## 3 Results
### Cipigs from Satellite Remote Sensing  
#### 3.2.1 Cipigs Validation and Their Seasonal Variation  
The ability of MuPI to capture the magnitudes of Cipigs and their seasonal variability from satellite \(R_{\rm rs}(\lambda)\) was then validated using a time series of HPLC measurements at BATS from the years 2002 to 2012. During this period of time, Cipigs varied in these ranges: [Chl-a]: 0.016-0.486 mg\(\cdot\)m\({}^{-3}\), [Chl-b]: 0.001-0.108 mg\(\cdot\)m\({}^{-3}\), [Chl-c]: 0.001-0.206 mg\(\cdot\)m\({}^{-3}\), [PPC]: 0.004-0.147 mg\(\cdot\)m\({}^{-3}\), and [PSC]: 0.003-0.106 mg\(\cdot\)m\({}^{-3}\). To obtain Cipigs from satellite \(R_{\rm rs}(\lambda)\), \(a_{\rm Ga}(\lambda)\) were inverted first from \(R_{\rm rs}(\lambda)\) using MuPI, then Equation (11) was applied to convert the retrieved \(a_{\rm Ga}(\lambda)\) to Cipigs. As shown in Figure 5, it is found \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multirow{2}{*}{**Peak Center**} & \multicolumn{2}{c}{**IOCCG**} & \multicolumn{2}{c}{**Tara Oceans**} & \multicolumn{2}{c}{**BIOSOPE**} & \multicolumn{2}{c}{**VIIRS Cruises**} \\ \cline{2-9}  & **Mea.** & **Med.** & **Mea.** & **Med.** & **Mea.** & **Med.** & **Mea.** & **Med.** \\ \hline
406 & 45 & 45 & 34 & 27 & 34 & 28 & 28 & 20 \\
434 & 37 & 36 & 34 & 28 & 26 & 25 & 28 & 13 \\
453 & 47 & 49 & 28 & 24 & 23 & 18 & 27 & 15 \\
470 & 35 & 34 & 29 & 25 & 30 & 27 & 31 & 18 \\
492 & 34 & 31 & 26 & 21 & 22 & 18 & 29 & 18 \\
523 & 44 & 34 & 38 & 28 & 34 & 29 & 48 & 44 \\
550 & 45 & 35 & 53 & 41 & 37 & 34 & 41 & 35 \\
584 & 55 & 48 & 48 & 37 & 38 & 36 & 53 & 57 \\
617 & 51 & 45 & 47 & 38 & 36 & 29 & 37 & 40 \\
638 & 54 & 42 & 66 & 68 & 41 & 35 & 41 & 35 \\
660 & 52 & 48 & 35 & 23 & 32 & 29 & 43 & 34 \\
675 & 46 & 40 & 30 & 26 & 60 & 56 & 32 & 21 \\ \hline \end{tabular}
\end{table} 
Table 5: Mean (Mea.) and median (Med.) of the unbiased percentage errors for \(a_{\rm Ga}(\lambda)\) retrieval from \(R_{\rm rs}(\lambda)\) for different datasets. Figure 4: MuPI retrieved \(a_{\rm dg}(440)\) and \(b_{\rm bp}(440)\) versus those from the International Ocean-Colour Coordinating Group (IOCCG) dataset. that there are good matches in the magnitudes and the seasonal cycles for the five pigments, with mean UAPD values as 38%, 78%, 65%, 36%, and 47% (and the medians are 34%, 79%, 64%, 30% and 55%) for [Chl-a], [Chl-b], [Chl-c], [PPC] and [PSC], respectively. The [Chl-a] accuracy is comparable with the NASA adopted standard [Chl-a] algorithms, for which the color index (CI) algorithm [5] showed a mean UAPD of 38.6% and OC4E of 46.7%. There are many reasons for the relatively low accuracy in the retrieval of [Chl-b] and [Chl-c], which include very low concentrations (e.g., in situ [Chl-b] and [Chl-c] were close to the HPLC detection minimum), as well as uncertainties in satellite measured \(R_{\text{rs}}(\lambda)\), and the derived \(a_{\text{Gau}}(\lambda)\) from \(R_{\text{rs}}(\lambda)\). Beyond the seasonal cycles in Cpig magnitudes, variation in pigment composition over time implied in the change of pigment ratios was also noticed in Figure 6A. On further examination, we found the ratios derived from MERIS \(R_{\text{rs}}(\lambda)\) using MuPI can pick up the variation in the [Chl-b], [Chl-c], [PPC], [PSC] to [Chl-a] ratios observed from HPLC measurements very well with the mean UAPD of 50%, 47%, 25%, 37%, and median of 38%, 39%, 19% and 29% respectively (Figure 6B). Since these phytoplankton pigment ratios do not co-vary with the [Chl-a] product and cannot be empirically estimated from [Chl-a] alone, the Gaussian peaks and multiple pigments retrieved here provide a valuable glimpse into potential applications of these ratios in ocean changes that can be studied at large spatial and high temporal scales. Figure 5: Time series of pigment concentrations from BATS HPLC and MERIS \(R_{\text{rs}}(\lambda)\), and the determination coefficients (R\({}^{2}\)).