## 2 Materials and Methods
### ESTARFM Fusion Model  
The ESTARFM is an enhanced spatiotemporal adaptive fusion model based on the STARFM model. The model assumes that for a given area, images acquired at the same time by different sensors are interrelated after preprocessing. However, due to the inconsistency in the parameter settings of different sensor systems, there is a certain systematic deviation between different surface reflectance data. The ESTARFM uses existing data to solve the above-mentioned interrelationships to achieve multi-source data fusion. The high- and low-spatial-resolution images are first resampled to make sure that their pixels have a one-to-one correspondence. The ESTARFM is mostly used in terrestrial areas where there are multiple types of land cover. Low-resolution pixels are mixed pixels with comprehensive reflection of all types of land cover. In this paper, the ESTARFM was applied to coastal Chl-a, whose concentration is distributed relatively smoothly, and most of the pixels are homogeneous. For homogeneous pixels, the corresponding pixels of different sensors express the same type of land cover, so the reflectivity change between the pixels is directly caused by the above-mentioned system deviation, and the relationship between the high- and low-spatial-resolution pixels is given below. \[F(x,y,t_{k})=a\times C(x,y,t_{k})+b \tag{4}\]  
where \(F\) and \(C\) represent the high- and low-spatial-resolution images, respectively, \((x,y)\) is the pixel position, \(t_{k}\) is the image acquisition time, and \(a\) and \(b\) are the linear regression parameters between the reflectivity of the high- and low-spatial-resolution pixels, respectively. For pixels in different positions, there are different observation angles, satellite attitudes, and other parameters. The ESTARFM assumes that the two coefficients, \(a\) and \(b\), should change with the position of the pixels, which can improve the applicability of the model. It subtracts the two equations when \(t_{k}\) is \(t_{0}\) and \(t_{p}\), respectively, and returns the following Equation (5). \[F\big{(}x,y,t_{p}\big{)}=F(x,y,t_{0})+a\times\big{(}C\big{(}x,y,t_{p}\big{)}- C(x,y,t_{0})\big{)} \tag{5}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(a_{0}\) & \(a_{1}\) & \(a_{2}\) & \(a_{3}\) & \(a_{4}\) \\ \hline
**OC3** & 0.2412 & \(-\)2.0546 & 1.1776 & \(-\)0.5538 & \(-\)0.4570 \\
**OC3g** & 0.0831 & \(-\)1.9941 & 0.5629 & 0.2944 & \(-\)0.5458 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The coefficients of OC3 and OC3g. \(F(x,y,t_{0})\), \(C(x,y,t_{p})\), and \(C(x,y,t_{0})\) in Equation (5) are already known. When a is calculated, the reflectance at the predicted time can be obtained. It can be seen that \(a\) is caused by the system deviation between the sensors. If the atmospheric conditions at the time of image acquisition are similar, it can be assumed that the coefficient is determined for a certain pixel. \(a\) can be calculated via linear regression, which is stable for homogeneous pixels with an unchanged land cover type. For mixed pixels, under the assumption that the endmembers are linearly combined to form mixed pixels and change stably from \(t_{m}\) to \(t_{n}\); similar to homogeneous pixels, there is a constant \(v_{k}\) between the high-resolution pixel and the low-resolution pixel. \(v_{(x,y)}\) is obtained via linear regression between high- and low-spatial-resolution pixels. In order to be consistent with the pure pixel, the same equation is used to express the high-resolution image of the target time:  
\[F\big{(}x,y,t_{p}\big{)}=F(x,y,t_{0})+v_{(x,y)}\times\big{(}C\big{(}x,y,t_{p} \big{)}-C(x,y,t_{0})\big{)} \tag{6}\]  
The ESTARFM uses a spatial sliding window method to make full use of the reflectivity information of similar pixels nearby [15]. It uses a preset threshold to search for similar pixels in the sliding window and integrates the information of similar pixels into the data fitting process.