## 3 Assessment of the Developed Algorithm Efficiency in Some Case Studies
### Bay of Biscay  
The Bay of Biscay is an area of incursion of the North Atlantic waters into the western periphery of the European continent. It resembles a gigantic triangular, which is a recipient of numerous rivers, some of them being fairly full-flowing and bringing large amounts of suspended minerals, dissolved  
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|} \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c|}{_In situ_ measurements} & \multicolumn{3}{c|}{**Remote sensing data**} \\ \cline{2-7}  & _chl_, **mg/L** & _doc_, **mgC/L** & _chl_, **mg/L** & _doc_, **mgC/L** & \begin{tabular}{c} _sm_, \\ **mg/L** \\ \end{tabular}  \\ \hline
**Lake** & 14.24 \(\pm\)2.14 & 2.45 \(\pm\)0.26 & 12.56 \(\pm\)3.28 & 2.68 \(\pm\)0.56 & 0.72 \\
**Ladoga** & 9.98 \(\pm\)1.5 &  
organic matter and nutrients into the bay. In the spatial distribution of the terrigenous suspended and dissolved matter, the important role is played by fronts of various nature, in particular the thermohaline front forming over the 100 m isobath. The coastal zone is conditionally bounded by the 200 m isobath, beyond which the pelagic zone extends out to the western boundary of the bay. The phytoplankton community within the coastal zone is mostly controlled by diatoms [35]. In the Bay of Biscay not only the coastal zone should be considered as the area of case 2 waters. The pelagic zone is known to be the realm of extensive blooms of a coccolithophore, _Emiliania Huxley_, which usually accounts for about 90% the phytoplankton, whereas the remaining \(\sim\)10% is the portion of diatoms. C coccolithophores are algal cells covered with calcium carbonate plates that, at the late phase of the algal life-cycle, become detached completely or partially from the cell's body. It implies that the algal _chl_ within the blooming areas generally does not correlate with this mineral residue. Hence, by definition (see Introduction), such waters subsume under the category of case 2 waters. We applied our LM-based algorithm to satellite data (SeaWiFS, MODIS, MERIS) collected over the Bay using two separate hydro-optical models: one for the coastal zone and one for the pelagic waters. The first hydro-optical model was obtained through multivariate optimization of the North Sea hydro-optical model. The optimization approach is similar to the one described in the section 2.5. This hydro-optical model considered _chl_, _tsm_ and yellow substance (_cdom_) as CPAs. For validation of the LM-algorithm we utilised the database of _in situ_ and SeaWiFS data matchups developed at IFREMER, Brest, France [36]. The database consists of more than 500 simultaneous _chl_ and _tsm_ measurements collected synchronously with SeaWiFS overflights during 6 years (1998 - 2004) on several tens of stations along the French coast of the Bay of Biscay and during several expeditions to the centre of the bay. Our comparison of _chl_ and _tsm_ obtained by applying the LM-based algorithm to \(R_{rsv}(\lambda)\) measured remotely showed (Fig. 6) that correlation is high (r\({}_{chl}\) = 0.67, r\({}_{sm}\) = 0.60), absolute difference is low (RMSE\({}_{chl}\) = 3.7 \(\upmu\)g/L, RMSE\({}_{sm}\) = 6.6 mg/L) and the retrieved values are slightly overestimated (\(chl_{\rm retrieved}\) = 0.3 \(chl_{\rm measured}\) + 0.4, \(sm_{\rm retrieved}\) = 0.4 \(chl_{\rm measured}\) + 1.5) indicating that the established dependence is governed exclusively by the parameter in question. The second hydro-optical model applied for the Bay of Biscay assumes coccolithophores, coccoliths and diatoms as CPAs in the pelagic waters (here, the symbol \(\lambda\) denoting wavelength dependence is dropped for simplicity):  
\[a=a_{w}+a*_{php}C_{php}+a*_{coc}^{\ast}C_{coc}+a*_{cc}^{\ast}C_{cc}+a*_{sm} ^{\ast}C_{sm}+a*_{cdom}^{\ast}C_{cdom}; \tag{9}\] \[b_{b}=b_{bw}+b_{b}*_{php}C_{php}+b_{b}*_{coc}\cdot C_{coc}+b_{ b}*_{cc}^{\ast}C_{cc}+b_{b}*_{sm}^{\ast}C_{sm}, \tag{10}\]  
where indices \(w\), \(php\), \(coc\) and \(cc\) refer to water, diatom phytoplankton, coccolithophores and coccoliths, respectively.