## 4 Image Analyses
### Image Analyses without Solar Shading by Tree Leaves above the Pond Surface
#### 4.1.8 Results and Discussion of Image Analyses  
The canopy openness on 24 April 2021, when the four images in Figure 13 were taken, was 28 % as shown in Figure 14. On the other hand, sunbeams were observed on 9 May 2021, 20 May, and 5 June and on these 3 days the canopy openness were from 14 to 19%. Therefore, it was considered that the influence of shielding over the pond surface was smaller on 24 April than on the later observation dates. Table 2 shows the parameter set obtained by image analyses. Figure 15 depicts the simulation results of the Ao-ike Pond image, shown in Figure 13, at 12:28 (JST) of 24 April 2021. In addition, Figure 16 displays the fitting results. In these graphs, we show plots of theoretically predicted RGB values versus observed ones. The observed RGB values corresponded to the colors displayed in the column \"Displays of utilized image elements\" in Figure 13. The plots on RGB elements are shown on the same scales without any partial expansions, since determination of the model parameters were obtained by minimization of the residual sum of squares of differences between observed and theoretical GB values without weighting on G and B values. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & \(\mathbf{\Lambda_{1}}\) & \(\mathbf{\Lambda_{2}}\) & \(\mathbf{X_{1}}\) \\ \hline
1 & 119 & 358 & 323 \\
2 & 93 & 331 & 306 \\
3 & 127 & 366 & 322 \\
4 & 101 & 348 & 313 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter sets for acquiring coordinates on the pond surface from the Ao-ike Pond images listed in Figure 13. \"No.\" corresponds to Figure 13.  
Figure 14: Images of the sky above Ao-ike Pond taken with the fisheye lens. The grid is cut in 10\({}^{\circ}\) increment. (**a**) 24 April 2021 (**b**) 9 May 2021. \begin{table}
\begin{tabular}{c c c} \hline
**Symbol** & **Meaning and Unit** & **Value** \\ \hline r & Radius (m) of the Paraboloid & 15.6 \\ w & Horizontal Distance (m) from the Pond Shore to the Observation Point & 9.5 \\ d & Maximum Depth (m) of Ao-ike Pond & 8.8 \\ h & Height (m) of Observation Point & 8.1 \\ h\({}^{\prime}\) & Height (m) of Tip of Observation Deck & 4.6 \\ \(\xi\) & Height (m) of the Slope around the Pond & 20 \\ \(\delta_{2}\) & Slope Angle (degree) of the Slope around the Pond & 60 \\ \(\eta\) & Observation Point Angle (degree) from the West Direction & 60 \\ \(\Delta\lambda\) & Increment of Wavelength (nm) in the Wavelength Integral & 5 \\ \(\beta_{2}\) & Non-Dimensional & 0.786 \\ \(\sigma\) & in m & 2.0 \\ k\({}_{1}\) & in m\({}^{-1}\) & 0 \\ \(\rho\) & Non-Dimensional & 0.00027 \\ \(\Delta\)x & Increment (m) of Horizontal x-Coordinate at which the Bottom and Scattering & 2 \\ \(\Delta\)y & Increment (m) of Horizontal y-Coordinate at which the Bottom and Scattering & 2 \\ \(\Delta\)z & Increment (m) of Vertical Points at which Scattering Points are Scanned & 0.5 \\ n\({}_{12}\) & Relative Refractive Index (non-dimension) of Water to Atmosphere & 1.333 \\ b\({}_{\rm Mie}\) & Scattering Coefficient (m\({}^{-1}\)) for Mie Scattering & 0.050 \\ w\({}_{\rm G}\) & White Balance Parameter of the Digital Camera, Enhancement Factor of G & 1 \\ w\({}_{\rm Irr,G}\) & Coefficient of Strength of G Element on Irregular Reflection Albedo at the & 3 \\ E\({}_{\rm obs}\) & \multicolumn{2}{c}{Dolluminance of Solar Radiation (lx)} & 76,100 \\ \hline \end{tabular}
\end{table} 
Table 2: Given and settled parameters in image analyses when the influence of shading over the pond surface by leaves was small. Figure 15: Simulation results for Ao-ike Pond image; **(a)** Image taken at 12:28 (JST) of 24 April 2021, standardized by digital camera sensitivity, **(b)** sum of contributions from pond bottom irregular reflection, density fluctuation scattering by water and white Mie scattering, **(c)** contribution from pond bottom irregular reflection only, **(d)** contribution from density fluctuation scattering by water only, **(e)** contribution form Mie scattering only. The numerical values in **(b–e)** indicate relative averaged luminance on the pond surface.