## 4 Results
### \(Z_{sd}\) Estimation Scheme for AHSI Imagery  
Semi-analytical methods with \(QAA_{V5}\) and \(QAA_{M14}\) were both tested with the match-up pixels of the in situ sampling points using the image \(R^{0}_{rs}\) described in Section 2.2. Figure 4 shows scatterplots of estimated and in situ measured \(Z_{sd}\) with their corresponding \(R^{2}\) values. As shown in Figure 4, the \(Z_{sd}\) values generated from the \(QAA_{V5}\)-based method have a significantly higher correlation and better consistency with the in situ measurements than the SAM incorporating the \(QAA_{M14}\) algorithm. An accuracy analysis (the same as in Section 4.1) was conducted for the imaged \(Z_{sd}\) estimations. Table 4 lists the MAEs and MREs of 84 match-up pixels at different clarity ranges based on different methods using the AHSI image-estimated remote sensing reflectance. Only the \(Z_{sd}\) determined from the \(QAA_{V5}\)-based semi-analytical method is acceptable for the AHSI data. For the 84 match-up measurements, the \(Z_{sd}\) calculated with the \(QAA_{V5}\) using \(R^{0}_{rs}\) yields higher accuracy in terms of both the MAE and MRE. The \(QAA_{V5}\)-derived image \(Z_{sd}\) is also more accurate than the \(QAA_{M14}\) for \(Z_{sd}\) at all ranges. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(Z_{sd}\) Range (m) & N & \(QAA_{V5}\) & \(QAA_{V6}\) & \(QAA_{L09}\) & \(QAA_{M14}\) \\ \hline \multirow{4}{*}{MAE (m)} & 0.3-1.0 & 23 & 0.34 & 0.49 & **0.13** & 0.18 \\  & 1.0–3.0 & 43 & 0.25 & 0.44 & 0.46 & **0.21** \\  & \textgreater{}3.0 & 18 & 0.57 & **0.56** & 1.96 & 1.26 \\ \cline{2-6}  & 0.3–4.5 & 84 & **0.35** & 0.48 & 0.69 & 0.42 \\ \hline \multirow{4}{*}{MRE} & 0.3-1.0 & 23 & 48.4\% & 72.1\% & **15.5\%** & 22.8\% \\  & 1.0–3.0 & 43 & 18.2\% & 28.7\% & 28.7\% & **12.8\%** \\  & \textgreater{}3.0 & 18 & 14.7\% & **14.2\%** & 50.3\% & 32.3\% \\ \cline{2-6}  & 0.3–4.5 & 84 & 25.7\% & 37.5\% & 29.7\% & **19.7\%** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The MAEs and MREs of the estimated \(Z_{sd}\) from the AHSI in situ \(R_{rs}\) based on the semi-analytical methods using various QAA algorithms. Optimal results listed in bold. Furthermore, we compared the accuracies of image-derived \(Z_{sd}\) based on MAE, MRE and \(R^{2}\) (see Table 5) of in situ samples collected within 3 h and before/after 1 day of the AHSI image acquisition (see Table 1). From Table 5, it can be observed that:  
(1) Samples collected within 3 h and before/after 1 day both yielded \(Z_{sd}\) with high accuracies on the AHSI images, which is likely owing to the stable weather conditions (i.e., no strong wind or rainfall) during the image acquisition and in situ measurement. (2) The \(R^{2}\) from the samples collected within 3 h is higher than that the other group, indicating that the image-retrieved \(Z_{sd}\) has better consistency with the in situ \(Z_{sd}\) measured on the same day. (3) Samples collected before/after 1 day have smaller MAE and MRE than those collected on the same day. This is because highly turbid sampling sites (i.e., \(Z_{sd}\) < 0.7 m) included in the latter have worse \(Z_{sd}\) predictions, leading to greater MAE and MRE in this group of samples. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Time Difference between**} & \multirow{2}{*}{**\(Z_{sd}\) Range (m)**} & \multirow{2}{*}{**N**} & \multirow{2}{*}{**MAE (m)**} & \multirow{2}{*}{**MRE**} & \multirow{2}{*}{**\(R^{2}\)**} \\  & & & & & \\ \hline Within 3 h & 0.3–4.5 & 56 & 0.38 & 26.1\% & 0.871 \\ Before/after 1 day & 0.7–2.1 & 28 & 0.28 & 23.7\% & 0.502 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: AHSI image-derived \(Z_{sd}\) accuracies for the 56 samples collected on the same day as the image acquisition, and 28 collected before/after one day. Figure 4: Estimated AHSI image \(Z_{sd}\) for 84 match-up in situ measurements using the semi-analytical method: (**a**) \(QAA_{V5}\), and (**b**) \(QAA_{M14}\).