\frac{f(x_{i+1})-f(x_{i})}{x_{i+1}-x_{i}}\right\|>\varepsilon \tag{8}\]  
The left side of Equation (8) represents the accumulation of gradients of \(n\) small segments. When it is greater than the threshold \(\varepsilon\), this part is regarded as a small group. \(f(x_{i+1})-f(x_{i})\) and \(x_{i+1}-x_{i}\) represent the changes in GOCI and Landsat data, respectively. This method uses gradient accumulation to characterize the energy changes of a small group of Chl-a data. By using the energy threshold \(\varepsilon\), the energy changes of each group are kept consistent. In this way, the data block can be merged with the energy fluctuation to control the error of the segmented fitting. The value of \(\varepsilon\) is related to the intensity of changes in Chl-a, so for different regions, \(\varepsilon\) can be determined experimentally. (2) Segment fitting: According to the above-mentioned segmentation strategy, GOCI data were segmented, and the corresponding Landsat segments were obtained using the same spatial index, as shown in Figure 3. A linear fitting was performed for each of the corresponding GOCI and Landsat segments, and conversion coefficients were obtained. (3) Target pixel calculation: To make full use of the information of similar pixels, a sliding window was used to traverse the GOCI basic data and GOCI target data, selecting similar pixels and calculating the distance weight using Equations (9) and (10).