## 3 Result
### Model Building
(**a**): The correlation analysis between P4/(P3 + P5) band combination and Chla; (**b**): The correlation analysis between log(P2/P3) band combination and LN(Chla); (**c**): The correlation analysis between (P3 + P4)/(P2 + P5) band combination and LN(Chla); (**d**): The correlation analysis between (P3 - P4)/(P3 + P4) band combination and Chla; (**e**): The correlation analysis between (P2 - P4)/(P2 + P4) band combination and LN(Chla); (**f**): The correlation analysis between (P5 - P4)/(P2 + P3) band combination and Chla,  
The modeling group data were applied, by linear, polynomial, and exponential models, to get curve fit for the above factors and the measured Chla concentration. The combination method with the largest correlation coefficient is selected to establish a Chla inversion model. The band combination with the highest correlation coefficient is the fifteenth combination in Table 4, so the final model (named PMS-1) for Chla inversion in the Bohai Sea area of PMS data is finally determined as follows:  
\[\rho=\ \exp\bigl{(}2.3315-6.5659X-32.588X^{2}\bigr{)}, \tag{2}\]  
\[X=(P2-P4)/(P2+P4), \tag{3}\]  
where \(\rho\) is the Chla concentration, the unit is \(\mu\)g/L, P2 and P4 are the reflectance of the 2 nd and 4 th bands of PMS data. Compared measurements from two sources (e.g., field and remote-sensing ones) are necessary [53]. In total, 146 in situ measurements, of which 78 were used to establish the inversion formula, and the rest 68 were used to verify the retrieval results (Figure 5). In this paper, the correlation coefficients of modeled Chla and in situ Chla were analyzed to test the significance of the above formula and showed a significant result with R\({}^{2}\) = 0.97, and the critical value of the correlation coefficient r0.05 = 0.374, r0.01 = 0.478, r \(>\) r0.01. This linear relationship is considered to be significant. In Figure 5a, the concentration range of Chla is 0-11\(\mu\)g/L, R\({}^{2}\) is 0.97, and RMSE is 0.30. In Figure 5b, the correlation analysis between the sampling point and the simulation point with Chla concentration below 6 \(\mu\)g/L, the R\({}^{2}\) is 0.96 and RMSE is 0.23. In Figure 5c, the correlation analysis between the sampling point and the simulation point with Chla concentration below 6 \(\mu\)g/L, the R\({}^{2}\) is 0.96 and RMSE is 0.17. The distribution of Chla from June 2017 to September 2018 in the study area was retrieved (Figure 6) using the new model. Twenty PMS images obtained from the National Satellite Ocean Application Service ([[https://osdds.nsoas.org.cn](https://osdds.nsoas.org.cn)]([https://osdds.nsoas.org.cn](https://osdds.nsoas.org.cn))) in China were analyzed and six PMS images were taken as examples (Figure 6). The Chla concentration in Bohai Sea is mainly below 14 \(\mu\)g/L and the high concentration areas are usually distributed in coastal waters, Laizhou Bay and the eastern Bohai Sea. The concentration of Chla in the Bohai Strait and northern Yellow Sea is relatively low with the value being around 5 \(\mu\)g/L. Furthermore, the average value of Chla concentration generally shows a trend high offshore, low in the distant sea, and the low value dominates most area of Bohai Sea. This is consistent with the actual situation and prior studies [4]. Figure 5: Comparison of modeled Chla concentration value and in situ Chla value, the x-coordinate is in situ Chla, and the y-coordinate is model Chla, both in units \(\mu\)g/L. In addition, **(a)** shows the correlation fitting of 68 test sampling points with Chla inversion simulated concentration, **(b)** shows the correlation fitting of 67 test sampling points with Chla inversion simulated concentration lower than 6 \(\mu\)g/L, **(c)** shows the correlation fitting of 64 test sampling points with Chla inversion simulated concentration lower than 5 \(\mu\)g/L.3.4. Model retrieved Chla concentration in the Bohai Sea.