AOPs Are Not Additive: On the Biogeo-Optical Modeling of the Diffuse Attenuation Coefficient

Abstract

Commonly we see the diffuse attenuation coefficient of downwelling irradiance (K d ) expressed as a sum of the contributions of various constituents. We show here that, both theoretically and numerically, because K d is an apparent optical property (AOP), this approach is not consistent with radiative transfer. We further advocate the application of models of K d developed in past decades that are not only consistent with radiative transfer but also provide more accurate estimates, in particular for coastal turbid waters.

Small Phytoplankton Shapes Colored Dissolved Organic Matter Dynamics in the North Atlantic Subtropical Gyre

“…The contribution of pure seawater was then subtracted from K d (380) to obtain K bio (380) (Morel & Maritorena, 2001). Note that this decomposition is accepted in NASTG because samples were acquired in very clear waters and under high solar elevation angles (Lee et al, 2018;Morel & Maritorena, 2001). Finally, K bio (380) coefficients were divided by mean [Chl] values within the mixed layer to obtain the chlorophyll-specific attenuation coefficient for CDOM (K star (380); units of square meters per milligram of chlorophyll).…”

An Empirically Derived Trimodal Parameterization of Underwater Light in Complex Coastal Waters – A Case Study in the North Sea

“…However, as it is exemplarily shown in Figure 2, the K d iSPM (λ) spectrum that results from the decomposition of total K d (λ) increases again toward the longer wavelengths, what is consistent with the observed higher K d * iSPM in band III compared band II. This results probably from the fact that the simple addition (or in this case: subtraction) of the K d (λ) contributions of the OAS are only an approximation, which is not fully consistent with radiative transfer theory (Lee et al, 2018). As demonstrated in the named publication, there are especially differences toward the red part of the spectrum, what fits to the observations made.…”

“…We are aware that this is only a simplification as shown recently by Lee et al (2018), however, this approach was chosen in order to keep the model as simple as possible. For the parameterization of K d (λ) using the mentioned variables, it is necessary to establish substance-specific diffuse attenuation coefficient values (K d * ) for the selected spectral regions.…”

The Two Faces of “Case-1” Water

“…Following the same approach, KðPARÞ also varies significantly in the upper water column [9] even for homogeneous waters, which is thus an "ambiguous" property if the depth information is not provided [10]. In a more general sense, since AOPs are dependent on the light field, they are not additive as expressed by Equation (3) [11].…”