## 3 Secchi Disk Depth Estimation Method
### IOPs Estimation Using the QAA Method  
[PERSON] et al. [17] developed a multi-band QAA algorithm to retrieve the absorption and backscattering coefficients from \(R_{rs}\). QAA has six steps, including analytical and empirical approaches. Originally proposed and applied in optically deep waters, this method has received certain modifications to achieve better performance in turbid inland waters [31; 32; 33]. These modifications mainly include shifting the reference band to longer wavelengths and the alteration of the empirical equation in the algorithm. Table 2 lists the steps of the fifth version of the QAA (\(QAA_{V5}\)), with modified QAA algorithm steps for turbid waters, referred to as \(QAA_{L09}\)[31] and \(QAA_{M14}\)[32], respectively. \(QAA_{L09}\) uses 710 nm as its reference wavelength, at which point neglects the absorption of suspended solids and phytoplankton, where \(a(710)\) is approximately equal to \(a_{w}(710)\). The pure-water backscattering coefficient \(b_{bw}(710)\) was also neglected in the \(b_{bp}(710)\) calculation. In addition, the \(r_{rs}\) wavelengths were assessed, with a selection of 560 and 750 nm. \(QAA_{M14}\) used 708 nm as the reference wavelength, obtaining a new empirical relationship between \(a(710)\) and \(\chi\), which is an intermediate parameter for the derivation of \(a(710)\) and calculated using a new equation based on the \(r_{rs}\) at 443 and 620 nm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Step** & **Property** & \(QAA_{VS}\) & \(QAA_{L00}\) & \(QAA_{M14}\) \\ \hline
0 & \(r_{rs}\) & \(=R_{rs}/(0.52+1.7R_{rs})\)1  & same as \(QAA_{VS}\) \\
1 & \(u(\lambda)\) & \(=\dfrac{-\delta_{0}+\sqrt{\frac{\delta_{0}^{2}}{4\delta_{1}r_{ns}(\lambda)}}}{ 2\delta_{1}}\) & same as \(QAA_{VS}\) \\  & & \(\delta_{0}=0.089\ \delta_{1}=0.125\) & same as \(QAA_{VS}\) \\
2 & \(a(\lambda_{0})\) & \(=a_{\mathrm{w}}(\lambda_{0})+10^{-114-136\chi(\lambda_{0}-46\mu_{0})^{2}}\) & \(=a_{\mathrm{w}}(\lambda_{0})\) & \(=a_{\mathrm{w}}(\lambda_{0})+10^{-0.27153-2.68\chi(-10\chi^{2}}\)\(\chi^{2}\) \\  & & \(\chi=log\dfrac{\left(\dfrac{r_{rs}(43)+r_{rs}(69)}{r_{ns}(40)}\right)}{r_{ns}(4 0)^{2}r_{ns}(60)}\) & \(X=log\dfrac{\left(\dfrac{0.01r_{ns}(443)+r_{ns}(69)}{r_{ns}(43)+0.05}\right)}{ r_{ns}(443)^{3}r_{ns}(60)}\) \\  & & \(\lambda_{0}=555\) & \(\lambda_{0}=710\) & \(\lambda_{0}=708\) \\
3 & \(b_{\mathrm{p}}(\lambda_{0})\) & \(=\dfrac{u(\lambda_{0})a(\lambda_{0})}{1-u(\lambda_{0})}\) & \(=\dfrac{u(\lambda_{0})a(\lambda_{0})}{1-u(\lambda_{0})}\) & same as \(QAA_{VS}\) \\
4 & \(\eta\) & \(=2\omega\big{\{}1-1.2\mathrm{exp}\big{[}-0.9\frac{r_{ns}(403)}{r_{ns}(385)} \big{\}}\big{]}\) & \(=22\big{\{}1-1.2\mathrm{exp}\big{[}-0.9\frac{r_{ns}(569)}{r_{ns}(580)}\big{\}} \big{]}\) & same as \(QAA_{VS}\) \\
5 & \(b_{\mathrm{p}}(\lambda)\) & \(=b_{\mathrm{p}}(\lambda_{0})(\lambda_{0})\) & same as \(QAA_{VS}\) & same as \(QAA_{VS}\) \\
6 & \(a(\lambda)\) & \(=\dfrac{\left[1-u(\lambda)\right]\left[b_{\mathrm{p}}(\lambda)+b_{\mathrm{p} }(\lambda)\right]}{\left(\lambda\right)}\) & same as \(QAA_{VS}\) & same as \(QAA_{VS}\) \\ \hline \hline \end{tabular}  
* \(R_{rs}\): above-surface remote-sensing reflectance, \(r_{rs}\): below-surface remote-sensing reflectance, \(u(\lambda)\): ratio of the backscattering coefficient to the sum of the absorption and backscattering coefficients (\(b_{\mathrm{f}}/(a+b_{\mathrm{h}})\), \(\lambda_{\mathrm{\gamma}}\): reference wavelength, \(\eta\): spectral power of the particle scattering coefficient.  
\end{table} 
Table 2: Steps to derive the absorption and backscattering coefficients from \(QAA_{VS}\), \(QAA_{L00}\) and \(QAA_{M14}\)In addition, QAA was updated to its sixth version (\(QAA_{V6}\)). In the \(QAA_{V6}\) algorithm, the same steps in \(QAA_{V5}\)[34] were used for both \(a\) and \(b_{bp}\) estimation when \(R_{rs}\) was less than 0.0015 \(sr^{-1}\).