## 4 Image Analyses
### Sunbeam Analyses
#### 4.2.4 Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Symbol** & **Meaning and Unit** & **(a)** & **(b)** & **(c)** & **(d)** \\ \hline \(\beta_{2}\) & Non-Dimensional & \(0.44\) & \(2.9\) & \(2.5\) & \(1.5\) \\ \(\sigma\) & in m for Fitting Integrated RGB Values & \(0.4\) & \(0.5\) & \(0.4\) & \(0.4\) \\ \(\sigma\) & in m for Drawing Simulated Sunbeam & \(0.1\) & \(0.1\) & \(0.1\) & \(0.1\) \\ \(\mathrm{k_{1}}\) & in m\({}^{-1}\) & \(0.13\) & \(0\) & \(0\) & \(0\) \\ \(\rho\) & Non-Dimensional & - & \(0.0003\) & \(0.0005\) & \(0.0003\) \\ \(\mathrm{b_{Mie}}\) & Scattering Coefficient (m\({}^{-1}\)) for Mie Scattering & \(0.2\) & \(0.005\) & \(0.04\) & \(0.009\) \\ \(\mathrm{x_{K}}\) & x-Coordinate (m) of Sunbeam Incident Point on the Pond Surface & \(0.18\) & \(-2.89\) & \(-0.44\) & \(-2.08\) \\ \(\mathrm{y_{K}}\) & y-Coordinate (m) of Sunbeam Incident Point on the Pond Surface & \(5.79\) & \(6.28\) & \(6.01\) & \(6.69\) \\ \(\mathrm{k_{d}}\) & Parameter Designating the Real Bottom Depth & - & \(0.76\) & \(0.88\) & \(0.63\) \\ \(\mathrm{x_{1}}\) & x-Coordinate (m) of the Pond Bottom Point & - & \(-4.73\) & \(-3.22\) & \(-4.17\) \\ \(\mathrm{y_{1}}\) & y-Coordinate (m) of the Pond Bottom Point & - & \(6.16\) & \(6.41\) & \(7.37\) \\ \(\mathrm{z_{1}}\) & z-Coordinate (m) of the Pond Bottom Point & - & \(-5.03\) & \(-6.10\) & \(-3.91\) \\ \(\mathrm{w_{G}}\) & White Balance Parameter of the Digital Camera, & \(0.85\) & \(1.2\) & \(1\) & \(1\) \\ \multicolumn{2}{c}{Enhancement Factor of G} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\ \multicolumn{2}{c}{Coefficient of Strength of G Value on Irregular Reflection} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\ \multicolumn{2}{c}{Albedo at the Pond Bottom} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} \\ \hline \(\Lambda_{1}\) & \multirow{2}{*}{\begin{tabular}{c} Conversion Parameters from Pixels on the Picture to \\ Coordinate Values on the Pond Surface \\ \end{tabular} } & \(20\) & \(95\) & \(2\) & \(32\) \\ \(\Lambda_{2}\) & \multirow{2}{*}{\
\begin{tabular}{c} Conversion Parameters from Pixels on the Picture to \\ Coordinate Values on the Pond Surface \\ \end{tabular} } & \(377\) & \(432\) & \(345\) & \(375\) \\ \(\mathrm{X_{1}}\) & \multirow{2}{*}{
\begin{tabular}{c} Conversion Parameters from Pixels on the Picture to \\ Coordinate Values on the Pond Surface \\ \end{tabular} } & \(332\) & \(334\) & \(342\) & \(333\) \\ \hline \hline \end{tabular} Common values of the parameters: \(\Delta\mathrm{x}=0.2\) m, \(\Delta\mathrm{y}=0.2\) m and \(\Delta\mathrm{z}=0.2\) m, which were used in the fitting of the integrated RGB values. \(\Delta\mathrm{x}=0.1\) m, \(\Delta\mathrm{y}=0.1\) m and \(\Delta\mathrm{z}=0.1\) m, which were used in simulations of the sunbeam images. \(\Delta\mathrm{a}=0.25\) m, \(r=15.6\) m, \(w=7.4\) m, d \(=8.8\) m, \(h=9.5\) m, h\({}^{\prime}=4.6\) m, \(\eta=60^{\circ}\), \(\Delta\mathrm{a}=5\) nm, n\({}_{12}=1.33\), \(\mathrm{E_{obs}}=1.13\times 10^{5}\) lx.  
\end{table} 
Table 3: Given and settled parameters applied in the image analyses. (**a–d**) correspond to the numbers in Figure 19. Common values of the parameters are listed below the table. were calculated to be larger than in other cases. It is suggested that suspended solids in the pond water were presumably brought by outflows of soil and/or sand from the slope surrounding the pond during and/or after rain and that these coefficients should become higher when the pond water contained suspended solids with the larger concentrations. In addition, in Figure 20a-c, each contribution of three coloration mechanisms is drawn by using the parameters obtained by the sunbeam analysis depicted in Figure 19d (14:35 (JST) of 5 June 2021). From these figures, it was shown that the blue colors of sunbeams were caused by the density fluctuation scattering of water and white Mie scattering by suspended solids.