## 3 Results and Discussion
### Overall Variability and Relationships Involving the Apparent Optical Properties
#### 3.2.3 Diffuse Attenuation Coefficients  
The diffuse attenuation coefficients \(K\) in our dataset span a relatively wide range of values. For example, the ranges for \(K_{d}\) at 440, 550, 650, and 683 nm are 0.031-0.246, 0.054-0.168, 0.072-0.514, and 0.044-0.635 m\({}^{-1}\), respectively. The ranges for \(K_{u}\) at the same wavelengths are 0.041-0.253, 0.021-0.192, 0.018-0.421, and \(-\)0.095-0.374 m\({}^{-1}\), respectively. The lowest values of \(K_{u}\) at longer wavelengths (green and red) were significantly smaller than those for \(K_{d}\) and can even include the negative values because the inelastic processes exerted a stronger reducing effect on \(K_{u}\) than \(K_{d}\). The possibility of negative values of the \(K\)-coefficients at 685 nm within the \(Chl_{max}\) layer were also demonstrated through earlier observations and modeling [37]. Because \(E_{d}\) has been by far the most commonly measured radiometric quantity in the ocean, \(K_{d}\) in the surface layer is relatively well documented in the literature. An overview of early data of \(K_{d}\), including the classification of optical water types based on the spectral \(K_{d}\) within the top 10 m layer of the ocean, is given in Jerlov [11]. The range of \(K_{d}\) values observed in our study in the blue spectral region indicates that the investigated waters in the Gulf of California fall between the oceanic water Types IB or II and the coastal water Type 1 according to Jerlov's classification. Following an increased interest in ocean color remote sensing in early 1970s and the introduction of the concept of bio-optical state of ocean waters representing a measure of the effect of biological processes on ocean optical properties [105], several studies examined experimental data of \(K_{d}\) in the context of the relationship with chlorophyll-\(a\) concentration over a broad range of these variables measured in various oceanic waters [35; 38; 39; 106]. In those studies, \(K_{d}\) was typically estimated to represent the top layer from the ocean surface to one attenuation depth (\(1/K_{d}\)) or euphotic depth (1% of surface PAR). The lowest limiting values of spectral \(K_{d}\) for the clearest natural waters were also estimated, for example 0.017 m\({}^{-1}\) or 0.00885 m\({}^{-1}\) at 440 nm, 0.0648 m\({}^{-1}\) or 0.05746 m\({}^{-1}\) at 550 nm, and 0.35 m\({}^{-1}\) or 0.34052 m\({}^{-1}\) at 650 nm by [PERSON] [39] and [PERSON] [107], respectively. These estimates were generally consistent with the lowest measured values in the datasets presented in [11; 38; 39] although, to our knowledge, the lowest reported measurements of \(K_{d}\) in the blue are 0.012 m\({}^{-1}\) at 420 nm [26]. The lowest \(K_{d}\) values in the blue in our dataset are thus 1.8 to 3.5 higher than these previous estimates for the clearest waters. In the red, our data of \(K_{d}\) collected within the top 10 m layer (Figures 6e and 7e) are similar or somewhat higher than the previous determinations for the clearest waters. At larger depths, \(K_{d}\) in the red was reduced owing to the increasing effect of inelastic processes with depth. This effect on the vertical changes in both \(K_{d}\) and \(K_{u}\) in the red spectral region is illustrated for our dataset in Figure 12. Both \(K\) coefficients decrease considerably with depth. This reduction is more pronounced at 683 nm than 650 nm. \(K_{u}\) decreased more rapidly than \(K_{d}\) and approached a relatively stable level of values at shallower depths (i.e., about 15-20 m) than \(K_{d}\).