## 2 Data and Methods
### Methods
#### 2.3.3 Satellite Inversion Method of Extracting Environmental Factors  
The method of Suspended Particulate Matter Model (SPM-CT) was used to extract the Suspended Sediment Concentration (SSC). SPM-CT is a model made up of the red band and near-infrared band used to estimate Suspended Particulate Matter Concentration (SPMC) in seawater, especially suitable for high turbidity waters such as Hangzhou Bay. By analyzing the relationship between SPMC and reflectance at different wavelengths, linear regression analysis is used to establish the relationship between SPMC and reflectance at the red band and near-infrared band. It was found that in the red and near-infrared bands, the near-infrared band showed the highest correlation with SPMC. Through the verification of the field data set, the regression formula of the model is obtained, and the highly significant correlation coefficient and determination coefficient are calculated. The model verification results show a good agreement with the measured values. Therefore, the SPM-CT model is suitable for the study area and provides a reliable method for the estimation of suspended particulate matter concentration [31].  
\[\text{SPMC}=314.435\times\text{B3}+3805.982\times\text{B4}+28.54 \tag{6}\]  
where B3 and B4 are the reflectance values of band 3 (Red) and band 4 (NIR) of GF WFV data.  
Landsat 8 RTM (Radiative Transfer Model) is used to extract the Sea Surface Temperature (SST). The SST of the large yellow croaker aquaculture areas can be obtained from the thermal infrared band of Landsat 8 satellite images. RTM [32; 33] was selected with higher accuracy for the SST inversion of Zhoushan marine ranching.  
Firstly, radiometric calibration can turn a DN image into a radiance image. The following is the calculation formula for the radiometric calibration.  
\[L(T_{\text{sensor}})=\text{DN}\cdot\text{G}_{\text{ain}}+\text{h} \tag{7}\]  
where DN is the gray value, h is the offset, and G\({}_{\text{ain}}\) is the absolute scaling coefficient gain. The above data can be obtained from the thermal infrared data header file of Landsat 8.  
Then, the blackbody radiation and brightness temperature inversion were performed. According to the thermal infrared radiation transfer model, the brightness of surface radiation \(L(T_{s})\) can be expressed as the following formula [28].  
\[L(T_{s})=\frac{L(T_{\text{sensor}})-L_{\text{up}}}{\tau\varepsilon}-\frac{1- \varepsilon}{\varepsilon}L_{\text{down}} \tag{8}\]  
\[\text{SST}=\frac{K2}{\text{ln}[1+K1/L(\text{T}_{s})]} \tag{9}\]  
where \(L_{\text{up}}\) is the effective bandpass upwelling radiance, and \(L_{\text{down}}\) is the effective bandpass downwelling radiance. \(\varepsilon\) is the sea surface emissivity. \(\tau\) is the atmospheric path transmittance from the sensor to the target. \(T_{\text{sensor}}\) is the band average atmospheric transmission. This set of data was obtained from the Atmospheric Correction Parameter Calculator ([[https://atmcorr.gsfc.nasa.gov/](https://atmcorr.gsfc.nasa.gov/)]([https://atmcorr.gsfc.nasa.gov/](https://atmcorr.gsfc.nasa.gov/)) (accessed on 1 September 2023)).  
Model coefficients \(K1\) and \(K2\) can be obtained from the Landsat 8 data header file. For the tenth band, \(K1\) is 774.8853, and \(K2\) is 1321.0789.  
Chlorophyll-a extraction: HY-1C CZI SS-1 [17]  
\[\rho=-12.81\times x^{3}+38.17\times x^{2}-39.17\times x+14.9 \tag{10}\]  
\[x=((\text{B1}/\text{B2})\times(\text{B3}/\text{B2})^{-0.45}) \tag{11}\]  
where \(\rho\) is the Chl-a concentration, the unit is ug/L; B1, B2, and B3 are the reflectance of the first, second, and third bands of the CZI data, respectively.