## 3 Results and Discussion
### Overall Variability and Relationships Involving the Apparent Optical Properties
#### 3.2.3 Diffuse Attenuation Coefficients
Because of unavailability or scarcity of scalar irradiance measurements, the measurements of downward plane irradiance have been typically used in the past for estimating photosynthetically available radiation in terms of PAR quantum downward irradiance, \(E_{dPAR}\)[11; 109; 110; 111; 105]. [PERSON] [10] provides a comprehensive overview of \(K_{dPAR}\) values for various oceanic, coastal, estuarine, and inland aquatic environments. Our dataset shows a strong linear relationship between \(K_{oPAR}\) and \(K_{dPAR}\) throughout the examined water column (Figure 13e):  
\[K_{d}(650)=0.4792\ \mathrm{exp}(-0.0451\ z)+0.0387\quad(r^{2}=0.925,\ RMSE=0.033\ \mathrm{m}^{-1},\ N=66) \tag{6a}\]6  
This relationship provides an alternative to Equation (10d) for the use in a situation when \(E_{oPAR}\) just below the surface and vertical measurements of spectral \(E_{d}\) are available. It is noteworthy to mention that because of widespread interest in the determinations of remote-sensing reflectance the contemporary underwater radiometric systems are often configured to include only two sensors, one for the spectral measurements of \(E_{d}\) and another for the spectral measurements of upwelling zenith radiance, \(L_{u}\). Because such systems lack the measurement of \(E_{u}\), it is useful to examine the relationship between \(K_{u}\) and \(K_{Lu}\). The analysis of our dataset indicates that a single linear relationship provides reasonably good estimates of \(K_{u}\) from \(K_{Lu}\) regardless of light wavelength and depth (Figure 13f):  
\[K_{d}(650)=0.4792\ \mathrm{exp}(-0.0451\ z)+0.0387\quad(r^{2}=0.925,\ RMSE=0.033\ \mathrm{m}^{-1},\ N=66) \tag{6a}\]7  
This relationship was obtained from data collected at three wavelengths, 440, 550, and 650 nm. Note that the slope coefficient of the regression is close to 1 but many data points of \(K_{u}\) in the blue and green spectral bands are higher than \(K_{Lu}\). This tendency is not seen in the red band, however. \[K_{d}(650)=0.4792\ \mathrm{exp}(-0.0451\ z)+0.0387\quad(r^{2}=0.925,\ RMSE=0.033\ \mathrm{m}^{-1},\ N=66) \tag{6a}\]8 Diffuse attenuation coefficients in the red spectral bands (650 and 683 nm) plotted as a function of depth \(z\) using data from all stations and depths. (**a**) \(K_{d}(z,650)\) (crosses) and \(K_{d}(z,683)\) (open circles) vs. \(z\). (**b**) Same as (**a**) but for \(K_{u}\). Solid lines represent the best-fit regression functions. \[K_{d}(650)=0.4792\ \mathrm{exp}(-0.0451\ z)+0.0387\quad(r^{2}=0.925,\ RMSE=0.033\ \mathrm{m}^{-1},\ N=66) \tag{6a}\]9 Relationships between diffuse attenuation coefficients based on measurements from all stations and depths. (**a**) \(K_{u}\) vs. \(K_{d}\); (**b**) \(K_{E}\) vs. \(K_{d}\); (**c**) \(K_{o}\) vs. \(K_{d}\). (**d**) \(K_{dPAR}\) vs. \(K_{d}\); (**e**) \(K_{dPAR}\) vs. \(K_{dPAR}\); and (**f**) \(K_{u}\) vs. \(K_{Lux}\). In (**a**–**c**,**f**), different symbols represent data at different light wavelengths as indicated. In (**d**) symbols indicate the relationships between \(K_{dPAR}(z)\) and different \(K\)-coefficients as indicated, including the relationship between \(K_{dPAR}(z)\) and [\(K_{d}(z,490)+K_{d}(z,550)\)]/2. The best fit regression functions (solid lines) are shown for (**a**) data at 440 nm and 550 nm analyzed separately, (**b**,**c**) combined data at 440 nm, 550 nm, and 650 nm, (**d**) data of \(K_{dPAR}(z)\) vs. [\(K_{d}(z,490)+K_{d}(z,550)\)]/2, and (**e**,**f**) all data displayed in these panels. Dashed lines represent the 1:1 agreement between the variables.