# Remote Sensing of the Water Quality Parameters for a Shallow Dam Reservoir
## 2 Data, Methods, and Techniques
### Model
It was found that the most important coefficients are related to the wavelengths: 665, 705, 740, and 842 nm. These are the lengths approximately corresponding to the local minimum and maximum on the spectral curve of chlorophyll a (Figures 1 and 2) and the local minimum and maximum on the spectral curve of the suspensions (Figures 2-4). In the case of the Sentinel satellite, there were no 760 and 810 nm wavelength channels corresponding to the local minimum and maximum on the spectral curve of the suspensions (Figures 2-4); hence, the 740 and 842 nm channels turned out to be statistically significant. Eventually, the model looked as follows:  
\[ \begin{array}{l}\mathbf{ln}C_{chl}=a_{0}+a_{3}\mathbf{ln}R_{665}+a_{4} \mathbf{ln}R_{705}+a_{5}\mathbf{ln}R_{740}+a_{7}\mathbf{ln}R_{842}+\\ a_{11}(\mathbf{ln}R_{665})^{2}+a_{12}(\mathbf{ln}R_{705})^{2}+a_{13}(\mathbf{ ln}R_{740})^{2}+a_{15}(\mathbf{ln}R_{842})^{2}\end{array}  \tag{4}\]  
To eliminate the influence of the lake bottom reflectance, some reflectance corrections in Equation (4) were required. The effect of light reflection by the lake bottom in four light wavelengths is shown in Figure 11. However, just the reflectance corrections for 665 nm and 705 nm are sufficient for a good model accuracy. Of course, the reflectance for 740 nm and 842 nm may also be corrected, but their impact is negligible for the quality of the model (4). Generally, the shorter the wave, the stronger the bottom reflectance. Such observation is also confirmed by the spectral curves (Figure 7), which show that the shorter the wave, the higher the reflectance. Following the Lambert-Beer law, absorbance (\(-\mathbf{ln}(I/I_{0})\)) of the medium for UV, Vis, and IR radiation is proportional to an optical path length 1 and a concentration of substance C. This means that a light intensity I in a water column decreases exponentially:  
\[I=I_{0}\cdot\mathbf{exp}(-k\cdot C\cdot l) \tag{5}\]  
\(I_{0}\)--incident light intensity [W/m\({}^{2}\)];  
\(k\)--absorption coefficient [m\({}^{3}\)/(g\(\cdot\)m)];  
\(C\)--concentration of a radiation absorber [g/m\({}^{3}\)];  
\(l\)--optical path length [m]. Assuming that the lake bottom reflectance \(R_{b}\) is approximately proportional to the intensity of the radiation reaching the depth of 1 = h, the reflectance over a water surface, recorded by a photosensitive sensor, would be described by the relationship:  
\[R_{b}=\frac{\alpha_{b}\cdot I_{0}\cdot\mathbf{exp}(-k\cdot C\cdot 2h)}{I_{0}}= \alpha_{b}\cdot\mathbf{exp}(-k\cdot C\cdot 2h) \tag{6}\]  
\(\alpha_{b}\)--coefficient of the radiation reflectance through the bottom;  
\(C\)--concentration of all substances (e.g., chlorophyll a, mineral suspensions, organic suspensions, water) responsible for absorption of radiation [g/m\({}^{3}\)], i.e., water turbidity [NTU];  
\(h\)--depth (actual length of an optical path, when shooting close to the zenith, is approximately equal to the depth h) [m]. The number 2 in Formula (6) means that radiation passes twice through the water layer. The reflectance \(R\), recorded by the satellite, is approximately equal to the sum of the four principal reflectances:  
\[ \begin{array}{l}R=\frac{\alpha_{s}I_{0}+I_{chl}+I_{m}+\alpha_{b}(\frac{I_{0}- \alpha_{s}I_{0})\mathbf{exp}(-k\cdot C\cdot 2h)}}{I_{0}}=\\ \alpha_{s}+\frac{I_{chl}}{I_{0}}+\frac{I_{m}}{I_{0}}+\alpha_{b}(1-\alpha_{s}) \mathbf{exp}(-k\cdot C\cdot 2h)=\\ \alpha_{s}+R_{chl}+R_{m}+\alpha_{b}(1-\alpha_{s})\mathbf{exp}(-k\cdot C\cdot 2 h)\end{array}  \tag{7}\]  
\(\alpha_{s}\)--coefficient of the radiation reflectance for the water surface (water surface reflectance); \(R_{chl}\)--reflectance related to chlorophyll a in water, as the total effect of radiation; \(I_{chl}\)--reflected at different water depths; \(R_{m}\)--reflectance related to the substances, other than chlorophyll a, in water, as the total effect of radiation \(I_{m}\) reflected at different water depths; \(\alpha_{b}(1-\alpha_{s})\mathbf{exp}(-k\cdot C\cdot 2h)\)--reflectance of the lake bottom \(R_{b}\).