## 5 Discussion
### Z\({}_{sd}\) Estimation Methods Evaluation  
Based on the \(Z_{sd}\) values estimated from the AHSI band in situ \(R_{rs}\), we can observe that the SAMs based on the \(QAA_{V6}\) and \(QAA_{L09}\) are unable to provide satisfactory predictions. In contrast, the SAMs with \(QAA_{V5}\) and \(QAA_{M14}\) gives good estimations for \(Z_{sd}\) from the in situ measured spectra. Therefore, we applied the \(QAA_{V5}\)- and \(QAA_{M14}\)-based SAMs to the AHSI \(R_{rs}\) images. Only \(QAA_{V5}\) can generate \(Z_{sd}\) with high accuracy from the AHSI data. The application of these SAMs to AHSI imagery were evaluated as follows. (1) \(QAA_{V6}\)-based SAM evaluation  
Based on the in situ acquired AHSI \(R_{rs}\), \(QAA_{V6}\) yielded good predictions only for \(Z_{sd}\) values higher than 3.0 m due to its limitations in turbid water. In addition, the semi-analytical method with \(QAA_{V6}\) was evaluated as being capable of retrieving the \(Z_{sd}\) for an oligo- to mesotrophic inland reservoir [37], but acquired an average relative error of 75.05%. (2) \(QAA_{L09}\)-based SAM evaluation  
\(QAA_{L09}\) was developed with limited samples collected from Lake Taihu, with sensitivity to water contents and optical properties as mentioned in Reference [31]. Specifically, the \(Z_{sd}\) range of Lake Taihu is 0-0.9 m, which is distinct from the water clarity range of our study regions. This is likely the reason for poor performance in terms of the \(Z_{sd}\) retrieval in our study regions. (3) \(QAA_{V5}\)-based SAM evaluation  
The estimated \(Z_{sd}\) values based on the \(QAA_{V5}\) using image \(R_{rs}^{0}\) and AHSI in situ \(R_{rs}\) have similar MAEs and MREs. In other words, the image \(Z_{sd}\) with \(R_{rs}^{0}\) is generally consistent with the AHSI in-situ \(R_{rs}\) generated results when using the \(QAA_{V5}\)-based semi-analytical method, despite an approximated \(R_{rs}^{0}\) for the image that is generally higher than the in situ measured reflectance due to insufficient atmospheric correction. Since \(a(\lambda)\) and \(b_{b}(\lambda)\) are mainly affected by the shape and magnitude of the \(R_{rs}\), respectively [38], \(a(\lambda)\) retrieved from the image is consistent with the in situ-derived values. In addition, \(a(\lambda)\) affects \(K_{d}\) and \(Z_{sd}\) to a more extent than does \(b_{b}(\lambda)\), and therefore, the image-retrieved \(Z_{sd}\) values are comparable to the in situ-derived results. However, the estimation accuracies were different at various \(Z_{sd}\) ranges between the image and in situ derived \(Z_{sd}\). For the clarity range of 1-3 m, the estimated image \(Z_{sd}\) has poorer accuracies (MRE of 29.1%) than the in situ determined  
Figure 6: In situ measured \(R_{rs}\) and image \(R_{rs}^{0}\) in the bands utilized in \(QAA_{V5}\) and \(QAA_{M14}\) (443 nm, 490 nm, 532 nm, 555 nm, 620 nm, 665 nm, 667 nm, 708 nm) of typical samples \(P_{1}\) and \(P_{2}\) in the study areas. (MRE of 18.2%). In contrast, the image-generated \(Z_{sd}\) was better than that of the in situ values for \(<\)1 m and \(>\)3 m clarity conditions. (4) \(QAA_{M14}\)-based SAM evaluation  
For the \(QAA_{M14}\)-based method, the image \(R_{rs}^{0}\), however, acquired distinct \(Z_{sd}\) results compared with those estimated from the AHSI band-equivalent in situ \(R_{rs}\). Unlike the AHSI in situ \(R_{rs}\) that generated desirable \(Z_{sd}\) predictions using the \(QAA_{M14}\), the \(Z_{sd}\) values calculated from the image \(R_{rs}^{0}\) have significantly poorer accuracies. Specifically, the MRE is 47.4% for a \(Z_{sd}\) of less than 1 m, while the MRE increases to 60.9 and 75.6% for \(Z_{sd}\) values ranging from 1-3 m and \(>\)3 m, respectively. Moreover, the absolute error also increases from 0.42 to 1.24 m. Such large errors are unacceptable when estimating the water clarity in ranges from 0.3 to 4.5 m. Figure 6 shows that image \(R_{rs}^{0}\) is higher than in situ \(R_{rs}\) but with similar spectral shapes.